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16-14

Step-by-Step Examples

the circle 

C

, 

M

 will move on a curve 

Γ

. In this exercise we 

will study and plot 

Γ

.

1. Let  

and 

m

 be the point on 

C

 of affix 

. Find the coordinates of 

M

 in terms of 

t

.

2. Compare x(–t) with x(t) and y(–t) with y(t).

3. Compute 

x

′

(

t

) and find the variations of 

x

 over [0, 

π

].

4. Repeat step 3 for 

y

.

5. Show the variations of 

x

 and 

y

 in the same table.

6. Put the points of 

Γ

 corresponding to 

t

 = 0, 

π

/3, 

2

π

/3 and 

π,

 and draw the tangent to 

Γ

 at these 

points.

Part 1

First go to CAS

 MODES

 

screen and make 

t

 the VX 

variable. To do this, press 

 to open the Equation 

Writer, and then press 

 

. This opens 

CAS

 MODES

 screen. Press 

 and delete the current 

variable. Type 

 

 T and press 

. 

Now enter the expression 

 and press 

 

to select it.

Now invoke the 

SUBST

 

command from the 

 

menu. Because the 
expression was 
highlighted, the 

SUBST

 

command is automatically 
applied to it.

Note that the cursor is 
positioned in the second 
parameter. Since we know 
that 

, we can 

enter this as the second 
parameter.

t

π

–

π

[ , ]

∉

z

e

i t

⋅

=

1
2

---

z

2

⋅

z

–

z

e

i t

⋅

=

hp40g+.book  Page 14  Friday, December 9, 2005  1:03 AM

Summary of Contents for 40gs

Page 1: ...HP 40gs graphing calculator user s guide Edition1 Part Number F2225AA 90001 hp40g book Page i Friday December 9 2005 1 03 AM ...

Page 2: ...LL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING PERFORMANCE OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN Copyright 1994 1995 1999 2000 2003 2006 Hewlett Packard Devel opment Company L P Reproduction adaptation or translation of this manual is prohibited without prior written permission of Hewlett Packard Company except as allow...

Page 3: ...iews Aplet views 2 1 About the Symbolic view 2 1 Defining an expression Symbolic view 2 1 Evaluating expressions 2 3 About the Plot view 2 5 Setting up the plot Plot view setup 2 5 Exploring the graph 2 7 Other views for scaling and splitting the graph 2 13 About the numeric view 2 16 Setting up the table Numeric view setup 2 16 Exploring the table of numbers 2 17 Building your own table of number...

Page 4: ... in equations 7 10 8 Linear Solver aplet About the Linear Solver aplet 8 1 Getting started with the Linear Solver aplet 8 1 9 Triangle Solve aplet About the Triangle Solver aplet 9 1 Getting started with the Triangle Solver aplet 9 1 10 Statistics aplet About the Statistics aplet 10 1 Getting started with the Statistics aplet 10 1 Entering and editing statistical data 10 6 Defining a regression mo...

Page 5: ... 18 Two Sample T Interval 11 19 12 Using the Finance Solver Background 12 1 Performing TVM calculations 12 4 Calculating Amortizations 12 7 13 Using mathematical functions Math functions 13 1 The MATH menu 13 1 Math functions by category 13 2 Keyboard functions 13 3 Calculus functions 13 6 Complex number functions 13 7 Constants 13 8 Conversions 13 8 Hyperbolic trigonometry 13 9 List functions 13 ...

Page 6: ... DIFF menu 14 16 REWRI menu 14 28 SOLV menu 14 33 TRIG menu 14 38 CAS Functions on the MATH menu 14 45 Algebra menu 14 45 Complex menu 14 45 Constant menu 14 46 Diff Int menu 14 46 Hyperb menu 14 46 Integer menu 14 46 Modular menu 14 51 Polynomial menu 14 55 Real menu 14 60 Rewrite menu 14 60 Solve menu 14 60 Tests menu 14 61 Trig menu 14 61 CAS Functions on the CMDS menu 14 62 15 Equation Writer ...

Page 7: ...trix arithmetic 18 6 Solving systems of linear equations 18 8 Matrix functions and commands 18 10 Argument conventions 18 10 Matrix functions 18 10 Examples 18 13 19 Lists Displaying and editing lists 19 4 Deleting lists 19 6 Transmitting lists 19 6 List functions 19 6 Finding statistical values for list elements 19 9 20 Notes and sketches Introduction 20 1 Aplet note view 20 1 Aplet sketch view 2...

Page 8: ...tending aplets Creating new aplets based on existing aplets 22 1 Using a customized aplet 22 3 Resetting an aplet 22 3 Annotating an aplet with notes 22 4 Annotating an aplet with sketches 22 4 Downloading e lessons from the web 22 4 Sending and receiving aplets 22 4 Sorting items in the aplet library menu list 22 6 Reference information Glossary R 1 Resetting the HP 40gs R 3 To erase all memory a...

Page 9: ... MATH menu categories R 13 Math functions R 13 Program constants R 15 Physical Constants R 16 CAS functions R 17 Program commands R 19 Status messages R 20 Limited Warranty Service W 3 Regulatory Notices W 5 Index hp40g book Page ix Friday December 9 2005 1 03 AM ...

Page 10: ...hp40g book Page x Friday December 9 2005 1 03 AM ...

Page 11: ...tp www hp com calculators Manual conventions The following conventions are used in this manual to represent the keys that you press and the menu options that you choose to perform the described operations Key presses are represented as follows etc Shift keys that is the key functions that you access by pressing the key first are represented as follows CLEAR MODES ACOS etc Numbers and letters are r...

Page 12: ...ticular purpose and Hewlett Packard Company shall not be liable for any errors or for incidental or consequential damage in connection with the furnishing performance or use of this manual and the examples herein Copyright 1994 1995 1999 2000 2003 2006 Hewlett Packard Development Company L P The programs that control your HP 40gs are copyrighted and all rights are reserved Reproduction adaptation ...

Page 13: ...o perform calculations or you want to quit the current activity such as an aplet a program or an editor press All mathematical functions are available in the HOME The name of the current aplet is displayed in the title of the home view Protective cover The calculator is provided with a slide cover to protect the display and keyboard Remove the cover by grasping both sides of it and pulling down Yo...

Page 14: ...at is the leftmost top row key on the calculator keyboard Edit line The line of current entry History The HOME display shows up to four lines of history the most recent input and output Older lines scroll off the top of the display but are retained in memory Title The name of the current aplet is displayed at the top of the HOME view RAD GRD DEG specify whether Radians Grads or Degrees angle mode ...

Page 15: ...unciator Description Shift in effect for next keystroke To cancel press again α Alpha in effect for next keystroke To cancel press again Low battery power Busy Data is being transferred HP 40gs Graphing Calculator Menu Key Labels Menu Keys Cursor Aplet Control Alpha Key Shift Key Enter Keys Key Keys hp40g book Page 3 Friday December 9 2005 1 03 AM ...

Page 16: ...et control keys The aplet control keys are Key Meaning Displays the Symbolic view for the current aplet See Symbolic view on page 1 16 Displays the Plot view for the current aplet See Plot view on page 1 16 Displays the Numeric view for the current aplet See Numeric view on page 1 17 Displays the HOME view See HOME on page 1 1 Displays the Aplet Library menu See Aplet library on page 1 16 Displays...

Page 17: ...ike When or is present as a menu key acts the same as pressing or Enters a negative number To enter 25 press 25 Note this is not the same operation that the subtract button performs Enters the independent variable by inserting X T θ or N into the edit line depending on the current active aplet Deletes the character under the cursor Acts as a backspace key if the cursor is at the end of the line CL...

Page 18: ...ss the operations printed in blue above the keys For instance to access the Modes screen press then press MODES is labeled in blue above the key You do not need to hold down when you press HOME This action is depicted in this manual as press MODES To cancel a shift press again The alphabetic keys are also shifted keystrokes For instance to type Z press Z The letters are printed in orange to the lo...

Page 19: ...ut this manual as CAS Keyboard keys The most common operations are available from the keyboard such as the arithmetic like and trigonometric like functions Press to complete the operation 256 displays 16 MATH menu Press to open the MATH menu The MATH menu is a comprehensive list of math functions that do not appear on the keyboard It also includes categories for all other functions and constants T...

Page 20: ...acter With this method you do not need to press first Just press the key that corresponds to the command s beginning alpha character Note that when the MATH menu is open you can also access CAS commands You do this by pressing This enables you to use CAS commands on the HOME screen without opening CAS See Chapter 14 for details of CAS commands Program commands Pressing CMDS displays the list of Pr...

Page 21: ...search a list type the first letter of the word For example to find the Matrix category in press the Alpha M key To go up a page you can press To go down a page press To cancel a menu Press for CANCEL or This cancels the current operation Input forms An input form shows several fields of information for you to examine and specify After highlighting the field to edit you can enter or edit a number ...

Page 22: ...le Grads 400 grads in a circle The angle mode you set is the angle setting used in both HOME and the current aplet This is done to ensure that trigonometric calculations done in the current aplet and HOME give the same result Number Format The number format mode you set is the number format used in both HOME and the current aplet Standard Full precision display Fixed Displays results rounded to a ...

Page 23: ...of decimal places Examples 123 456789 becomes 123 in Fraction 2 format and 333 becomes 1 3 and 0 142857 becomes 1 7 See Using fractions on page 1 25 Mixed Fraction Displays results as mixed fractions based on the specified number of decimal places A mixed fraction has an integer part and a fractional part Examples 123 456789 becomes 123 16 35 in Fraction 2 format and 7 3 returns 2 1 3 See Using fr...

Page 24: ...fferent classes of mathematical operations You select the aplet that you want to work with Aplets come from a variety of sources Built in the HP 40gs initial purchase Aplets created by saving existing aplets which have been modified with specific configurations See Creating new aplets based on existing aplets on page 22 1 Downloaded from HP s Calculators web site Copied from another calculator Apl...

Page 25: ...ar functions y in terms of x Example Inference Confidence intervals and Hypothesis tests based on the Normal and Students t distributions Parametric Parametric relations x and y in terms of t Example x cos t and y sin t Polar Polar functions r in terms of an angle θ Example Sequence Sequence functions U in terms of n or in terms of previous terms in the same or another sequence such as and Example...

Page 26: ...d at the top right corner of the screen while the original graph is retained for comparison In this mode the graph controls the equation It is also possible to have the equation control the graph Pressing displays a sub expression of your equation Pressing the and key moves between sub expressions while pressing the and key changes their values Pressing allows the user to select whether all three ...

Page 27: ...e between and When is chosen the point of control is at the origin 0 0 and the and keys control vertical and horizontal transformations When is chosen the point of control is on the first extremum of the graph i e for the sine graph at The arrow keys change the amplitude and frequency of the graph This is most easily seen by experimenting Pressing displays the equation at the top of the screen The...

Page 28: ... six supporting aplet views from the VIEWS menu and the two user defined views Note and Sketch Note some aplets such as the Linear Solver aplet and the Triangle Solver aplet only have a single view the Numeric view Symbolic view Press to display the aplet s Symbolic view You use this view to define the function s or equation s that you want to explore See About the Symbolic view on page 2 1 for fu...

Page 29: ...ling and splitting the graph on page 2 13 for futher information Plot Detail view The VIEWS menu contains the Plot Detail view Select Plot Detail Splits the screen into the plot and a close up See Other views for scaling and splitting the graph on page 2 13 for further information Overlay Plot view The VIEWS menu contains the Overlay Plot view Select Overlay Plot Plots the current expression s wit...

Page 30: ...on page 20 1 for further information Aplet view configuration You use the SETUP keys and to configure the aplet For example press SETUP PLOT to display the input form for setting the aplet s plot settings Angle measure is controlled using the MODES view Plot Setup Press SETUP PLOT Sets parameters to plot a graph Numeric Setup Press SETUP NUM Sets parameters for building a table of numeric values S...

Page 31: ...ee Computer Algebra System CAS on page 14 1 for further information To access programming commands press CMDS See Programming commands on page 21 13 for further information Where to start The home base for the calculator is the HOME view You can do all non symbolic calculations here and you can access all operations Symbolic calculations are done using CAS Entering expressions In the HOME view you...

Page 32: ...Scientific notation powers of 10 A number like or is written in scientific notation that is in terms of powers of ten This is simpler to work with than 50000 or 0 000000321 To enter numbers like these use EEX This is easier than using 10 Example Calculate 4 EEX 13 6 EEX 23 3 EEX 5 Explicit and implicit multiplication Implied multiplication takes place when two operands appear with no operator in b...

Page 33: ...on A at the value B 4 and function A does not exist When in doubt insert the sign manually Parentheses You need to use parentheses to enclose arguments for functions such as SIN 45 You can omit the final parenthesis at the end of an edit line The calculator inserts it automatically Parentheses are also important in specifying the order of operation Without parentheses the HP 40gs calculates accord...

Page 34: ...resent is 1 10 499 1E 499 A smaller result is displayed as zero The largest number is 9 99999999999 10499 1E499 A greater result is displayed as this number Clearing numbers clears the character under the cursor When the cursor is positioned after the last character deletes the character to the left of the cursor that is it performs the same as a backspace key CANCEL clears the edit line CLEAR cle...

Page 35: ...ning the ANS the calculation is repeated iteratively Example See how ANS retrieves and reuses the last result 50 and updates ANS from 50 to 75 to 100 50 25 You can use the last result as the first expression in the edit line without pressing ANS Pressing or or other operators that require a preceding argument automatically enters ANS before the operator You can reuse any other expression or value ...

Page 36: ... result as ANS into the edit line Storing a value in a variable You can save an answer in a variable and use the variable in later calculations There are 27 variables available for storing real values These are A to Z and θ See Chapter 17 Variables and memory management for more information on variables For example 1 Perform a calculation 45 8 3 2 Store the result in the A variable A 3 Perform ano...

Page 37: ...sults are saved until you clear them Using fractions To work with fractions in HOME you set the number format to Fraction or Mixed Fraction as follows Setting Fraction mode 1 In HOME open the HOME MODES input form MODES Key Function Scrolls through the display history Copies the highlighted expression to the position of the cursor in the edit line Displays the current expression in standard mathem...

Page 38: ...decimal value to a fraction The greater the precision value that is set the closer the fraction is to the decimal value By choosing a precision of 1 you are saying that the fraction only has to match 0 234 to at least 1 decimal place 3 13 is 0 23076 The fractions used are found using the technique of continued fractions When converting recurring decimals this can be important For example at precis...

Page 39: ... the denominator part of the fraction To enter a mixed fraction for example 11 2 you enter it in the format 1 1 2 For example to perform the following calculation 3 23 4 57 8 1 Set the Number format mode to Fraction or Mixed Fraction and specify a precision value of 4 In this example we ll select Fraction as our format MODES Select Fraction 4 hp40g book Page 27 Friday December 9 2005 1 03 AM ...

Page 40: ... the value on the command line 3 Press to convert the number to a fraction When converting a decimal to a fraction keep the following points in mind When converting a recurring decimal to a fraction set the fraction precision to about 6 and ensure that you include more than six decimal places in the recurring decimal that you enter In this example the fraction precision is set to 6 The top calcula...

Page 41: ... numbers Enter the number in either of these forms where x is the real part y is the imaginary part and i is the imaginary constant x y or x iy To enter i press or press or keys to select Constant to move to the right column of the menu to select i and Storing complex numbers There are 10 variables available for storing complex numbers Z0 to Z9 To store a complex number in a variable Enter the com...

Page 42: ...ontents Aplet library Aplets Sketch editor SKETCH Sketches and diagrams See Chapter 20 Notes and sketches List LIST Lists In HOME lists are enclosed in See Chapter 19 Lists Matrix MATRIX One and two dimensional arrays In HOME arrays are enclosed in See Chapter 18 Matrices Notepad NOTEPAD Notes short text entries See Chapter 20 Notes and sketches Program PROGRM Programs that you create or associate...

Page 43: ...s for each Function Parametric Polar and Sequence aplet You can graph any of the relations in the same aplet simultaneously by selecting them Defining an expression Symbolic view Choose the aplet from the Aplet Library Press or to select an aplet The Function Parametric Polar and Sequence aplets start in the Symbolic view If the highlight is on an existing expression scroll to an empty line unless...

Page 44: ...enter the first term or the first and second terms for U U1 or U9 or U0 Then define the nth term of the sequence in terms of N or of the prior terms U N 1 and or U N 2 The expressions should produce real valued sequences with integer domains Or define the nth term as a non recursive expression in terms of n only In this case the calculator inserts the first two terms based on the expression that y...

Page 45: ...view press If a function calls another function then resolves all references to other functions in terms of their independent variable 1 Choose the Function aplet Select Function 2 Enter the expressions in the Function aplet s Symbolic view A B F1 F2 3 Highlight F3 X 4 Press Note how the values for F1 X and F2 X are substituted into F3 X hp40g book Page 3 Friday December 9 2005 1 03 AM ...

Page 46: ... checked expression s are evaluated in the Plot and Numeric views Enters the independent variable in the Function aplet Or you can use the key on the keyboard Enters the independent variable in the Parametric aplet Or you can use the key on the keyboard Enters the independent variable in the Polar aplet Or you can use the key on the keyboard Enters the independent variable in the Sequence aplet Or...

Page 47: ...n and press or If there is an option to choose press highlight your choice and press or As a shortcut to just highlight the field to change and press to cycle through the options If there is an option to select or deselect press to check or uncheck it 2 Press to view more settings 3 When done press to view the new plot Displays the menu for entering math operations CHARS Displays special character...

Page 48: ...ues T for the graph θRNG Polar aplet Specifies the angle θ value range for the graph NRNG Sequence aplet Specifies the index N values for the graph TSTEP For Parametric plots the increment for the independent variable θSTEP For Polar plots the increment value for the independent variable SEQPLOT For Sequence aplet Stairstep or Cobweb types XTICK Horizontal spacing for tickmarks YTICK Vertical spac...

Page 49: ...ails the keys that you use to work with the graph CONNECT Connect the plotted points The Sequence aplet always connects them LABELS Label the axes with XRNG and YRNG values AXES Draw the axes GRID Draw grid points using XTICK and YTICK spacing Field Meaning Continued Key Meaning CLEAR Erases the plot and axes Offers additional pre defined views for splitting the screen and for scaling zooming the ...

Page 50: ... the plot To move between relations If there is more than one relation displayed press or to move between relations Turns menu key labels on and off When the labels are off pressing turns them back on Pressing once displays the full row of labels Pressing a second time removes the row of labels to display only the graph Pressing a third time displays the coordinate mode Displays the ZOOM menu list...

Page 51: ...ether the zoom is centered about the cursor ZOOM options Press select an option and press If is not displayed press Not all options are available in all aplets Option Meaning Center Re centers the plot around the current position of the cursor without changing the scale Box Lets you draw a box to zoom in on See Other views for scaling and splitting the graph on page 2 13 In Divides horizontal and ...

Page 52: ...for the supplied x axis settings For Sequence and Statistics aplets autoscaling rescales both axes The autoscale process uses the first selected function only to determine the best scale to use Decimal Rescales both axes so each pixel 0 1 units Resets default values for XRNG 6 5 to 6 5 and YRNG 3 1 to 3 2 Not in Sequence or Statistics aplets Integer Rescales horizontal axis only making each pixel ...

Page 53: ...o move to the bottom of the Zoom list Zoom Out Out Now un zoom X Zoom In X Zoom In Now un zoom X Zoom Out X Zoom Out Now un zoom Un zoom Returns the display to the previous zoom or if there has been only one zoom un zoom displays the graph with the original plot settings Option Meaning Continued 3 x sin 3 x sin hp40g book Page 11 Friday December 9 2005 1 03 AM ...

Page 54: ...ea you want to zoom in on by selecting the endpoints of one diagonal of the zoom rectangle 1 If necessary press to turn on the menu key labels 2 Press and select Box 3 Position the cursor on one corner of the rectangle Press 4 Use the cursor keys etc to drag to the opposite corner 5 Press to zoom in on the boxed area hp40g book Page 12 Friday December 9 2005 1 03 AM ...

Page 55: ...ot using certain pre defined configurations This is a shortcut for changing Plot view settings For instance if you have defined a trigonometric function then you could select Trig to plot your function on a trigonometric scale It also contains split screen options In certain aplets for example those that you download from the world wide web the preset viewing options menu can also contain options ...

Page 56: ... representative piece of the plot for the supplied x axis settings For Sequence and Statistics aplets autoscaling rescales both axes The autoscale process uses the first selected function only to determine the best scale to use Decimal Rescales both axes so each pixel 0 1 unit Resets default values for XRNG 6 5 to 6 5 and YRNG 3 1 to 3 2 Not in Sequence or Statistics aplets Integer Rescales horizo...

Page 57: ...en functions use the and cursor keys to move the cursor from one graph to another 4 To return to a full Numeric or Plot view press or Overlay plots If you want to plot over an existing plot without erasing that plot then use Overlay Plot instead of Note that tracing follows only the current functions from the current aplet Decimal scaling Decimal scaling is the default scaling If you have changed ...

Page 58: ... field If there is a number to enter type it in and press or To modify an existing number press If there is an option to choose press highlight your choice and press or Shortcut Press the key to copy values from the Plot Setup into NUMSTART and NUMSTEP Effectively the menu key allows you to make the table match the pixel columns in the graph view 2 When done press to view the table of numbers Nume...

Page 59: ...Type of numeric table Automatic or Build Your Own To build your own table you must type each independent value into the table yourself NUMZOOM Allows you to zoom in or out on a selected value of the independent variable Field Meaning Continued Key Meaning Displays ZOOM menu list Toggles between two character sizes Displays the defining function expression for the highlighted column To cancel this ...

Page 60: ...for the independent variable so a narrower range is shown Uses the NUMZOOM factor in Numeric Setup Out Increases the intervals for the independent variable so that a wider range is shown Uses the NUMZOOM factor in Numeric Setup Decimal Changes intervals for the independent variable to 0 1 units Starts at zero Shortcut to changing NUMSTART and NUMSTEP Integer Changes intervals for the independent v...

Page 61: ...you want The dependent values are then calculated and displayed Build a table 1 Start with an expression defined in Symbolic view in the aplet of your choice Note Function Polar Parametric and Sequence aplets only 2 In the Numeric Setup NUM choose NUMTYPE Build Your Own 3 Open the Numeric view 4 Clear existing data in the table CLEAR 5 Enter the independent values in the left hand column Type in a...

Page 62: ...ressing replaces this variable with its current value Inserts a zero value at the position of the highlight Replace a zero by typing the number you want and pressing Sorts the independent variable values into ascending or descending order Press and select the ascending or descending option from the menu and press Toggles between two character sizes Displays the defining function expression for the...

Page 63: ...to the default settings SETUP PLOT CLEAR 3 Plot the two functions and hide the menu so that you can see all the circle 4 Reset the numeric setup to the default settings SETUP NUM CLEAR 5 Display the functions in numeric form hp40g book Page 21 Friday December 9 2005 1 03 AM ...

Page 64: ...hp40g book Page 22 Friday December 9 2005 1 03 AM ...

Page 65: ...y stepping you through an example See Aplet views on page 2 1 for further information about the functionality of the Symbolic Numeric and Plot views Getting started with the Function aplet The following example involves two functions a linear function and a quadratic equation Open the Function aplet 1 Open the Function aplet Select Function The Function aplet starts in the Symbolic view The Symbol...

Page 66: ...he plot You can change the scales of the x and y axes graph resolution and the spacing of the axis ticks 3 Display plot settings SETUP PLOT Note For our example you can leave the plot settings at their default values since we will be using the Auto Scale feature to choose an appropriate y axis for our x axis settings If your settings do not match this example press CLEAR to restore the default val...

Page 67: ... example choose Auto Scale See VIEWS menu options on page 2 13 for a description of Auto Scale Select Auto Scale Trace a graph 7 Trace the linear function 6 times Note By default the tracer is active 8 Jump from the linear function to the quadratic function hp40g book Page 3 Friday December 9 2005 1 03 AM ...

Page 68: ...or further information To find a root of the quadratic function 10 Move the cursor to the graph of the quadratic equation by pressing the or key Then move the cursor so that it is near by pressing the or key Select Root The root value is displayed at the bottom of the screen Note If there is more than one root as in our example the coordinates of the root closest to the current cursor position are...

Page 69: ... current cursor position are displayed To find the slope of the quadratic function 13 Find the slope of the quadratic function at the intersection point Select Slope The slope value is displayed at the bottom of the screen To find the signed area of the two functions 14 To find the area between the two functions in the range 2 x 1 first move the cursor to and select the signed area option Select S...

Page 70: ... Display the numerical value of the integral Note See Shading area on page 3 11 for another method of calculating area To find the extremum of the quadratic 19 Move the cursor to the quadratic equation and find the extremum of the quadratic Select Extremum The coordinates of the extremum are displayed at the bottom of the screen hp40g book Page 6 Friday December 9 2005 1 03 AM ...

Page 71: ...re locate the cursor to find other roots or extrema that may exist Display the numeric view 20 Display the numeric view Set up the table 21 Display the numeric setup SETUP NUM See Setting up the table Numeric view setup on page 2 16 for more information 22 Match the table settings to the pixel columns in the graph view Explore the table 23 Display the table of values hp40g book Page 7 Friday Decem...

Page 72: ...ns 26 Zoom in on X 10 by a factor of 4 Note NUMZOOM has a setting of 4 In To change font size 27 Display table numbers in large font To display the symbolic definition of a column 28 Display the symbolic definition for the F1 column The symbolic definition of F1 is displayed at the bottom of the screen hp40g book Page 8 Friday December 9 2005 1 03 AM ...

Page 73: ...d graph The results of the FCN functions are saved in the following variables Area Extremum Isect Root Slope For example if you use the Root function to find the root of a plot you can use the result in calculations in HOME Access FCN variables The FCN variables are contained on the VARS menu To access FCN variables in HOME Select Plot FCN or to choose a variable To access FCN variable in the Func...

Page 74: ...um or minimum of the current function nearest the cursor This displays the coordinate values and moves the cursor to the extremum The resulting value is saved in a variable named EXTREMUM Slope Select Slope to find the numeric derivative at the current position of the cursor The result is saved in a variable named SLOPE Signed area Select Signed area to find the numeric integral If there are two o...

Page 75: ...ress choose the function that will act as the boundary of the shaded area and press 8 Press the or key to shade in the area 9 Press to calculate the area The area measurement is displayed near the bottom of the screen To remove the shading press to re draw the plot Intersection Select Intersection to find the intersection of two graphs nearest the cursor You need to have at least two selected expr...

Page 76: ...Function 2 Highlight the line you want to use and enter the expression You can press to delete an existing line or CLEAR to clear all lines 2 CHARS 1 CHARS 1 AND CHARS 1 4 CHARS 1 Note You can use the menu key to assist in the entry of equations It has the same effect as pressing f x x 2 x 1 x 2 1 x 1 4 x x 1 hp40g book Page 12 Friday December 9 2005 1 03 AM ...

Page 77: ...forms and Getting started with the Parametric aplet The following example uses the parametric equations Note This example will produce a circle For this example to work the angle measure must be set to degrees Open the Parametric aplet 1 Open the Parametric aplet Select Parametric Define the expressions 2 Define the expressions 3 3 x f t y g t x t 3 t y t 3 t cos sin hp40g book Page 1 Friday Decem...

Page 78: ...p input form has two fields not included in the Function aplet TRNG and TSTEP TRNG specifies the range of t values TSTEP specifies the step value between t values 5 Set the TRNG and TSTEP so that t steps from 0 to 360 in 5 steps 360 5 Plot the expression 6 Plot the expression 7 To see all the circle press twice hp40g book Page 2 Friday December 9 2005 1 03 AM ...

Page 79: ...n and scaling functionality available in the Function aplet See Exploring the graph on page 2 7 for further information Display the numbers 9 Display the table of values You can highlight a t value type in a replacement value and see the table jump to that value You can also zoom in or zoom out on any t value in the table You are able to explore the table using build your own table and split scree...

Page 80: ...hp40g book Page 4 Friday December 9 2005 1 03 AM ...

Page 81: ...Polar aplet opens in the Symbolic view Define the expression 2 Define the polar equation 2 π 2 Specify plot settings 3 Specify the plot settings In this example we will use the default settings except for the θRNG fields SETUP PLOT CLEAR 4 π Plot the expression 4 Plot the expression r 2π θ 2 θ 2 cos cos hp40g book Page 1 Friday December 9 2005 1 03 AM ...

Page 82: ...Function aplet See Exploring the graph on page 2 7 for further information Display the numbers 6 Display the table of values for θ and R1 The Numeric view options available are the same as those found in the Function aplet See Exploring the table of numbers on page 2 17 for further information hp40g book Page 2 Friday December 9 2005 1 03 AM ...

Page 83: ...he Sequence aplet The following example defines and then plots an expression in the Sequence aplet The sequence illustrated is the well known Fibonacci sequence where each term from the third term on is the sum of the preceding two terms In this example we specify three sequence fields the first term the second term and a rule for generating all subsequent terms However you can also define a seque...

Page 84: ...e preceding two terms for In the Symbolic view of the Sequence aplet highlight the U1 1 field and begin defining your sequence 1 1 Note You can use the and menu keys to assist in the entry of equations Specify plot settings 3 In Plot Setup first set the SEQPLOT option to Stairstep Reset the default plot settings by clearing the Plot Setup view SETUP PLOT CLEAR 8 8 U1 1 U2 1 Un Un 1 Un 2 n 3 hp40g ...

Page 85: ...e sequence 4 Plot the Fibonacci sequence 5 In Plot Setup set the SEQPLOT option to Cobweb SETUP PLOT Select Cobweb Display the table 6 Display the table of values for this example hp40g book Page 3 Friday December 9 2005 1 03 AM ...

Page 86: ...hp40g book Page 4 Friday December 9 2005 1 03 AM ...

Page 87: ...u can use the Solve aplet to solve an equation for any one of its variables When the Solve aplet is started it opens in the Solve Symbolic view In Symbolic view you specify the expression or equation to solve You can define up to ten equations or expressions named E0 to E9 Each equation can contain up to 27 real variables named A to Z and θ In Numeric view you specify the values of the known varia...

Page 88: ... distance of 100 m The equation to solve is Open the Solve aplet 1 Open the Solve aplet Select Solve The Solve aplet starts in the symbolic view Define the equation 2 Define the equation V U 2 A D Note You can use the menu key to assist in the entry of equations Enter known variables 3 Display the Solve numeric view screen V 2 U 2 2AD hp40g book Page 2 Friday December 9 2005 1 03 AM ...

Page 89: ...ause the variable A in the equation is linear we know that we need not look for any other solutions Plot the equation The Plot view shows one graph for each side of the selected equation You can choose any of the variables to be the independent variable The current equation is One of these is with that is This graph will be a horizontal line The other graph will be with and that is This graph is a...

Page 90: ...ric view Solve option See Plotting to find guesses on page 7 7 for more information Solve aplet s NUM view keys The Solve aplet s NUM view keys are Key Meaning Copies the highlighted value to the edit line for editing Press when done Displays a message about the solution see Interpreting results on page 7 6 Displays other pages of variables if any Displays the symbolic definition of the current ex...

Page 91: ...osest to the initial guess is returned Number format You can change the number format for the Solve aplet in the Numeric Setup view The options are the same as in HOME MODES Standard Fixed Scientific Engineering Fraction and Mixed Fraction For all except Standard you also specify how many digits of accuracy you want See Mode settings on page 1 10 for more information You might find it handy to set...

Page 92: ...value of the expression has different signs but is not precisely zero This might be because either the two points are neighbours they differ by one in the twelfth digit or the equation is not real valued between the two points Solve returns the point where the value or difference is closer to zero If the equation or expression is continuously real this point is Solve s best approximation of an act...

Page 93: ...guess For example 2 2 219330555745 1 21 31111111149 You can watch as the root finder either finds a sign reversal or converges on a local extrema or does not converge at all If there is no convergence in process you might want to cancel the operation press and start over with a different initial guess Plotting to find guesses The main reason for plotting in the Solve aplet is to help you find init...

Page 94: ... X V T A T 2 2 Find the solution for T time when X 30 V 2 and A 4 Enter the values for X V and A then highlight the independent variable T 30 2 4 to highlight T 3 Use the Plot view to find an initial guess for T First set appropriate X and Y ranges in the Plot Setup With equation X V x T A x T 2 2 the plot will produce two graphs one for and one for X V x T A x T 2 2 Since we have set in this exam...

Page 95: ...lution for the intersection on the right side of the y axis 6 Return to the Numeric view Note the T value is filled in with the position of the cursor from the Plot view 7 Ensure that the T value is highlighted and solve the equation Use this equation to solve for another variable such as velocity How fast must a body s initial velocity be in order for it to travel 50 m within 3 seconds Assume the...

Page 96: ... this Solve equation When you then redefine the value for T in this Solve equation that value is applied to T in all other contexts until it is changed again This sharing allows you to work on the same problem in different places such as HOME and the Solve aplet without having to update the value whenever it is recalculated H I N T As the Solve aplet uses existing variable values be sure to check ...

Page 97: ... three equation sets The hp40gs will alert you if no solution can be found or if there is an infinite number of solutions Note that the Linear Solver aplet only has a numeric view Getting started with the Linear Solver aplet The following example defines a set of three equations and then solves for the unknown variables Open the Linear Solver aplet 1 Open the Linear Sequence aplet Select Linear So...

Page 98: ...of x in the first equation Enter that co efficient and press or 4 The cursor moves to the next co efficient Enter that co efficient press or and continue doing likewise until you have defined all the equations Note you can enter the name of a variable for any co efficient or constant Press and begin entering the name The menu key appears Press that key to lock alphabetic entry mode Press it again ...

Page 99: ... the remaining known values the solution changes The example at the right shows the final solution once all the co efficients and constants are entered for the set of equations we set out to solve hp40g book Page 3 Friday December 9 2005 1 03 AM ...

Page 100: ...hp40g book Page 4 Friday December 9 2005 1 03 AM ...

Page 101: ...ill alert you if no solution can be found or if you have provided insufficient data If you are determining the properties of a right angled triangle a simpler input form is available by pressing the menu key Note that the Triangle Solver aplet only has a numeric view Getting started with the Triangle Solver aplet The following example solves for the unknown length of the side of a triangle whose t...

Page 102: ... type it is you should use the general input form illustrated in the previous step To switch to the general input form press If the general input form is displayed and you are investigating a right angled triangle press to display the simpler input form Specify the known values 3 Using the arrow keys move to a field whose value you know enter the value and press or Repeat for each known value Note...

Page 103: ...Note if two sides and an adjacent acute angle are entered and there are two solutions only one will be displayed initially In this case an menu key is displayed as in this example You press to display the second solution and again to return to the first solution Errors No solution with given data If you are using the general input form and you enter more than 3 values the values might not be consi...

Page 104: ...o calculate the remaining attributes of the triangle If you specify less than three Not enough data appears on the screen If you are using the simplified input form for a right angled triangle you must specify at least two values In addition you cannot specify only angles and no lengths hp40g book Page 4 Friday December 9 2005 1 03 AM ...

Page 105: ...alues in HOME and recall the values of specific statistics variables The values computed in the Statistics aplet are saved in variables and many of these variables are listed by the function accessible from the Statistics aplet s Numeric view screen Getting started with the Statistics aplet The following example asks you to enter and analyze the advertising and sales data in the table below comput...

Page 106: ...orations one variable or two variable The 5th menu key label in the Numeric view toggles between these two options and shows the current option 2 Select You need to select because in this example we are analyzing a dataset comprising two variables advertising minutes and resulting sales Enter data 3 Enter the data into the columns 2 1 3 5 5 4 to move to the next column 1400 920 1100 2265 2890 2200...

Page 107: ...olumns that hold the data you want to analyze You could have entered your data into columns other than C1 and C2 Explore statistics 6 Find the mean advertising time MEANX and the mean sales MEANY MEANX is 3 3 minutes and MEANY is about 1796 7 Scroll down to display the value for the correlation coefficient CORR The CORR value indicates how well the linear model fits the data 9 times The value is 8...

Page 108: ... regression curve 10 Draw the regression curve a curve to fit the data points This draws the regression line for the best linear fit Display the equation for best linear fit 11 Return to the Symbolic view 12 Display the equation for the best linear fit to move to the FIT1 field The full FIT1 expression is shown The slope m is 425 875 The y intercept b is 376 25 hp40g book Page 4 Friday December 9 ...

Page 109: ...ertising were to go up to 6 minutes S to highlight Stat Two to highlight PREDY 6 14 Return to the Plot view 15 Jump to the indicated point on the regression line 6 Observe the predicted y value in the left bottom corner of the screen hp40g book Page 5 Friday December 9 2005 1 03 AM ...

Page 110: ...opy of the list L1 into the data column variable C1 Statistics aplet s NUM view keys The Statistics aplet s Numeric view keys are Key Meaning Copies the highlighted item into the edit line Inserts a zero value above the highlighted cell Sorts the specified independent data column in ascending or descending order and rearranges a specified dependent or frequency data column accordingly Switches bet...

Page 111: ...tistics aplet Select Statistics 2 Enter the measurement data 160 165 170 175 180 Deletes the currently highlighted value CLEAR Clears the current column or all columns of data Pregss CLEAR to display a menu list then select the current column or all columns option and press cursor key Moves to the first or last row or first or last column Key Meaning Continued hp40g book Page 7 Friday December 9 2...

Page 112: ...stics Symbolic setup view 4 Press to close the statistics window and press key to see the data set definitions The first column indicates the associated column of data for each data set definition and the second column indicates the constant frequency or the column that holds the frequencies The keys you can use from this window are Key Meaning Copies the column variable or variable expression to ...

Page 113: ...mathematical form Press when done Evaluates the variables in the highlighted column C1 etc expression Displays the menu for entering variable names or contents of variables Displays the menu for entering math operations Deletes the highlighted variable or the current character in the edit line CLEAR Resets default specifications for the data sets or clears the edit line if it was active Note If CL...

Page 114: ...lay the computed statistics The mean height is approximately 167 63cm 9 Setup a histogram plot for the data SETUP PLOT Enter set up information appropriate to your data 10 Plot a histogram of the data Save data The data that you enter is automatically saved When you are finished entering data values you can press a key for another Statistics view like or you can switch to another aplet or HOME hp4...

Page 115: ... Highlight the entry following the point of insertion Press then enter a number It will write over the zero that was inserted Sort data values 1 In Numeric view highlight the column you want to sort and press 2 Specify the Sort Order You can choose either Ascending or Descending 3 Specify the INDEPENDENT and DEPENDENT data columns Sorting is by the independent column For instance if Age is C1 and ...

Page 116: ... definition in Symbolic view involves a trigonometric function In this case you should specify in the mode screen whether the trigonometric units are to be interpreted in degrees radians or grads To choose the fit 1 In Numeric view make sure is set 2 Press SETUP SYMB to display the Symbolic Setup view Highlight the Fit number S1FIT to S5FIT you want to define 3 Press and select from the list Press...

Page 117: ...d Quadratic Fits to a quadratic curve y ax2 bx c Needs at least three points Cubic Fits to a cubic curve y ax3 bx2 cx d Needs at least four points Logistic Fits to a logistic curve where L is the saturation value for growth You can store a positive real value in L or if L 0 let L be computed automatically Exponent Fits to an exponent curve Trigonometric Fits to a trigonometric curve Needs at least...

Page 118: ... to calculate Q3 Statistic Definition NΣ Number of data points TOTΣ Sum of data values with their frequencies MEANΣ Mean value of data set PVARΣ Population variance of data set SVARΣ Sample variance of data set PSDEV Population standard deviation of data set SSDEV Sample standard deviation of data set MINΣ Minimum data value in data set Q1 First quartile median of values to left of median MEDIAN M...

Page 119: ...ependent values ΣX Sum of x values ΣX2 Sum of x2 values MEANY Mean of y dependent values ΣY Sum of y values ΣY2 Sum of y2 values ΣXY Sum of each xy SCOV Sample covariance of independent and dependent data columns PCOV Population covariance of independent and dependent data columns CORR Correlation coefficient of the independent and dependent data columns for a linear fit only regardless of the Fit...

Page 120: ...relied upon to give a good starting scale which can then be adjusted in the Plot Setup view Plot types Histogram One variable statistics The numbers below the plot mean that the current bar where the cursor is starts at 0 and ends at 2 not including 2 and the frequency for this column that is the number of data elements that fall between 0 and 2 is 1 You can see information about the next bar by p...

Page 121: ...up This is not a regression curve Fitting a curve to 2VAR data In the Plot view press This draws a curve to fit the checked two variable data set s See To choose the fit on page 10 12 The expression in Fit2 shows that the slope 1 98082191781 and the y intercept 2 2657 Correlation coefficient The correlation coefficient is stored in the CORR variable It is a measure of fit to a linear curve only Re...

Page 122: ...Plot type 1VAR STATPLOT enables you to specify either a histogram or a box and whisker plot for one variable statistics when is set Press to change the highlighted setting Histogram width HWIDTH enables you to specify the width of a histogram bar This determines how many bars will fit in the display as well as how the data is distributed how many values each bar represents Histogram range HRNG ena...

Page 123: ...anges of the axes and the width of histogram bars HWIDTH In mode ensure that both paired columns contain data and that they are the same length In mode ensure that a paired column of frequency values is the same length as the data column that it refers to Exploring the graph The Plot view has menu keys for zooming tracing and coordinate display There are also scaling options under These options ar...

Page 124: ...e of Y In HOME Enter PREDX y value to find the predicted value for the independent variable given a hypothetical dependent value Displays ZOOM menu Turns trace mode on off The white box appears next to the option when Trace mode is active Turns fit mode on or off Turning on draws a curve to fit the data points according to the current regression model 2var statistics only Enables you to specify a ...

Page 125: ...ne or you can copy these function names from the MATH menu under the Stat Two category H I N T In cases where more than one fit curve is displayed the PREDY function uses the most recently calculated curve In order to avoid errors with this function uncheck all fits except the one that you want to work with or use the Plot View method hp40g book Page 21 Friday December 9 2005 1 03 AM ...

Page 126: ...hp40g book Page 22 Friday December 9 2005 1 03 AM ...

Page 127: ...Inference test by default the input form contains example data This example data is designed to return meaningful results that relate to the test It is useful for gaining an understanding of what the test does and for demonstrating the test The calculator s on line help provides a description of what the example data represents Getting started with the Inference aplet This example describes the In...

Page 128: ...thesis Tests Confidence Intervals Z 1 μ the Z Test on 1 mean Z Int 1 μ the confidence interval for 1 mean based on the Normal distribution Z μ1 μ2 the Z Test on the difference of two means Z Int μ1 μ2 the confidence interval for the difference of two means based on the Normal distribution Z 1 π the Z Test on 1 proportion Z Int 1 π the confidence interval for 1 proportion based on the Normal distri...

Page 129: ...lternative hypothesis μ μ0 Enter data 5 Enter the sample statistics and population parameters setup NUM The table below lists the fields in this view for our current Z Test 1 μ example Field name Definition μ0 Assumed population mean σ Population standard deviation Sample mean n Sample size α Alpha level for the test x hp40g book Page 3 Friday December 9 2005 1 03 AM ...

Page 130: ...view of the test results Horizontal axes are presented for both the distribution variable and the test statistic A generic bell curve represents the probability distribution function Vertical lines mark the critical value s of the test as well as the value of the test statistic The rejection region is marked and the test numeric results are displayed between the horizontal axes Importing sample st...

Page 131: ... input form modes is set to Comma use instead of 3 If necessary select 1 variable statistics Do this by pressing the fifth menu key until is displayed as its menu label Calculate statistics 4 Calculate statistics The mean of 0 592 seems a little large compared to the expected value of 0 5 To see if the difference is statistically significant we will use the statistics computed here to construct a ...

Page 132: ... method and type 7 Select an inference method Select CONF INTERVAL 8 Select a distribution statistic type Select T Int 1 μ Set up the interval calculation 9 Set up the interval calculation Note The default values are derived from sample data from the on line help example Setup NUM hp40g book Page 6 Friday December 9 2005 1 03 AM ...

Page 133: ... interval in the C field to move to the C field 0 9 DisplayNumeric view 12 Display the confidence interval in the Numeric view Note The interval setting is 0 5 Display Plot view 13 Display the confidence interval in the Plot view You can see from the second text row that the mean is contained within the 90 confidence interval CI of 0 3469814 to 0 8370186 Note The graph is a simple generic bell cur...

Page 134: ...t 1 μ On the basis of statistics from a single sample the One Sample Z Test measures the strength of the evidence for a selected hypothesis against the null hypothesis The null hypothesis is that the population mean equals a specified value Η0 μ μ0 You select one of the following alternative hypotheses against which to test the null hypothesis Inputs The inputs are H1 μ1 μ2 H1 μ1 μ2 H1 μ1 μ2 Field...

Page 135: ...e following alternative hypotheses against which to test the null hypothesis Inputs The inputs are Result Description Test Z Z test statistic Prob Probability associated with the Z Test statistic Critical Z Boundary values of Z associated with the α level that you supplied Critical Boundary values of required by the α value that you supplied x x H1 μ1 μ2 H1 μ1 μ2 H1 μ1 μ2 Field name Definition Sam...

Page 136: ...ion of successes in the two populations is equal H0 π π0 You select one of the following alternative hypotheses against which to test the null hypothesis σ2 Population 2 standard deviation α Significance level Field name Definition Result Description Test Z Z Test statistic Prob Probability associated with the Z Test statistic Critical Z Boundary value of Z associated with the α level that you sup...

Page 137: ...ses in the two populations is equal H0 π1 π2 You select one of the following alternative hypotheses against which to test the null hypothesis Field name Definition x Number of successes in the sample n Sample size π0 Population proportion of successes α Significance level Result Description Test P Proportion of successes in the sample Test Z Z Test statistic Prob Probability associated with the Z ...

Page 138: ...mple mean has some assumed value Η0 μ μ0 You select one of the following alternative hypotheses against which to test the null hypothesis Field name Definition X1 Sample 1 mean X2 Sample 2 mean n1 Sample 1 size n2 Sample 2 size α Significance level Result Description Test π1 π2 Difference between the proportions of successes in the two samples Test Z Z Test statistic Prob Probability associated wi...

Page 139: ... Hypothetical population mean α Significance level x Result Description Test T T Test statistic Prob Probability associated with the T Test statistic Critical T Boundary value of T associated with the α level that you supplied Critical Boundary value of required by the α value that you supplied x x hp40g book Page 13 Friday December 9 2005 1 03 AM ...

Page 140: ...thesis The null hypothesis is that the two populations means are equal H 0 μ1 μ2 You select one of the following alternative hypotheses against which to test the null hypothesis Inputs The inputs are H1 μ1 μ2 H1 μ1 μ2 H1 μ1 μ2 Field name Definition Sample 1 mean Sample 2 mean S1 Sample 1 standard deviation S2 Sample 2 standard deviation n1 Sample 1 size n2 Sample 2 size α Significance level _Poole...

Page 141: ...bution to calculate a confidence interval for m the true mean of a population when the true population standard deviation s is known Inputs The inputs are Result Description Test T T Test statistic Prob Probability associated with the T Test statistic Critical T Boundary values of T associated with the α level that you supplied Field name Definition Sample mean σ Population standard deviation n Sa...

Page 142: ...own Inputs The inputs are Results The results are Result Description Critical Z Critical value for Z μ min Lower bound for μ μ max Upper bound for μ Field name Definition Sample 1 mean Sample 2 mean n1 Sample 1 size n2 Sample 2 size σ1 Population 1 standard deviation σ2 Population 2 standard deviation C Confidence level x1 x2 Result Description Critical Z Critical value for Z μ Min Lower bound for...

Page 143: ...oportion Z Interval Menu name Z INT π1 π2 This option uses the Normal Z distribution to calculate a confidence interval for the difference between the proportions of successes in two populations Inputs The inputs are Field name Definition x Sample success count n Sample size C Confidence level Result Description Critical Z Critical value for Z π Min Lower bound for π π Max Upper bound for π Field ...

Page 144: ...is unknown Inputs The inputs are n1 Sample 1 size n2 Sample 2 size C Confidence level Field name Definition Continued Result Description Critical Z Critical value for Z π Min Lower bound for the difference between the proportions of successes π Max Upper bound for the difference between the proportions of successes Δ Δ Field name Definition Sample mean Sx Sample standard deviation n Sample size C ...

Page 145: ...ndard deviations s1and s2 are unknown Inputs The inputs are Result Description Critical T Critical value for T μ Min Lower bound for μ μ Max Upper bound for μ Field name Definition Sample 1 mean Sample 2 mean s1 Sample 1 standard deviation s2 Sample 2 standard deviation n1 Sample 1 size n2 Sample 2 size C Confidence level _Pooled Whether or not to pool the samples based on their standard deviation...

Page 146: ... 20 Inference aplet Results The results are Result Description Critical T Critical value for T μ Min Lower bound for μ1 μ2 μ Max Upper bound for μ1 μ2 Δ Δ hp40g book Page 20 Friday December 9 2005 1 03 AM ...

Page 147: ...cial problems with your HP 40gs calculator Background information on and applications of financial calculations are provided next Background The Finance Solver application provides you with the ability of solving time value of money TVM and amortization problems These problems can be used for calculations involving compound interest applications as well as amortization tables Compound interest is ...

Page 148: ... compounding periods Arrows represent the cash flows which could be positive upward arrows or negative downward arrows depending on the point of view of the lender or borrower The following cash flow diagram shows a loan from a borrower s point of view On the other hand the following cash flow diagram shows a load from the lender s point of view In addition cash flow diagrams specify when payments...

Page 149: ... PMT N The total number of compounding periods or payments I YR The nominal annual interest rate or investment rate This rate is divided by the number of payments per year P YR to compute the nominal interest rate per compounding period which is the interest rate actually used in TVM calculations PV The present value of the initial cash flow To a lender or borrower PV is the amount of the loan to ...

Page 150: ...s required 5 Use the arrow keys to highlight the TVM variable you wish to solve for and press the soft menu key PMT The periodic payment amount The payments are the same amount each period and the TVM calculation assumes that no payments are skipped Payments can occur at the beginning or the end of each compounding period an option you control by setting the Payment mode to Beg or End FV The futur...

Page 151: ...ing cash flow diagram illustrates the loan calculations Start the Finance Solver selecting P YR 12 and End payment option Enter the known TVM variables as shown in the diagram above Your input form should look as follows Highlighting the PMT field press the soft menu key to obtain a payment of 315 17 i e PMT 315 17 To determine the maximum loan possible if the monthly payments are only 300 type th...

Page 152: ... above Your input form for calculating monthly payments for the 30 yr mortgage should look as follows Highlighting the PMT field press the soft menu key to obtain a payment of 948 10 i e PMT 948 10 To determine the balloon payment or future value FV for the mortgage after 10 years use N 120 highlight the FV field and press the soft menu key The resulting value is FV 127 164 19 The negative value i...

Page 153: ...amortize in this batch 5 Press the soft menu key to amortize a batch of payments The calculator will provide for you the amount applied to interest to principal and the remaining balance after this set of payments have been amortized Example 3 Amortization for home mortgage For the data of Example 2 above find the amortization of the loan after the first 10 years 12x10 120 payments Pressing the so...

Page 154: ...sults shown below To amortize a series of future payments starting at payment p 1 Calculate the balance of the loan at payment p 1 2 Store the new balance in PV using the soft menu key 3 Amortize the series of payments starting at the new PV The amortization operation reads the values from the TVM variables rounds the numbers it gets from PV and PMT to the current display mode then calculates the ...

Page 155: ...is chapter covers only the use of mathematical functions in HOME view The use of mathematical functions in CAS is described in Chapter14 Computer Algebra System CAS The MATH menu The MATH menu provides access to math functions physical constants and programming constants You can also access CAS commands The MATH menu is organized by category For each category of functions on the left there is a li...

Page 156: ...TH menu is open CAS functions and commands are displayed You can select a CAS function or command in the same way that you select a function from the MATH menu by pressing the arrow keys and then The function or command selected appears on the edit line in HOME and with an initial parenthesis if appropriate Function categories MATH menu Math functions by category Syntax Each function s definition ...

Page 157: ...ption see on page 11 7 AND For a description see AND on page 13 19 For a description see COMB 5 2 returns 10 That is there are ten different ways that five things can be combined two at a time on page 13 12 For a description see S on page 13 11 EEX For a description see Scientific notation powers of 10 on page 1 20 For a description see on page 11 7 The multiplicative inverse function finds the in...

Page 158: ...so accepts complex numbers 10 value Example 10 3 returns 1000 Common logarithm Also accepts complex numbers LOG value Example LOG 100 returns 2 Sine cosine tangent Inputs and outputs depend on the current angle format Degrees Radians or Grads SIN value COS value TAN value Example TAN 45 returns 1 Degrees mode ASIN Arc sine sin 1x Output range is from 90 to 90 π 2 to π 2 or 100 to 100 grads Inputs ...

Page 159: ...s mode ATAN Arc tangent tan 1x Output range is from 90 to 90 2π 2 to π 2 or 100 to 100 grads Inputs and outputs depend on the current angle format Also accepts complex numbers ATAN value Example ATAN 1 returns 45 Degrees mode Square Also accepts complex numbers value2 Example 182 returns 324 Square root Also accepts complex numbers value Example returns 18 Negation Also accepts complex numbers val...

Page 160: ...respect to the variable of differentiation From the command line use a formal name S1 etc for a non numeric result See Finding derivatives on page 13 21 variable expression Example s1 s12 3 s1 returns 2 s1 3 Integrates expression from lower to upper limits with respect to the variable of integration To find the definite integral both limits must have numeric values that is be numbers or real varia...

Page 161: ...ber functions These functions are for complex numbers only You can also use complex numbers with all trigonometric and hyperbolic functions and with some real number and keyboard functions Enter complex numbers in the form x y where x is the real part and y is the imaginary part ARG Argument Finds the angle defined by a complex number Inputs and outputs use the current angle format set in Modes AR...

Page 162: ...re described in Program constants and physical constants on page 13 24 e Natural logarithm base Internally represented as 2 71828182846 e i Imaginary value for the complex number 0 1 i MAXREAL Maximum real number Internally represented as 9 99999999999 x 10499 MAXREAL MINREAL Minimum real number Internally represented as 1x10 499 MINREAL π Internally represented as 3 14159265359 π Conversions The ...

Page 163: ... from pounds to kilograms LBS Convert from kilograms to pounds KM Convert from miles to kilometers MILE Convert from kilometers to miles DEG Convert from radians to degrees RAD Convert from degrees to radians Hyperbolic trigonometry The hyperbolic trigonometry functions can also take complex numbers as arguments ACOSH Inverse hyperbolic cosine cosh 1 x ACOSH value ASINH Inverse hyperbolic sine sin...

Page 164: ...se to zero EXPM1 value LNP1 Natural log plus 1 ln x 1 This is more accurate than the natural logarithm function when x is close to zero LNP1 value List functions These functions work on list data See List functions on page 19 6 Loop functions The loop functions display a result after evaluating an expression a given number of times ITERATE Repeatedly for times evaluates an expression in terms of v...

Page 165: ...nalvalue expression Example Σ C 1 5 C2 returns 55 Matrix functions These functions are for matrix data stored in matrix variables See Matrix functions and commands on page 18 10 Polynomial functions Polynomials are products of constants coefficients and variables raised to powers terms POLYCOEF Polynomial coefficients Returns the coefficients of the polynomial with the specified roots POLYCOEF roo...

Page 166: ... often not be easily seen in HOME due to the number of decimal places especially if they are complex numbers It is better to store the results of POLYROOT to a matrix For example POLYROOT 1 0 0 8 M1 will store the three complex cube roots of 8 to matrix M1 as a complex vector Then you can see them easily by going to the Matrix Catalog and access them individually in calculations by referring to M1...

Page 167: ...fferent for each calculator so using RANDSEED Time is guaranteed to produce a set of numbers which are as close to random as possible You can set the seed using the command RANDSEED UTPC Upper Tail Chi Squared Probability given degrees of freedom evaluated at value Returns the probability that a χ2 random variable is greater than value UTPC degrees value UTPF Upper Tail Snedecor s F Probability gi...

Page 168: ...s 3 DEG RAD Degrees to radians Converts value from Degrees angle format to Radians angle format DEG RAD value Example DEG RAD 180 returns 3 14159265359 the value of π FLOOR Greatest integer less than or equal to value FLOOR value Example FLOOR 3 2 returns 4 FNROOT Function root finder like the Solve aplet Finds the value for the given variable at which expression most nearly evaluates to zero Uses...

Page 169: ...mber of hours or degrees with a decimal fraction to H MMSSs format time or angle up to fractions of a second HMS x x Example HMS 8 5 returns 8 3 INT Integer part INT value Example INT 23 2 returns 23 MANT Mantissa significant digits of value MANT value Example MANT 21 2E34 returns 2 12 MAX Maximum The greater of two values MAX value1 value2 Example MAX 210 25 returns 210 MIN Minimum The lesser of ...

Page 170: ...Converts value from radians to degrees RAD DEG value Example RAD DEG π returns 180 ROUND Rounds value to decimal places Accepts complex numbers ROUND value places Round can also round to a number of significant digits as showed in example 2 Examples ROUND 7 8676 2 returns 7 87 ROUND 0 0036757 3 returns 0 00368 SIGN Sign of value If positive the result is 1 If negative 1 If zero result is zero For ...

Page 171: ...formal or numeric but the result is usually in symbolic form not a number You will find the symbols for the symbolic functions and where in the CHARS menu CHARS as well as the MATH menu equals Sets an equality for an equation This is not a logical operator and does not store values See Test functions on page 13 19 expression1 expression2 ISOLATE Isolates the first occurrence of variable in express...

Page 172: ...variable S1 to represent any sign or QUAD expression variable Example QUAD X 1 2 7 X returns 2 s1 2 7 2 QUOTE Encloses an expression that should not be evaluated numerically QUOTE expression Examples QUOTE SIN 45 F1 X stores the expression SIN 45 rather than the value of SIN 45 Another method is to enclose the expression in single quotes For example X 3 2 X F1 X puts the expression X 3 2 X into F1...

Page 173: ... value2 Greater than Returns 1 if true 0 if false value1 value2 Greater than or equal to Returns 1 if true 0 if false value1 value2 AND Compares value1 and value2 Returns 1 if they are both non zero otherwise returns 0 value1 AND value2 IFTE If expression is true do the trueclause if not do the falseclause IFTE expression trueclause falseclause Example IFTE X 0 X2 X3 NOT Returns 1 if value is zero...

Page 174: ...ides the richest environment for performing symbolic calculations you can perform some symbolic calculations in HOME and with the Function aplet CAS functions that you can perform in HOME such as DERVX and INTVX are discussed in Using CAS functions in HOME on page 14 7 In HOME When you perform calculations that contain normal variables the calculator substitutes values for any variables For exampl...

Page 175: ...ic calculations in the Function aplet You can perform symbolic operations in the Function aplet s Symbolic view For example to find the derivative of a function in the Function aplet s Symbolic view you define two functions and define the second function as a derivative of the first function You then evaluate the second function See To find derivatives in the Function aplet s Symbolic view on page...

Page 176: ...he function 3 Show the result To find derivatives in the Function aplet s Symbolic view To find the derivative of the function in the Function aplet s Symbolic view you define two functions and define the second function as a derivative of the first function For example to differentiate 1 Access the Function aplet s Symbolic view and define F1 2 2 Define F2 X as the derivative of F 1 dx x 2 sin 2 ...

Page 177: ...ire function You could also just define To find the indefinite integral using formal variables For example to find the indefinite integral of use 1 Enter the function 0 S1 3 X 5 X 2 Show the result format 3 Press to close the show window F1 x x x 2 2 x cos sin d 3x 2 5 x d X X S 5 3 1 0 2 hp40g book Page 23 Friday December 9 2005 1 03 AM ...

Page 178: ...r The extra constant of 32 5 results from the substitution of into x 2 5 5 and should be disregarded if an indefinite integral is required Program constants and physical constants When you press three menus of functions and constants become available the math functions menu which appears by default the program constants menu and the physical constants menu The math functions menu is described exte...

Page 179: ...quently test for that particular format To access the menu of program constants 1 Press 2 Press 3 Use the arrow keys to navigate through the options 4 Click and then to display the number assigned to the option you selected in the previous step The use of program constants is illustrated in more detail in Programming on page 21 1 Physical constants There are 29 physical constants from the fields o...

Page 180: ...ing example shows the information available about the speed of light one of the physics constants 5 To use the selected constant in a calculation press The constant appears at the position of the cursor on the edit line Example Suppose you want to know the potential energy of a mass of 5 units according to the equation 1 Enter 5 2 Press and then press E mc 2 hp40g book Page 26 Friday December 9 20...

Page 181: ... light s from the Physics menu 4 Press The menu closes and the value of the selected constant is copied to the edit line 5 Complete the equation as you would normally and press to get the result hp40g book Page 27 Friday December 9 2005 1 03 AM ...

Page 182: ...hp40g book Page 28 Friday December 9 2005 1 03 AM ...

Page 183: ...you are working in the HOME screen however 1 2 1 6 returns 2 3 if you are working with CAS HOME calculations are restricted to approximate or numeric mode while CAS calculations always work in exact mode unless you specifically change the default CAS modes Each mode has advantages and disadvantages For example in exact mode there is no rounding error but some calculations will take much longer to ...

Page 184: ...quation Writer You can however manually copy them to HOME see page 14 8 CAS functions are described in detail in CAS functions in the Equation Writer on page 14 9 Chapter 15 Equation Writer explains in detail how to enter an expression in the Equation Writer and contains numerous worked examples of CAS in operation An example To give you an idea of how CAS works let s consider a simple example Sup...

Page 185: ...ted term 5 Press to factor the selected term 6 Press to select the entire second term and then press to simplify it 7 Press to select the 45 in the first term 8 As you did earlier press the menu key and choose FACTOR Then press and to factor the selected term 9 Press to select the entire second term and then press to simplify it 20 hp40g book Page 3 Friday December 9 2005 1 03 AM ...

Page 186: ...in HOME where implied multiplication is assumed For example ABC is interpreted as A B C in HOME For these reasons variables used in the Equation Writer cannot be used in HOME and vice versa Using the PUSH command you can transfer expressions from the HOME screen history to CAS history see page 14 8 Likewise you can use the POP command to transfer expressions from CAS history to the HOME screen his...

Page 187: ... X upper case as shown in CAS MODES screen above However you can change this variable to any other letter or combination of letters and numbers by editing the INDEP VAR field in CAS MODES screen To change the setting press enter a new value and then press The variable VX in the calculator s HOME CASDIR directory takes by default the value of X This is the name of the preferred independent variable...

Page 188: ... don t select COMPLEX mode unless requested by the calculator in the performance of a particular operation Verbose vs non verbose mode When VERBOSE is selected certain calculus applications are provided with comment lines in the main display The comment lines will appear in the top lines of the display but only while the operation is being calculated Default unselected Step by step mode When STEP ...

Page 189: ...nd This command converts an approximate argument into an exact argument For example if Radians is your angle setting then ARG XQ 1 i π 4 but ARG 1 i 0 7853 Similarly FACTOR XQ 45 32 5 but FACTOR 45 45 Note too that the symbolic HOME variable S1 serves as the current variable for CAS functions in HOME For example DERVX S12 2 S1 2 S1 2 The result 2 S1 2 does not depend on the Equation Writer variabl...

Page 190: ...mmand to send expressions to CAS history For example if you enter PUSH S1 1 S1 1 is written to CAS history Send expressions from CAS to HOME history In the HOME screen you can use the POP command to retrieve the last expression written to CAS history For example if S1 1 is the last expression written to CAS history and you enter POP in the HOME screen S1 1 is written to the HOME screen history and...

Page 191: ...ening the Equation Writer and selecting a function from a soft key menu or opening the Equation Writer and pressing You can also directly type the name of a CAS function when you are in ALPHA mode Note that in this section CAS functions available from the sot key menus in the Equation Writer are described CAS functions available from the MATH menu are described in CAS Functions on the MATH menu on...

Page 192: ...ecify the full function name F X as in the third case above ALGB menu COLLECT Factors over the integers COLLECT combines like terms and factors the expression over the integers Example To factor over the integers you would type COLLECT X2 4 which gives in real mode Example To factor over the integers you would type COLLECT X2 2 which gives DEF Define a function For its argument DEF takes an equali...

Page 193: ...d in the MATH key s Integer menu The response is 1 which means TRUE Using the history which you access by pressing the SYMB key you put the expression into the Equation Writer with ECHO and change it to Or better define a function F K by selecting DEF from the ALGB menu on the menu bar and type The response is and F is now listed amongst the variables which you can verify using the VARS key For K ...

Page 194: ... 6 gives 18446744073709551617 Using FACTOR to factor it then yields 274177 67280421310721 EXPAND Distributivity EXPAND expands and simplifies an expression Example Typing gives FACTOR Factorization FACTOR factors an expression Example To factor type FACTOR X4 1 FACTOR is located in the ALGB menu XPAND X 2 2 X 1 X 2 2 X 1 x 4 1 x 4 1 hp40g book Page 12 Friday December 9 2005 1 03 AM ...

Page 195: ...decomposition of a rational function such as you use the PARTFRAC command In real and direct mode this produces In complex mode this produces QUOTE Quoted expression QUOTE expression is used to prevent an expression from being evaluated or simplified Example 1 Typing gives x 2 2 x 1 x 2 2 x 1 1 16 2x 1 i 2 2x 1 i 2 2x 1 i 2 2x 1 i 2 x 5 2 x 3 1 x 4 2 x 3 2 x 2 2 x 1 x 2 x 3 2 x 2 2 1 2 x 2 x 2 1 3...

Page 196: ...variable ABC To clear the variable press VARS in the Equation Writer then choose PURGE on the menu bar or select UNASSIGN on the ALGB menu by typing for example UNASSIGN ABC Substitute a value for a variable is an infix operator used to substitute a value for a variable in an expression similar to the function SUBST has two parameters an expression dependent on a parameter and an equality paramete...

Page 197: ...BST A2 1 A 2 gives TEXPAND Develop in terms of sine and cosine TEXPAND has a trigonometric expression or transcendental function as an argument TEXPAND develops this expression in terms of sin x and cos x Example Typing TEXPAND COS X Y gives Example Typing TEXPAND COS 3 X gives UNASSIGN Clear a variable UNASSIGN is used to clear a variable for example UNASSIGN ABC 2 2 1 y cos x cos y x sin sin 4 x...

Page 198: ...al derivatives Example Calculate Typing DERIV X Y2 Z3 X Y Z gives DERVX Derivative DERVX has one argument an expression DERVX calculates the derivative of the expression with respect to the variable stored in VX For example given calculate the derivative of f Type Or if you have stored the definition of f x in F that is if you have typed then type x y 2 z 3 x y z 3 x y 2 z 2 f x x x 2 1 x 1 x 1 ln...

Page 199: ...ing order by exponent and with deg Q n or Q 0 Q X is then the limited nth order expansion of in the vicinity of X 0 Typing DIVPC 1 X2 X3 1 X2 5 gives N O T E When the calculator displays a request to change to increasing powers mode respond yes FOURIER Fourier coefficients FOURIER has two parameters an expression f x and a whole number N FOURIER returns the Fourier coefficient cN of f x considered...

Page 200: ...0 2π by f x x2 Typing STORE 2π PERIOD FOURIER X2 N The calculator does not know that N is a whole number so you have to replace EXP 2 i N π with 1 and then simplify the expression We get So if then Typing FOURIER X2 0 gives so if then IBP Partial integration IBP has two parameters an expression of the form and f x cNe 2iNxπ T N 2 i N π 2 N 2 N 0 cN 2 i N π 2 N 2 4 π 2 3 N 0 c0 4 π 2 3 u x v x v x ...

Page 201: ...INTVX parameter is an AND of two elements IBP concerns itself only with the second element of the AND adding the integrated term to the first element of the AND so that you can perform multiple IBP in succession INTVX Primitive and defined integral INTVX has one argument an expression INTVX calculates a primitive of its argument with respect to the variable stored in VX Example Calculate a primiti...

Page 202: ...dy typed then type INTVX F X The result in all cases is equivalent to You will obtain absolute values only in Rigorous mode See CAS modes on page 14 5 for instructions on setting and changing modes Example Calculate Typing f x x x 2 1 LN x 1 x 1 NTVX X X 2 1 LN X 1 X 1 TORE X X 2 1 LN X 1 X 1 F DEF F X X X 2 1 LN X 1 X 1 X LN X 1 X 1 3 2 LN X 1 3 2 LN X 1 2 x 6 2 x 4 x 2 x d hp40g book Page 20 Fri...

Page 203: ...ent lim Calculate limits LIMIT or lim has two arguments an expression dependent on a variable and an equality a variable the value to which you want to calculate the limit You can omit the name of the variable and the sign when this name is in VX It is often preferable to use a quoted expression NTVX 2 X 6 2 X 4 X 2 3 x atan 2 x x x 2 1 2 X 6 2 X 4 X 2 X d 1 X 3 x atan 2 x x x 2 1 3 π 10 4 1 x sin...

Page 204: ...X is the current variable To find a left limit for example type gives if X is the current variable It is not necessary to quote the second argument when it is written with for example gives Example For n 2 in the following expression find the limit as x approaches 0 You can use the LIMIT command to do this lim QUOTE 2X 1 EXP 1 X 1 X lim 1 X 1 QUOTE 1 0 lim 1 X 1 QUOTE 1 0 lim 1 X 1 X 1 0 n x tan n...

Page 205: ...bol is obtained by typing SHIFT 0 To obtain To obtain You can also find the symbol in the MATH key s Constant menu PREVAL Evaluate a primitive PREVAL has three parameters an expression F VX dependent on the variable contained in VX and two expressions A and B For example if VX contains X and if F is a function PREVAL F X A B returns F B F A lim N TAN X TAN N X SIN N X N SIN X 0 x x x x lim X X X X...

Page 206: ...lements RISCH concerns itself only with the second element of the AND and adds the result to the first argument SERIES Limited nth order expansion SERIES has three arguments an expression dependent on a variable an equality the variable x the value a to which you want to calculate the expansion and a whole number the order n of the limited expansion You can omit the name of the variable and the si...

Page 207: ...finitely small gives Unidirectional expansion To perform an expansion in the vicinity of x a where x a use a positive real such as 4 0 for the order To perform an expansion in the vicinity of x a where x a use a negative real such as 4 0 for the order SERIES COS 2 X 2 X π 6 4 1 4 3h 2h 2 8 3 3 h 3 8 3 h 4 0 h 5 4 h X π 6 h 1 x π 2 h h 3 3 h 5 5 0 π h 6 2 h 1 x 2x 1 e 1 x 1 h 1 x SERIES 2X 1 EXP 1 ...

Page 208: ...ote that h x is positive as x 0 Example 3 If you enter the order as an integer rather than a real as in you will get the following error SERIES Error Unable to find sign Note that if you had been in Sloppy rather than Rigorous mode all three examples above would have returned the same answer as you got when exploring in the vicinity of x 0 x 2 x 3 SERIES X 2 X 3 X 0 3 0 1 16 h 4 1 8 h 3 1 2 h 2 h ...

Page 209: ...hat the function F x decreases for x in the interval reaching a minimum of at x It then increases in the interval reaching a maximum of Note that appearing in the variation table indicates that the function is not defined in the corresponding interval TAYLOR0 Limited expansion in the vicinity of 0 TAYLOR0 has a single argument the function of x to expand It returns the function s limited 4th relat...

Page 210: ... a polynomial and Xn TRUNC returns the polynomial truncated at order n 1 that is the returned polynomial has no terms with exponents n Typing gives REWRI menu The REWRI menu contains functions that enable you to rewrite an expression in another form DISTRIB Distributivity of multiplication DISTRIB enables you to apply the distributivity of multiplication in respect to addition in a single instance...

Page 211: ...form a trigonometric expression into complex exponentials EXPLN takes as an argument a trigonometric expression It transforms the trigonometric function into exponentials and logarithms without linearizing it EXPLN puts the calculator into complex mode Typing EXPLN SIN X gives EXP2POW Transform exp n ln x as a power of x EXP2POW transforms an expression of the form exp n ln x rewriting it as a pow...

Page 212: ...ing ENTER x3 6 x2 11 x 6 LIN Linearize the exponentials LIN has as an argument an expression containing exponentials and trigonometric functions LIN does not linearize trigonometric expressions as does TLIN but converts a trigonometric expression to exponentials and then linearizes the complex exponentials LIN puts the calculator into complex mode when dealing with trigonometric functions Example ...

Page 213: ...x 1 x 1 POWEXPAND Transform a power POWEXPAND writes a power in the form of a product Typing POWEXPAND X 1 3 gives x 1 x 1 x 1 This allows you to do the development of x 1 3 in step by step using DISTRIB several times on the preceding result SINCOS Transform the complex exponentials into sin and cos SINCOS takes as an argument an expression containing complex exponentials SINCOS then rewrites this...

Page 214: ...NUM has an expression as a parameter XNUM puts the calculator into approximate mode and returns the numeric value of the expression Typing XNUM 2 gives 1 41421356237 XQ Rational approximation XQ has a real numeric expression as a parameter XQ puts the calculator into exact mode and gives a rational or real approximation of the expression Typing XQ 1 41421 gives SIMPLIFY SIN 3 X SIN 7 X SIN 5 X 664...

Page 215: ...coefficients it is better to use LDEC DESOLVE has two arguments 1 the differential equation where is written as d1Y X or the differential equation and the initial conditions separated by AND 2 the unknown Y X The mode must be set to real Example 1 Solve y y cos x y 0 c0 y 0 c1 Typing DESOLVE d1d1Y X Y X COS X Y X gives cC0 and cC1 are integration constants y 0 cC0 y 0 cC1 You can then assign value...

Page 216: ... zeros of an expression ISOLATE returns the values that are the zeros of an expression or an equation ISOLATE has two parameters an expression or equation and the name of the variable to isolate ignoring REALASSUME Typing ISOLATE X4 1 3 X gives in real mode x 2 OR x 2 and in complex mode x 2 i OR x 2 OR x 2 i OR x 2 SUBST Y X cC0 COS X X 2 cC1 2 SIN X cC0 1 y x 2 x cos x 2 cC1 x sin 2 Y x x cos 2 ...

Page 217: ...tion constants y 0 cC0 and y 0 cC1 LINSOLVE Solve linear system LINSOLVE enables you to solve a system of linear equations It is assumed that the various equations are of the form expression 0 LINSOLVE has two arguments the first members of the various equations separated by AND and the names of the various variables separated by AND Example 1 Typing LINSOLVE X Y 3 AND X Y 1 X AND Y gives x 2 AND ...

Page 218: ...Z 1 AND X 2 Y Z 4 Then invoke LINSOLVE and type the unknowns X AND Y AND Z and press the ENTER key The following result is produced if you are in Step by step mode CFG etc L2 2L2 L1 ENTER L3 2L3 L1 and so on until finally Reduction Result 1 1 3 0 2 2 2 0 4 0 2 2 2 1 1 1 1 1 2 1 1 2 1 4 2 1 1 1 0 1 3 1 1 2 1 4 8 0 0 4 0 8 0 20 0 0 8 4 hp40g book Page 36 Friday December 9 2005 1 03 AM ...

Page 219: ...de x 2 OR x 2 or in complex mode x 2 OR x 2 OR x i 2 OR x i 2 Solve systems SOLVE also enables you to solve a system of non linear equations if they are polynomials If they are not polynomials use MSOLV in the HOME screen to get a numerical solution It is assumed that the various equations are of the form expression 0 SOLVE has as arguments the first members of the various equations separated by A...

Page 220: ... in real mode x 2 OR x 2 or in complex mode even if you have chosen X as real x 2 OR x 2 OR x i 2 OR x i 2 Example 2 Typing SOLVEVX 2X2 X gives in real mode x 1 2 OR x 0 TRIG menu The TRIG menu contains functions that enable you to transform trigonometric expressions ACOS2S Transform the arccos into arcsin ACOS2S has as a trigonometric expression as an argument ACOS2S transforms the expression by ...

Page 221: ...X ASIN X gives when simplified ASIN2T Transform the arccos into arctan ASIN2T has a trigonometric expression as an argument ASIN2T transforms the expression by replacing arcsin x with Typing ASIN2T ASIN X gives ATAN2S Transform the arctan into arcsin ATAN2S has a trigonometric expression as an argument ATAN2S transforms the expression by replacing arctan x with π 2 π 2 π 2 arc x 1 x 2 tan x 1 x 2 ...

Page 222: ...ication 1 SINCOS Transform the complex exponentials into sin and cos SINCOS takes an expression containing complex exponentials as an argument SINCOS then rewrites this expression in terms of sin x and cos x Typing SINCOS EXP i X gives after turning on complex mode if necessary cos x i sin x TAN2CS2 Transform tan x with sin 2x and cos 2x TAN2CS2 has a trigonometric expression as an argument x x 2 ...

Page 223: ...ing TAN2SC TAN X gives TAN2SC2 Transform tan x with sin 2x and cos 2x TAN2SC2 has a trigonometric expression as an argument TAN2SC2 transforms this expression by replacing tan x with Typing TAN2SC2 TAN X gives TCOLLECT Reconstruct the sine and the cosine of the same angle TCOLLECT has a trigonometric expression as an argument 1 2 x cos 2 x sin 1 2 x cos 2 x sin x sin x cos x sin x cos 2 x sin 1 2 ...

Page 224: ...ND has as an argument a transcendental expression that is an expression with trigonometric exponential or logarithmic functions TEXPAND develops this expression in terms of sin x cos x exp x or ln x Example 1 Typing TEXPAND EXP X Y gives exp x exp y Example 2 Typing TEXPAND LN X Y gives ln y ln x Example 3 Typing TEXPAND COS X Y gives cos y cos x sin y sin x Example 4 Typing TEXPAND COS 3 X 2 x π ...

Page 225: ...in n x and cos n x Example 1 Typing TLIN COS X COS Y gives Example 2 Typing TLIN COS X 3 gives Example 3 Typing TLIN 4 COS X 2 2 gives TRIG Simplify using sin x 2 cos x 2 1 TRIG has as an argument a trigonometric expression TRIG simplifies this expression using the identity sin x 2 cos x 2 1 1 2 x y cos 1 2 x y cos 1 4 3 x cos 3 4 x cos 2 2 x cos hp40g book Page 43 Friday December 9 2005 1 03 AM ...

Page 226: ...s as an argument a trigonometric expression TRIGSIN simplifies this expression using the identity sin x 2 cos x 2 1 to rewrite it in terms of sines Typing TRIGSIN SIN X 4 COS X 2 1 gives TRIGTAN Simplify using the tangents TRIGTAN has as an argument a trigonometric expression TRIGTAN simplifies this expression using the identity sin x 2 cos x 2 1 to rewrite it in terms of tangents Typing TRIGTAN S...

Page 227: ...ss in the Equation Writer grouped by main menu name Algebra menu All the functions on this menu are also available on the menu in the Equation Writer See ALGB menu on page 14 10 for a description of these functions Complex menu i Inserts i ABS Determines the absolute value of the argument Example Typing ABS 7 4i yields as does ABS 7 4i ARG See ARG on page 13 7 CONJ See CONJ on page 13 7 DROITE DRO...

Page 228: ...nu e i π See Constants on page 13 8 Enters the sign for infinity Diff Int menu All the functions on this menu are also available on the menu in the Equation Writer See DIFF menu on page 14 16 for a description of these functions Hyperb menu All the functions on this menu are described in Hyperbolic trigonometry on page 13 9 Integer menu Note that many integer functions also work with Gaussian inte...

Page 229: ...ers less than n that are prime with n Example Typing EULER 21 gives 12 Explanation 2 4 5 7 8 10 11 13 15 16 17 19 is the set of whole numbers less than 21 and prime with 21 There are 12 members of the set so the Euler index is12 FACTOR Decomposes an integer into its prime factors Example Typing FACTOR 90 gives 2 32 5 GCD Returns the greatest common divisor of two integers Example Typing GCD 18 15 ...

Page 230: ...he quotient and the remainder of the Euclidean division between two integers Example Typing IDIV2 148 5 gives 29 AND 3 In step by step mode the calculator shows the division process in longhand IEGCD Returns the value of Bézout s Identity for two integers For example IEGCD A B returns U AND V D with U V D such that AU BV D and D GCD A B Example Typing IEGCD 48 30 gives 2 AND 3 6 In other words 2 4...

Page 231: ...integers at the beginning of the vector these integers being the sequence of remainders IQUOT Returns the integer quotient of the Euclidean division of two integers Example Typing IQUOT 148 5 gives 29 In step by step mode the division is carried out as if in longhand Pressing or then causes 29 to be written to the Equation Writer IREMAINDER Returns the integer remainder from the Euclidean division...

Page 232: ...if n is a prime or pseudo prime and 0 FALSE if n is not prime Definition For numbers less than 1014 pseudo prime and prime mean the same thing For numbers greater than 1014 a pseudo prime is a number with a large probability of being prime Example 1 Typing ISPRIME 13 gives 1 Example 2 Typing ISPRIME 14 gives 0 LCM Returns the least common multiple of two integers Example Typing LCM 18 15 gives 90 ...

Page 233: ...yping PREVPRIME 75 gives 73 Modular menu All the examples of this section assume that p 13 that is you have entered MODSTO 13 or STORE 13 MODULO or have specified 13 for Modulo in CAS MODES screen as explained on page 15 16 ADDTMOD Performs an addition in Z pZ Example 1 Typing ADDTMOD 2 18 gives 6 ADDTMOD can also perform addition in Z pZ X Example 2 Typing ADDTMOD 11X 5 8X 6 gives 6x 2 hp40g book...

Page 234: ...uments are two polynomials A X and B X The result is a rational fraction A X B X simplified as Z pZ X Typing DIVMOD 2X2 5 5X2 2X 3 gives EXPANDMOD Expand and simplify expressions in Z pZ or Z pZ X Example 1 In Z pZ the argument is an integer expression Typing EXPANDMOD 2 3 5 4 gives 0 Example 2 In Z pZ X the argument is a polynomial Typing EXPANDMOD 2X2 12 5X 4 gives 4x 5 3x 3 3 x 3 5 x 2 5 x 4 hp...

Page 235: ...D 3X3 5X2 5X 4 gives GCDMOD Calculates the GCD of the two polynomials in Z pZ X Example Typing GCDMOD 2X2 5 5X2 2X 3 gives INVMOD Calculates the inverse of an integer in Z pZ Example Typing INVMOD 5 gives 5 since 5 5 25 1 mod 13 MODSTO Sets the value of the MODULO variable p Example Typing MODSTO 11 sets the value of p to 11 3x 5 x 2 6 6x 1 hp40g book Page 53 Friday December 9 2005 1 03 AM ...

Page 236: ... gives POWMOD Calculates A to the power of N in Z pZ X and A X to the power of N in Z pZ X Example 1 If p 13 typing POWMOD 11 195 gives 5 In effect 1112 1 mod 13 so 11195 1116 12 3 5 mod 13 Example 2 Typing POWMOD 2X 1 5 gives since 32 6 mod 13 80 2 mod 13 40 1 mod 13 10 3 mod 13 3x 2 2x 4 6x 5 2x 4 2x 3 x 2 3x 1 hp40g book Page 54 Friday December 9 2005 1 03 AM ...

Page 237: ...1X 5 8X 6 gives Polynomial menu EGCD Returns Bézout s Identity the Extended Greatest Common Divisor EGCD EGCD A X B X returns U X AND V X D X with D U V such that D X U X A X V X B X Example 1 Typing EGCD X2 2 X 1 X2 1 gives AND Example 2 Typing EGCD X2 2 X 1 X3 1 gives AND 3x 1 1 1 2x 2 x 2 1 3x 3 hp40g book Page 55 Friday December 9 2005 1 03 AM ...

Page 238: ...Greatest Common Divisor of two polynomials Example Typing GCD X2 2 X 1 X2 1 gives HERMITE Returns the Hermite polynomial of degree n where n is a whole number This is a polynomial of the following type Example Typing HERMITE 6 gives x 2 x 2 x 1 2 x 1 Hn x 1 n e x 2 2 d n dx n e x 2 2 64x 6 480x 4 720x 2 120 hp40g book Page 56 Friday December 9 2005 1 03 AM ...

Page 239: ...quation where n is a whole number Example Typing LEGENDRE 4 gives PARTFRAC Returns the partial fraction decomposition of a rational fraction Example Typing gives in real and direct mode and gives in complex mode x 2 2x 1 x 1 x 2 1 y 2 x y n n 1 y 0 35 x 4 30 x 2 3 8 ARTFRAC X 5 2X 3 1 X 4 2X 3 2X 2 2X 1 x 2 x 3 2x 2 2 1 2x 2 x 2 1 3 i 4 x i 1 2 x 1 1 3 i 4 x i hp40g book Page 57 Friday December 9 ...

Page 240: ...Example Typing gives PTAYL PTAYL rewrites a polynomial P X in order of its powers of X a Example Typing PTAYL X2 2 X 1 2 produces the polynomial Q X namely Note that P X Q X 2 QUOT QUOT returns the quotient of two polynomials A X and B X divided in decreasing order by exponent Example Typing QUOT X2 2 X 1 X gives Q X R X B X ROPFRAC 5X 3 X 1 X 2 5x 12 21 x 2 x 2 6x 9 x 2 hp40g book Page 58 Friday ...

Page 241: ...X2 1 gives Note that in step by step mode synthetic division is shown with each polynomial represented as the list of its coefficients in descending order of power TCHEBYCHEFF For n 0 TCHEBYCHEFF returns the polynomial Tn such that Tn x cos n arccos x For n 0 we have For n 0 we also have For n 1 we have If n 0 TCHEBYCHEFF returns the 2nd species Tchebycheff polynomial x 1 Tn x C 2k n x 2 1 k x n 2...

Page 242: ...See MAX on page 13 15 MIN See MIN on page 13 15 Rewrite menu All the functions on this menu are also available on the menu in the Equation Writer See REWRI menu on page 14 28 for a description of these functions Solve menu All the functions on this menu are also available on the menu in the Equation Writer See SOLV menu on page 14 33 for a description of these functions 8x 4 8x 2 1 8x 3 4x hp40g b...

Page 243: ...variable press select REALASSUME and press UNASSUME Use this function to cancel all previously specified assumptions about a particular argument or variable Example Typing UNASSUME X cancels any assumptions made about X It returns X in the Equation Writer To see the assumptions press select REALASSUME and press See Test functions on page 13 19 AND See AND on page 13 19 OR See OR on page 13 19 NOT ...

Page 244: ...lies the Bézout identity like EGCD but the arguments are three polynomials A B and C C must be a multiple of GCD A B ABCUV A X B X C X returns U X AND V X where U and V satisfy C X U X A X V X B X Example 1 Typing ABCUV X2 2 X 1 X2 1 X 1 gives CHINREM Chinese Remainders CHINREM has two sets of two polynomials as arguments each separated by AND CHINREM A X AND R X B X AND Q X returns an AND with tw...

Page 245: ...IC has an integer n as its argument Example 1 When n 4 the fourth roots of unity are 1 i 1 i Among them the primitive roots are i i Therefore the cyclotomic polynomial of order 4 is X i X i X2 1 Example 2 Typing CYCLOTOMIC 20 gives EXP2HYP EXP2HYP has an expression enclosing exponentials as an argument It transforms that expression with the relation exp a sinh a cosh a x 2 2x 1 2 AND x 4 1 2 P X x...

Page 246: ...the Γ function at a given point The Γ function is defined as We have Γ 1 1 Γ x 1 x Γ x Example 1 Typing GAMMA 5 gives 24 Example 2 Typing GAMMA 1 2 gives IABCUV IABCUV A B C returns U AND V such that AU BV C where A B and C are whole numbers C must be a multiple of GCD A B to obtain a solution Γ x e t t x 1 t d 0 π hp40g book Page 64 Friday December 9 2005 1 03 AM ...

Page 247: ...s The numbers X C k R where k is an integer are such that X A mod P and X B mod Q A solution X always exists when P and Q are mutually prime GCD P Q 1 and in this case all the solutions are congruent modulo R P Q Example Typing ICHINREM 7 AND 10 12 AND 15 gives 3 AND 30 ILAP LAP is the Laplace transform of a given expression The expression is the value of a function of the variable stored in VX t ...

Page 248: ...s with constant coefficients for example The following relations hold where c is a closed contour enclosing the poles of f The following property is used The solution y of is then Example To solve c type LAP X EXP 3 X The result is y p y q y f x y 0 a y 0 b LAP y x e x t y t t d 0 ILAP f x 1 2iπ e zx f z z d c LAP y x y 0 x LAP y x y p y q y f x y 0 a y 0 b ILAP LAP f x x p a b x 2 px q y 6 y 9 y ...

Page 249: ...result as a b i Example 1 Typing PA2B2 17 gives 4 i that is 17 42 12 Example 2 Typing PA2B2 29 gives 5 2 i that is 29 52 22 PSI Returns the value of the nth derivative of the Digamma function at a The Digamma function is the derivative of ln Γ x Example Typing PSI 3 1 ILAP 1 X 2 6X 9 X 6 a b X 2 6X 9 x 3 6 3a b x a e 3x hp40g book Page 67 Friday December 9 2005 1 03 AM ...

Page 250: ...ample Typing REORDER X2 2 X A A2 Z2 X Z A AND X AND Z gives SEVAL SEVAL simplifies the given expression operating on all but the top level operator of the expression Example Typing SEVAL SIN 3 X X SIN X X gives SIGMA Returns the discrete antiderivative of the input function that is the function G that satisfies the relation G x 1 G x f x It has two arguments the first is a function f x of a variab...

Page 251: ...x 1 G x f x SIGMAVX has as its argument a function f of the current variable VX Example Typing SIGMAVX X2 gives because STURMAB Returns the number of zeros of P in a b where P is a polynomial and a and b are numbers Example 1 Typing STURMAB X2 X3 2 2 0 gives 1 Example 2 Typing STURMAB X2 X3 2 2 1 gives 3 2x 3 3x 2 x 6 2 x 1 3 3 x 1 2 x 1 2x 3 3x 2 x 6x 2 hp40g book Page 69 Friday December 9 2005 1...

Page 252: ...n the process Example Typing gives VER Returns the version number of your CAS Example Typing VER might give 4 20050219 This particular result means that you have a version 4 CAS dated 19 February 2005 Note that this is not the same as VERSION which returns the version of the calculator s ROM TSIMP SIN 3X SIN 7X SIN 5X EXP i x 4 1 EXP i x 2 hp40g book Page 70 Friday December 9 2005 1 03 AM ...

Page 253: ...to apply CAS functions to an expression or subexpression and how to store values in the Equation Writer variables Chapter 14 explains all the symbolic calculation functions contained in the various menus and chapter 16 provides numerous examples showing the use of the Equation Writer The Equation Writer menu bar The Equation Writer has a number of soft menu keys TOOL menu Unlike the other soft men...

Page 254: ...0 Edit expr Enables you to edit the highlighted expression on the edit line just as you do in the HOME screen see page 15 11 Change font Enables you to choose to type using large or small characters see page 15 10 Cut Copies the selection to the clipboard and erases the selection from Equation Writer Copy Copies the selection to the clipboard Paste Copies the contents of the clipboard to the locat...

Page 255: ... can directly see and change CAS modes while working with the Equation Writer The first line in each of the Equation Writer menus except indicates the current CAS mode settings In the example at the right the first line of the menu reads CFG R X S CFG stands for configuration and the symbols to the right of it indicate various mode settings The first symbol R indicates that you are in real mode If...

Page 256: ... you want to choose is highlighted and then press Note that the configuration menu includes only those options that are not currently selected For example if Rigorous is a current setting its opposite Sloppy will appear on the menu If you choose Sloppy then Rigorous appears in its place To return your CAS modes to their default settings select Default cfg and press To close the configuration menu ...

Page 257: ...h the tree the and keys enable you to move from one branch to another the and keys enable you to move up and down a particular tree the and key combinations enable you to make multiple selections How do I select There are two ways of going into selection mode Pressing takes you into selection mode and selects the element adjacent to the cursor For example 1 2 3 4 selects 4 Pressing it again select...

Page 258: ...ith x 3 now selected If you press again the selection moves up the tree and now the entire expression is selected If you had pressed instead of when the cursor was positioned to the right of 3 the leaves of the branch get selected that is x 3 If you press again the selection moves up the tree and now the entire expression is selected If you now press just the numerator is selected If you now press...

Page 259: ...e expression as earlier but press after the first X as in 2 X 3 X the 2 X is selected and the next operation multiplication is applied to to it The expression becomes 2 X 3 X Pressing selects the entire expression and pressing evaluates it resulting in 2X 6 Now enter the same expression but press after the 3 as in 2 X 3 X Note that selects the expression so far entered 2 X thus making the next ope...

Page 260: ... twice to ensure that the exponent applies to X and not just to X Example 3 Suppose you want to enter Each fraction can be viewed as a separate branch on the equation tree In the Equation Writer type the first branch 1 2 and then select this branch by pressing Now type and enter the second branch 1 3 Select the second branch by pressing Now type and enter the third branch 1 4 Likewise select the t...

Page 261: ...to the right of it If you want you can evaluate the selected part by pressing The result is shown at the right Suppose now you want to perform the partial calculation Because the two terms in this partial calculation are not contiguous that is side by side you must first perform a permutation so that they are side by side To do this press This exchanges the selected element with its neighbour to t...

Page 262: ...ous parts of the expression are enclosed n in a box When what you want to select is enclosed press to select it Changing the font If you are entering a long expression you may find it useful to reduce the size of the font used in the Equation Writer Select Change font from the menu This enables you to view a large expression in its entirety when you need to Selecting Change font again returns the ...

Page 263: ... by pressing Delete a selected unary operator at the top of the expression tree by pressing For example to replace SIN expr with COS expr select SIN expr press and then press COS Delete a binary infix operator and one of its arguments by selecting the argument you want delete and pressing For example if you have the expression 1 2 and select 1 pressing deletes 1 and leaves only 2 Similarly to dele...

Page 264: ...You can move the cursor from argument to argument by pressing or Enter the expressions according to the rules of selection explained earlier but you must first go into selection mode by pressing N O T E Do not use the index i to define a summation because i designates the complex number solution of x2 1 0 Σ performs exact calculations if its argument has a discrete primitive otherwise it performs ...

Page 265: ...re automatically placed when you type the comma If you want to type 1 2 you must select 1 before you type the comma How to enter prefix functions A prefix function is one that is typed before its arguments To enter a prefix function you can type the first argument select it then select the function from a menu or you can select the function from a menu or by directly entering it in Alpha mode and ...

Page 266: ... described earlier 2 4 The entire expression is now selected Press then produce the result With a blank Equation Writer screen press select SUBST and then press or With the cursor between the parentheses at the location of the first argument type your expression Note that SUBST has two arguments When you have finished entering the first argument the expression press to move to the second argument ...

Page 267: ...tever was selected which is automatically placed in parentheses Press to evaluate the expression The result is the factors of the expression Because the result of an evaluation is always selected you can immediately apply another command to it To illustrate this press select SUBST and then press or Note that SUBST is applied to whatever was selected which is automatically placed in parentheses Not...

Page 268: ...In HOME or in the program editor use to store an object in a variable In CAS use the STORE command on the menu to store a value in a variable The key displays a menu that contains all the available variables Pressing while you are in HOME displays the names of the variables defined in HOME and in the Aplets Pressing while you are in the Equation Writer displays the names of the variables defined i...

Page 269: ...eal vars option on the CFG configuration menu all symbolic variables are considered reals You can also use an assumption to define a variable such as X 1 In a case like this you use the ASSUME X 1 command to make REALASSUME contain X 1 The command UNASSUME X cancels all the assumptions you have previously made about X To see these variables as well as those that you ve defined in CAS press in the ...

Page 270: ...ic to common real number calculations The Tests menu containing logic functions for working with hypotheses SHIFT MATH keys The key combination opens an alphabetical menu of all CAS commands You can enter a command by selecting it from this menu so that you don t have to type it in ALPHA mode VARS key Pressing while you re in the Equation Writer displays the names of the variables defined in CAS T...

Page 271: ...the Equation Writer Press or to replace the current selection in Equation Writer with the highlighted entry in CAS history Press to leave CAS history without changing it in any way SHIFT SYMB or SHIFT HOME keys While you are working in the Equation Writer pressing or opens CAS MODES screen The various CAS modes are described in CAS modes on page 14 5 SHIFT key Pressing followed by the comma key un...

Page 272: ...d the graph will be of Parametric type To summarize If you choose the Function Aplet the highlighted expression is copied into the chosen function Fi and the current variable is changed to X the Parametric Aplet the real part and the imaginary part of the highlighted expression are copied into the chosen functions Xi Yi and the current variable is changed to T the Polar Aplet the highlighted expre...

Page 273: ...on Writer 15 21 Short cut keys In the Equation Writer the following are short cut keys to the symbols indicated 0 for 1 for i 3 for π 5 for 6 for 8 for 9 for hp40g book Page 21 Friday December 9 2005 1 03 AM ...

Page 274: ...hp40g book Page 22 Friday December 9 2005 1 03 AM ...

Page 275: ...examination papers The examples are given in order of increasing difficulty Example 1 If A is calculate the result of A in the form of an irreducible fraction showing each step of the calculation Solution In the Equation Writer enter A by typing 3 2 1 1 2 1 Now press to select the denominator as shown above Press to simplify the denominator Now select the numerator by pressing 3 2 1 1 2 1 hp40g bo...

Page 276: ...n giving the result shown at the right Example 2 Given that write C in the form where d is a whole number Solution In the Equation Writer enter C by typing 2 45 3 12 20 6 3 Press to select Press to select and to select 20 Now press select FACTOR and press C 2 45 3 12 20 6 3 d 5 6 3 20 hp40g book Page 2 Friday December 9 2005 1 03 AM ...

Page 277: ...select and to exchange with Press to select and to select 45 Press select FACTOR and press Press to factor 45 into Press to select and to simplify the selection Press to select and to select 2 2 5 2 2 5 2 5 3 12 2 5 2 45 3 2 5 3 2 5 2 3 5 2 3 5 2 5 hp40g book Page 3 Friday December 9 2005 1 03 AM ...

Page 278: ...d so the final two terms cancel each other out Hence the result is Example 3 Given the expression expand and reduce D factor D solve the equation and evaluate D for x 5 Solution First enter D using the Equation Writer 3 X 1 2 81 Press to select and to expand the expression This gives 3 12 6 3 3 12 6 3 C 4 5 D 3x 1 2 81 3x 10 3x 8 0 3X 1 2 9x 2 6x 1 81 hp40g book Page 4 Friday December 9 2005 1 03 ...

Page 279: ... expression and then to obtain the intermediate result shown Press once more to yield the result Therefore when Example 4 A baker produces two assortments of biscuits and macaroons A packet of the first assortment contains 17 biscuits and 20 macaroons A packet of the second assortment contains 10 biscuits and 25 macaroons Both packets cost 90 cents Calculate the price of one biscuit and the price ...

Page 280: ...s again to produce the reduction result Pressing again produces the final result If you select and press you get X 2 and Y 2 8 In other words the price of one biscuit is 2 cents and the price of one macaroon is 2 8 cents Exercise 5 Suppose that A and B are points having the coordinates 1 3 and 3 1 respectively and where the unit of measure is the centimetre 17x 20y 90 10x 25y 90 14 5 hp40g book Pa...

Page 281: ...ssary Note that pressing returns the coordinates in complex form 1 3i Now type STORE 3 1 B and press The coordinates this time are represented as 3 1 i The vector AB has coordinates B A Type B A Press The result is Now apply the DROITE command to determine the equation of the line AB Complex DROITE A B Pressing gives an intermediate result 2 5 hp40g book Page 7 Friday December 9 2005 1 03 AM ...

Page 282: ...3 3 1 Pressing then gives the result obtained before Y 2X 5 Exercise 6 In this exercise we consider some examples of integer arithmetic Part 1 For n a strictly positive integer we define 1 Compute a1 b1 c1 a2 b2 c2 a3 b3 and c3 2 Determine how many digits the decimal representations of an and cn can have Show that an and cn are divisible by 3 3 Using a list of prime numbers less than 100 show that...

Page 283: ...select the DEF command by pressing Now press A N 4 10 N 1 Finally press Do likewise to define the other two expressions You can now calculate various values of A N B N and C N simply by typing the defined variable and a value for N and then pressing For example A 1 yields 39 A 2 yields 399 A 3 yields 3999 B 1 yields 19 B 2 yields 199 B 3 yields 1999 and so on In determining the number of digits th...

Page 284: ...om from CAS FUNCTIONS menu while you are in the Equation Writer by pressing choosing the INTEGER menu and scrolling to the ISPRIME function To prove that is a prime number it is necessary to show that 1999 is not divisible by any of the prime numbers less than or equal to As that means testing the divisibility of 1999 by n 2 3 5 7 11 13 17 19 23 29 31 37 41 1999 is not divisible by any of these nu...

Page 285: ...actors are listed separated by a medial period In this case the factors are 3 23 29 and 1999 Now let s consider whether bn and cn are relatively prime Here the calculator is useful only for trying out different values of n To show that bn and cn are relatively prime it is enough to note that That means that the common divisors of bn and cn are the common divisors of bn and 2 as well as the common ...

Page 286: ...n effect Bézout s Theorem states that if a and b are relatively prime there exists an x and y such that Therefore the equation has at least one solution Now enter IEGCD B 3 C 3 Note that the IEGCD function can be found on the INTEGER submenu of the MATH menu Pressing a number of times returns the result shown at the right In other words Therefore we have a particular solution x 1000 y 999 The rest...

Page 287: ... for This gives us The general solution for all is therefore Exercise 7 Let m be a point on the circle C of center O and radius 1 Consider the image M of m defined on their affixes by the transformation When m moves on b3 999 c3 b3 1 b3 1000 c3 999 1 b3 x c3 y 1 b3 1000 c3 999 1 b3 x 1000 c3 y 999 0 b3 x 1000 c3 y 999 c3 b3 c3 x 1000 k Z x 1000 k c3 y 999 k b3 x 1000 k c3 y 999 k b3 k Z b3 x c3 y ...

Page 288: ... the tangent to Γ at these points Part 1 First go to CAS MODES screen and make t the VX variable To do this press to open the Equation Writer and then press This opens CAS MODES screen Press and delete the current variable Type T and press Now enter the expression and press to select it Now invoke the SUBST command from the menu Because the expression was highlighted the SUBST command is automatic...

Page 289: ...he result in variable M Note that STORE is on the menu To calculate the real part of the expression apply the RE command available on the COMPLEX submenu of the MATH menu Pressing yields the result at the right We are now going to define this result as x t To do this enter X t highlight the X t by pressing and press to swap the two parts of the expression as shown at the right Now select the entir...

Page 290: ... result as Y t in the same way that you defined X t by firstly adding Y t to the expression as shown at the right and then applying the DEF command We have now found the coordinates of M in terms of t Part 2 To find an axis of symmetry for Γ calculate and by typing X t Press to highlight the expression Then press to produce the result at the right In other words Now type Y t Press to highlight the...

Page 291: ...ess to highlight the expression Pressing returns the result at the right Press to simplify the result You can now define the function by invoking DEF Note You will first need to type X1 t then exchange X1 t with the previous expression To do this highlight X1 t and type Now select the entire expression and apply the DEF command to it Finally press to finish the definition y t y t M1 x t y t Γ Mx x...

Page 292: ...pendent variable must be t which it should be as a result of the previous calculations You can check this by pressing Type X t in the Equation Writer and press The corresponding expression is displayed Now press select Function press select F1 as the destination and press Now do the same thing with Y t making F2 the destination To graph the functions quit CAS by pressing choose the Function aplet ...

Page 293: ...plification For example pressing X 0 gives the result at the right Likewise pressing X 3 gives this answer at the right The other results are The slope of the tangents is We can find the values of for by using the lim command x t y t t 0 π 3 2 π 3 π π X 2π 3 1 4 X π 3 2 Y 0 0 Y π 3 3 4 Y 2π 3 3 3 4 Y π 0 m y t x t y t x t t 0 π 3 2 π 3 π hp40g book Page 19 Friday December 9 2005 1 03 AM ...

Page 294: ... pressing displays the message shown at the right Accept YES and press Press again to get the result The next example is for t 2π 3 Selecting the entire expression and pressing displays the result 0 The final example is for the case where t π Press accept YES to the message UNSIGNED INF SOLVE press and press to get the result Here then are the variations of and x t y t hp40g book Page 20 Friday De...

Page 295: ...ssion and press Now press select Parametric and press Select X1 Y1 as the destination and press To make the graph of Γ quit CAS and choose the Parametric aplet Check X1 T and Y1 T Now press to see the graph t 0 π 0 0 0 0 0 0 1 0 2 m 0 0 π 3 2π 3 x t 3 x t 1 2 3 4 1 4 3 2 y t 3 4 3 3 4 y t hp40g book Page 21 Friday December 9 2005 1 03 AM ...

Page 296: ... 0 2 where 1 Find the variations of g over 0 2 Show that for every real x in 0 2 2 Show that for every real x in 0 2 3 After integration show that 4 Using show that if has a limit L as n approaches infinity then un 2x 3 x 2 e x n x d 0 2 g x 2x 3 x 2 3 2 g x 7 4 3 2 e x n g x e x n 7 4 e x n 3 2 ne 2 n n un 7 4 ne 2 n n e x 1 x x 0 lim 1 un 3 L 7 2 hp40g book Page 22 Friday December 9 2005 1 03 AM...

Page 297: ...mber of times until the variation table appears shown above The first line of the variation table gives the sign of according to x and the second line the variations of g x Note that for TABVAR the function is always called F We can deduce then that g x increases over 0 2 If you had been in step by step mode you would have obtained Press to get the result at the right g x F 2 X 3 X 2 hp40g book Pa...

Page 298: ...e g 0 by typing G 0 and pressing The answer is Now calculate g 2 by typing G 2 and pressing The answer is The two results prove that for Solution 2 The calculator is not needed here Simply stating that for is sufficient to show that for we have Solution 3 To integrate the preceding inequality type the expression at the right Pressing produces the result at the right 1 x 2 2 3 2 7 4 3 2 g x 7 4 x 0...

Page 299: ...ssing twice is shown at the right Solution 4 To find the limit of when enter the expression at the right Note that the lim command is on the menu The infinity sign can be selected from the character map opened by pressing Pressing once after selecting the infinity sign adds a character to the infinity sign Select the entire expression ans press to get the result which is 2 3 2 ne 2 n n un 7 4 ne 2...

Page 300: ...f the limit of exists as approaches in the inequalities in solution 2 above we get Part 2 1 Show that for every x in 0 2 2 Find the value of 3 Show that for every x in 0 2 4 Deduce that 5 Show that is convergent and find its limit L e x 1 x x 0 lim 1 e 2 n 1 2 n n lim 1 e 2 n 1 n n lim 2 L un n 3 2 2 L 7 4 2 2x 3 x 2 2 1 x 2 I 2x 3 x 2 dx 0 2 1 e x n e 2 n 1 un e 2 n I un hp40g book Page 26 Friday...

Page 301: ...lds the result shown at the right Solution 2 Enter the integral Pressing yields the result shown at the right Pressing again yields Working by hand so Then integrating term by term between 0 and 2 produces that is since g x 2 1 x 2 I g x x d 0 2 2x 3 2 x 2 1 g x 2 1 x 2 g x x 2x x 2 ln d 0 2 x 2 x 0 4 2 2 ln ln g x x 4 2 ln d 0 2 hp40g book Page 27 Friday December 9 2005 1 03 AM ...

Page 302: ...selected the infinity sign from the character map places a character in front of the infinity sign Selecting the entire expression and pressing yields 1 In effect tends to 0 as tends to so tends to as tends to As tends to is the portion between and a quantity that tends to Hence converges and its limit is We have therefore shown that e x n x 0 2 1 e x n e 2 n g x g x g x e x n g x e 2 n I un e 2 n...

Page 303: ...Step by Step Examples 16 29 hp40g book Page 29 Friday December 9 2005 1 03 AM ...

Page 304: ...hp40g book Page 30 Friday December 9 2005 1 03 AM ...

Page 305: ...s of calculations These variables are available within all aplets and within any programs Aplet variables apply only to a single aplet Aplets have specific variables allocated to them which vary from aplet to aplet You use the calculator s memory to store the following objects copies of aplets with specific configurations new aplets that you download aplet variables home variables variables create...

Page 306: ...n displayed not the full internal precision On the other hand the variable Ans always contains the most recent result to full precision To store a value 1 On the command line enter the value or the calculation for the result you wish to store 2 Press 3 Enter a name for the variable 4 Press To store the results of a calculation If the value you want to store is in the HOME view display history for ...

Page 307: ...ble and press A To use variables in calculations You can use variables in calculations The calculator substitutes the variable s value in the calculation 65 A To clear a variable You can use the CLRVAR command to clear a specified variable For example if you have stored 1 2 3 4 in variable L1 entering CLRVAR L1 will clear L1 You can find the CLRVAR command by pressing and choosing the PROMPT categ...

Page 308: ... and then select a variable in the category 1 Open the VARS menu 2 Use the arrow keys or press the alpha key of the first letter in the category to select a variable category For example to select the Matrix category press Note In this instance there is no need to press the ALPHA key 3 Move the highlight to the variables column 4 Use the arrow keys to select the variable that you want For example ...

Page 309: ...alue or name on the command line The selected object appears on the command line Note The VARS menu can also be used to enter the names or values of variables into programs Example This example demonstrates how to use the VARS menu to add the contents of two list variables and to store the result in another list variable 1 Display the List Catalog LIST to select L1 2 Enter the data for L1 88 90 89...

Page 310: ...nd line Note Because the option is highlighted the variable s name rather than its contents is copied to the command line 8 Insert the operator and select the L2 variable from the List variables 9 Store the answer in the List catalog L3 variable L3 Note You can also type list names directly from the keyboard hp40g book Page 6 Friday December 9 2005 1 03 AM ...

Page 311: ...on page 21 21 for more information on storing graphic objects via programming commands See To store into a graphics variable on page 20 5 for more information on storing graphic object via the sketch view Library Aplet library variables can store aplets that you have created either by saving a copy of a standard aplet or downloading an aplet from another source List L0 to L9 For example 1 2 3 L1 M...

Page 312: ...ss to access the variables in the right column 4 Use the arrow keys to select a variable in the right column 5 To copy the name of the variable onto the edit line press is the default setting 6 To copy the value of the variable into the edit line press and press Category Available names Function F0 to F9 Symbolic view See Function aplet variables on page R 7 Parametric X0 Y0 to X9 Y9 Symbolic view...

Page 313: ... up memory Example 1 Start the Memory Manager A list of variable categories is displayed MEMORY Free memory is displayed in the top right corner and the body of the screen lists each category the memory it uses and the percentage of the total memory it uses 2 Select the category with which you want to work and press Memory Manager displays memory details of variables within the category 3 To delet...

Page 314: ...hp40g book Page 10 Friday December 9 2005 1 03 AM ...

Page 315: ...e composed of just one row A vector is represented with single brackets for example 1 2 3 A vector can be a real number vector or a complex number vector for example 1 2 7 3 Matrices Matrices are two dimensional arrays They are composed of more than one row and more than one column Two dimensional matrices are represented with nested brackets for example 1 2 3 4 5 6 You can create complex matrices...

Page 316: ...s in the Matrix Catalog as well as the use of Delete and Clear CLEAR To create a matrix in the Matrix Catalog 1 Press MATRIX to open the Matrix Catalog The Matrix catalog lists the 10 available matrix variables M0 to M9 x 3 x 0 Key Meaning Opens the highlighted matrix for editing Prompts for a matrix type then opens an empty matrix with the highlighted name Transmits the highlighted matrix to anot...

Page 317: ... part and b is the imaginary part You must include the parentheses and the comma 5 Use the cursor keys to move to a different row or column You can change the direction of the highlight bar by pressing The menu key toggles between the following three options specifies that the cursor moves to the cell below the current cell when you press specifies that the cursor moves to the cell to the right of...

Page 318: ...t a matrix In the Matrix catalog highlight the name of the matrix you want to edit and press Matrix edit keys The following table lists the matrix edit key operations Key Meaning Copies the highlighted element to the edit line Inserts a row of zeros above or a column of zeros to the left of the highlighted cell You are prompted to choose row or column A three way toggle for cursor advancement in t...

Page 319: ...ix and each row with square brackets the shifted and keys 2 Separate each element and each row with a comma Example 1 2 3 4 3 Press to enter and display the matrix The left screen below shows the matrix 2 5 729 16 2 being stored into M5 The screen on the right shows the vector 66 33 11 being stored into M6 Note that you can enter an expression like 5 2 for an element of the matrix and it will be e...

Page 320: ...essage Matrix arithmetic You can use the arithmetic functions and powers with matrix arguments Division left multiplies by the inverse of the divisor You can enter the matrices themselves or enter the names of stored matrix variables The matrices can be real or complex For the next examples store 1 2 3 4 into M1 and 5 6 7 8 into M2 Example 1 Create the first matrix MATRIX 1 2 3 4 2 Create the seco...

Page 321: ... keys M1 M 2 To multiply a matrix by a vector enter the matrix first then the vector The number of elements in the vector must equal the number of columns in the matrix To raise a matrix to a power You can raise a matrix to any power as long as the power is an integer The following example shows the result of raising matrix M1 created earlier to the power of 5 M1 5 Note You can also raise a matrix...

Page 322: ...ous example press the following keys M1 M2 To invert a matrix You can invert a square matrix in HOME by typing the matrix or its variable name and pressing x 1 Or you can use the matrix INVERSE command Enter INVERSE matrixname in HOME and press To negate each element You can change the sign of each element in a matrix by pressing before the matrix name Solving systems of linear equations Example S...

Page 323: ...2 3 4 1 1 1 4 1 2 In this example the matrix you created is listed as M2 6 Return to HOME and enter the calculation to left multiply the constants vector by the inverse of the coefficients matrix M2 x 1 M1 The result is a vector of the solutions x 2 y 3 and z 2 An alternative method is to use the RREF function See RREF on page 18 12 hp40g book Page 9 Friday December 9 2005 1 03 AM ...

Page 324: ...rackets For example CROSS M1 1 2 About commands Matrix commands are listed in the CMDS menu CMDS in the matrix category See Matrix commands on page 21 24 for details of the matrix commands available for use in programming Functions differ from commands in that a function can be used in an expression Commands cannot be used in an expression Argument conventions For row or column supply the number o...

Page 325: ...rix Displays a list of two arrays The first contains the eigenvectors and the second contains the eigenvalues EIGENVV matrix IDENMAT Identity matrix Creates a square matrix of dimension size size whose diagonal elements are 1 and off diagonal elements are zero IDENMAT size INVERSE Inverts a square matrix real or complex INVERSE matrix LQ LQ Factorization Factors an m n matrix into three matrices m...

Page 326: ...0 QR QR Factorization Factors an m n matrix into three matrices m m orthogonal m n uppertrapezoidal n n permutation QR matrix RANK Rank of a rectangular matrix RANK matrix ROWNORM Row Norm Finds the maximum value over all rows for the sums of the absolute values of all elements in a row ROWNORM matrix RREF Reduced Row Echelon Form Changes a rectangular matrix to its reduced row echelon form RREF m...

Page 327: ...es matrix For a complex matrix TRN finds the conjugate transpose TRN matrix Examples Identity Matrix You can create an identity matrix with the IDENMAT function For example IDENMAT 2 creates the 2 2 identity matrix 1 0 0 1 You can also create an identity matrix using the MAKEMAT make matrix function For example entering MAKEMAT I J 4 4 creates a 4 4 matrix showing the numeral 1 for all elements ex...

Page 328: ... this to reduced row echelon form storing it in any matrix variable M2 is used in this example The reduced row echelon matrix gives the solution to the linear equation in the fourth column An advantage of using the RREF function is that it will also work with inconsistent matrices resulting from systems of equations which have no solution or infinite solutions For example the following set of equa...

Page 329: ...Matrices 18 15 The final row of zeros in the reduced row echelon form of the augmented matrix indicates an inconsistent system with infinite solutions hp40g book Page 15 Friday December 9 2005 1 03 AM ...

Page 330: ...hp40g book Page 16 Friday December 9 2005 1 03 AM ...

Page 331: ... Retrieve the list names from the VARS menu or just type their names from the keyboard You can create edit delete send and receive named lists in the List catalog LIST You can also create and store lists named or unnnamed in HOME lists List variables are identical in behaviour to the columns C1 C0 in the Statistics aplet You can store a statistics column to a list or vice versa and use any of the ...

Page 332: ...ist catalog keys The list catalog keys are Key Meaning Opens the highlighted list for editing Transmits the highlighted list to another HP 40gs or a PC See Sending and receiving aplets on page 22 4 for further information Receives a list from another HP 40gs or a PC See Sending and receiving aplets on page 22 4 for further information Clears the highlighted list CLEAR Clears all lists or Moves to ...

Page 333: ...y after typing in the list you can store it in a variable by pressing listname The list variable names are L0 through L9 This example stores the list 25 147 8 in L1 Note You can omit the final brace when entering a list Key Meaning Copies the highlighted list item into the edit line Inserts a new value before the highlighted item Deletes the highlighted item from the list CLEAR Clears all elements...

Page 334: ...listname element For example if L2 is 3 4 5 6 then L2 2 returns 4 To edit a list 1 Open the List catalog LIST 2 Press or to highlight the name of the list you want to edit L1 etc and press to display the list contents 3 Press or to highlight the element you want to edit In this example edit the third element so that it has a value of 5 5 4 Press hp40g book Page 4 Friday December 9 2005 1 03 AM ...

Page 335: ... are inserted above the highlighted position In this example an element with the value of 9 is inserted between the first and second elements in the list 3 Press to the insertion position then press and press 9 4 Press To store one element In HOME enter value listname element For example to store 148 as the second element in L1 type 148 L1 2 hp40g book Page 5 Friday December 9 2005 1 03 AM ...

Page 336: ...culator and choose the method of receiving For more information on sending and receiving files see Sending and receiving aplets on page 22 4 List functions List functions are found in the MATH menu You can use them in HOME as well as in programs You can type in the name of the function or you can copy the name of the function from the List category of the MATH menu Press the alpha L character key ...

Page 337: ...ist Example 5 1 2 3 returns 5 10 15 Besides the common operators that can take numbers matrices or lists as arguments there are commands that can only operate on lists CONCAT Concatenates two lists into a new list CONCAT list1 list2 Example CONCAT 1 2 3 4 returns 1 2 3 4 ΔLIST Creates a new list composed of the first differences that is the differences between the sequential elements in list1 The ...

Page 338: ...lect MAKELIST A A 23 27 1 ΠLIST Calculates the product of all elements in list ΠLIST list Example ΠLIST 2 3 4 returns 24 POS Returns the position of an element within a list The element can be a value a variable or an expression If there is more than one instance of the element the position of the first occurrence is returned A value of 0 is returned if there is no occurrence of the specified elem...

Page 339: ...o find values such as the mean median maximum and minimum values of the elements in a list use the Statistics aplet Example In this example use the Statistics aplet to find the mean median maximum and minimum values of the elements in the list L1 1 Create L1 with values 88 90 89 65 70 and 89 88 90 89 65 70 89 L1 2 In HOME store L1 into C1 You will then be able to see the list data in the Numeric v...

Page 340: ...atistics Note Your list values are now in column 1 C1 4 In the Symbolic view define H1 for example as C1 sample and 1 frequency 5 Go to the Numeric view to display calculated statistics See One variable on page 10 14 for the meaning of each computed statistic hp40g book Page 10 Friday December 9 2005 1 03 AM ...

Page 341: ... also be sent to another calculator via the Notepad Catalog Aplet note view You can attach text to an aplet in its Note view To write a note in Note view 1 In an aplet press NOTE for the Note view 2 Use the note editing keys shown in the table in the following section 3 Set Alpha lock for quick entry of letters For lowercase Alpha lock press 4 While Alpha lock is on To type a single letter of the ...

Page 342: ...tes character Deletes current character Starts a new line CLEAR Erases the entire note Menu for entering variable names and contents of variables Menu for entering math operations and constants CMDS Menu for entering program commands CHARS Displays special characters To type one highlight it and press To copy a character without closing the CHARS screen press hp40g book Page 2 Friday December 9 20...

Page 343: ...r in any direction to the end point of the line by pressing the keys 5 Press to finish the line Key Meaning Stores the specified portion of the current sketch to a graphics variable G1 through G0 Adds a new blank page to the current sketch set Displays next sketch in the sketch set Animates if held down Opens the edit line to type a text label Displays the menu key labels for drawing Deletes the c...

Page 344: ...sor the distance of the radius 4 Press to draw the circle DRAW keys Key Meaning Dot on Turns pixels on as the cursor moves Dot off Turns pixels off as the cursor moves Draws a line from the cursor s starting position to the cursor s current position Press when you have finished You can draw a line at any angle Draws a box from the cursor s starting position to the cursor s current position Press w...

Page 345: ...This allows for simple animation After making a sketch press to add a new blank page You can now make a new sketch which becomes part of the current set of sketches To view the next sketch in an existing set press Hold down for animation To remove the current page in the current sketch series press To store into a graphics variable You can define a portion of a sketch inside a box and then store t...

Page 346: ...the box to where you would like to copy the graphic then press The notepad Subject to available memory you can store as many notes as you want in the Notepad NOTEPAD These notes are independent of any aplet The Notepad catalog lists the existing entries by name It does not include notes that were created in aplets Note views but these can be imported See To import a note on page 20 8 To create a n...

Page 347: ...exit Notepad Your work is automatically saved Notepad Catalog keys Key Meaning Opens the selected note for editing Begins a new note and asks for a name Transmits the selected note to another HP 40gs or PC Receives a note being transmitted from another HP 40gs or PC Deletes the selected note CLEAR Deletes all notes in the catalog hp40g book Page 7 Friday December 9 2005 1 03 AM ...

Page 348: ...ssignments in the right column 3 Press to copy the contents of Assignments to the Function Note view Note To recall the name instead of the contents press instead of Suppose you want to copy the Note view from the current aplet into the note Assignments in the Notepad 1 In the Notepad NOTEPAD open the note Assignments 2 Press highlight Note in the left column then press and highlight NoteText in t...

Page 349: ...equence of numbers mathematical expressions and commands that execute automatically to perform a task These items are separated by a colon Commands that take multiple arguments have those arguments separated by a semicolon For example PIXON xposition yposition Structured Programming Inside a program you can use branching structures to control the execution flow You can take advantage of structured...

Page 350: ...am stop a program copy a program send and receive a program delete a program or its contents customize an aplet Open Program Catalog 1 Press PROGRM The Program Catalog displays a list of program names The Program Catalog contains a built in entry called Editline Editline contains the last expression that you entered from the edit line in HOME or the last data you entered in an input form If you pr...

Page 351: ...y program Transmits the highlighted program to another HP 40gs or to a disk drive Receives the highlighted program from another HP 40gs or from a disk drive Runs the highlighted program or Moves to the beginning or end of the Program catalog Deletes the highlighted program CLEAR Deletes all programs in the program catalog hp40g book Page 3 Friday December 9 2005 1 03 AM ...

Page 352: ...Don t use the symbol within your program name 3 Type your program name then press When you press the Program Editor opens 4 Enter your program When done start any other activity Your work is saved automatically Entercommands Until you become familiar with the HP 40gs commands the easiest way to enter commands is to select them from the Commands menu from the Program editor You can also type in com...

Page 353: ... the command into the program editor Edit a program 1 Press PROGRM to open the Program catalog 2 Use the arrow keys to highlight the program you want to edit and press The HP 40gs opens the Program Editor The name of your program appears in the title bar of the display You can use the following keys to edit your program hp40g book Page 5 Friday December 9 2005 1 03 AM ...

Page 354: ...Press A Z to lock lower case Backspaces cursor and deletes character Deletes current character Starts a new line CLEAR Erases the entire program Displays menus for selecting variable names contents of variables math functions and program constants CMDS Displays menus for selecting program conmmands CHARS Displays all characters To type one highlight it and press To enter several characters in a ro...

Page 355: ...you start the program from the Program catalog the HP 40gs returns you to the Program catalog when the program ends Debug a program If you run a program that contains errors the program will stop and you will see an error message To debug the program 1 Press to edit the program The insert cursor appears in the program at the point where the error occurred 2 Edit the program to fix the error 3 Run ...

Page 356: ...gramming routine often save the routine under a different program name then use the above method to copy it into your programs Transmit a program You can send programs to and receive programs from other calculators just as you can send and receive aplets matrices lists and notes After connecting the calculators with an appropriate cable open the Program catalogs on both calculators Highlight the p...

Page 357: ...e SETVIEWS command to create a custom VIEWS menu which links specially written programs to the new aplet A useful method for customizing an aplet is illustrated below 1 Decide on the built in aplet that you want to customize For example you could customize the Function aplet or the Statistics aplet The customized aplet inherits all the properties of the built in aplet Save the customized aplet wit...

Page 358: ...wing naming convention when setting up an aplet s programs Start all program names with an abbreviation of the aplet name We will use APL in this example Name programs called by menu entries in the VIEWS menu number after the entry for example APL ME1 for the program called by menu option 1 APL ME2 for the program called by menu option 2 Name the program that configures the new VIEWS menu option A...

Page 359: ...ons for the aplet and runs the program that you can use to configure the angle mode 4 Create a program called EXP ANG which the previous two programs call 5 Create a program called EXP S which runs when you start the aplet as shown This program sets the angle mode to degrees and sets up the initial function that the aplet plots Configuring the Setviews menu option programs In this section we will ...

Page 360: ...is to be included in the new menu The empty quotes will ensure that the old name of Auto scale appears on the new menu See SETVIEWS on page 21 14 My Entry1 EXP ME1 1 Sets the second menu option This option runs program EXP ME1 then returns to view 1 Plot view My Entry2 EXP ME2 3 Sets the third menu option This option runs the program EXP ME2 then returns to view 3 the NUM view EXP SV 0 This line s...

Page 361: ...WS menu is configured it remains that way until you run SETVIEWS again You do not need to include this program for your aplet to work but it is useful to specify that the program is attached to the aplet and transmitted when the aplet is transmitted 7 Return to the program catalog The programs that you created should appear as follows 8 You must now the program EXP SV to execute the SETVIEWS comma...

Page 362: ...VIEWS menu changes remain unless you apply the command again Typically you develop a program that uses the SETVIEWS command only The command contains a trio of arguments for each menu option to create or program to attach Keep the following points in mind when using this command The SETVIEWS command deletes an aplet s standard Views menu options If you want to use any of the standard options on yo...

Page 363: ...orresponding entry in the Views menu Enclose the prompt text in double quotes Associating programs with your aplet If Prompt consists of a single space then no entry appears in the view menu The program specified in the ProgramName item is associated with the aplet and transferred whenever the aplet is transmitted Typically you do this if you want to transfer the Setviews program with the aplet or...

Page 364: ...n aplet s standard VIEWS menu options in your customized menu set up the arguments trio as follows The first argument specifies the menu item name Leave the argument empty to use the standard Views menu name for the item or Enter a menu item name to replace the standard name The second argument specifies the program to run Leave the argument empty to run the standard menu option Insert a program n...

Page 365: ...gram make a decision based on the result of one or more tests Unlike the other programming commands the branch commands work in logical groups Therefore the commands are described together rather than each independently IF THEN END Executes a sequence of commands in the true clause only if the test clause evaluates to true Its syntax is IF test clause THEN true clause END 0 1 2 3 4 5 6 7 8 9 10 HO...

Page 366: ...ence of commands Its syntax is CASE IF test clause1 THEN true clause1 END IF test clause2 THEN true clause2 END IF test clausen THEN true clausen END END When CASE is executed test clause1 is evaluated If the test is true true clause1 is executed and execution skips to END If test clause1 if false execution proceeds to test clause2 Execution with the CASE structure continues until a true clause is...

Page 367: ... file name in double quotes RUN program name or RUN programname STOP Stops the current program STOP Drawing commands The drawing commands act on the display The scale of the display depends on the current aplet s Xmin Xmax Ymin and Ymax values The following examples assume the HP 40gs default settings with the Function aplet as the current aplet ARC Draws a circular arc of given radius whose centr...

Page 368: ...display ERASE FREEZE Halts the program freezing the current display Execution resumes when any key is pressed LINE Draws a line from x1 y1 to x2 y2 LINE x1 y1 x2 y2 PIXOFF Turns off the pixel at the specified coordinates x y PIXOFF x y PIXON Turns on the pixel at the specified coordinates x y PIXON x y TLINE Toggles the pixels along the line from x1 y1 to x2 y2 on and off Any pixel that was turned...

Page 369: ... display in graphicname DISPLAY graphicname DISPLAY Displays graphic from graphicname in the display DISPLAY graphicname GROB Creates a graphic from expression using font_size and stores the resulting graphic in graphicname Font sizes are 1 2 or 3 If the fontsize argument is 0 the HP 40gs creates a graphic display like that created by the SHOW operation GROB graphicname expression fontsize GROBNOT...

Page 370: ...EZE This program stores the current PLOT view to the first page in the sketch view of the current aplet and then displays the sketch as a graphic object until any key is pressed PLOT Puts graph from graphicname into the Plot view display PLOT graphicname REPLACE Replaces portion of graphic in graphicname1 with graphicname2 starting at position REPLACE also works for lists and matrices REPLACE grap...

Page 371: ...lause END 1 X A DO A 1 X A DISP 3 A UNTIL A 12 END WHILE REPEAT END While Repeat End is a loop command that repeatedly evaluates test clause and executes loop clause sequence if the test is true Because the test clause is executed before the loop clause the loop clause is not executed if the test is initially false Its syntax is WHILE test clause REPEAT loop clause END 1 X A WHILE A 12 REPEAT A 1 ...

Page 372: ...rix name ADDROW name value1 valuen row_number DELCOL Delete Column Deletes the specified column from the specified matrix DELCOL name column_number DELROW Delete Row Deletes the specified row from the specified matrix DELROW name row_number EDITMAT Starts the Matrix Editor and displays the specified matrix If used in programming returns to the program when user presses EDITMAT name RANDMAT Creates...

Page 373: ... SUB Extracts a sub object a portion of a list matrix or graphic from object and stores it into name start and end are each specified using a list with two numbers for a matrix a number for vector or lists or an ordered pair X Y for graphics SUB name object start end SWAPCOL Swaps Columns Exchanges column1 and column2 of the specified matrix SWAPCOL name column1 column2 SWAPROW Swap Rows Exchanges...

Page 374: ...ult of the choose command is to store the number of the option chosen in a variable The syntax is CHOOSE variable_name title option1 option2 optionn where variable_name is the name of a variable for storing a default option number title is the text displayed in the title bar of the choose box and option1 optionn are the options listed in the choose box By pre storing a value into variable_name you...

Page 375: ...on line 3 DISPXY Displays object at position x_pos y_pos in size font The syntax is DISPXY x_pos y_pos font object The value of object can be a text string a variable or a combination of both x_pos and y_pos are relative to the current settings of Xmin Xmax Ymin and Ymax which you set in the PLOT SETUP view The value of font is either 1 small or 2 large Example DISPXY 3 5 1 5 2 HELLO WORLD DISPTIM...

Page 376: ...ws you to view the graphics created by the program Cancel FREEZE by pressing any key FREEZE GETKEY Waits for a key then stores the keycode rc p in name where r is row number c is column number and p is key plane number The key planes numbers are 1 for unshifted 2 for shifted 4 for alpha shifted and 5 for both alpha shifted and shifted GETKEY name INPUT Creates an input form with a title bar and on...

Page 377: ...variable to provide text arguments This can be used to insert line breaks For example press NOTE and type AREA IS The position line MSGBOX NoteText π A 2 will display the same message box as the previous example PROMPT Displays an input box with name as the title and prompts for a value for name name can be a variable such as A Z θ L1 L9 C1 C9 or Z1 Z9 PROMPT name WAIT Halts program execution for ...

Page 378: ...SAMPLE Sets datasetname sample according to column Datasetname can be H1 H5 and column can be CO C9 SETSAMPLE datasetname column Stat Two commands DO2VSTATS Calculates STATS using datasetname and stores the results in corresponding variables MeanX ΣX ΣX2 MeanY ΣY ΣY2 ΣXY Corr PCov SCov and RELERR Datasetname can be SI S2 or S5 Datasetname must include at least two pairs of data points DO2VSTATS da...

Page 379: ...iables are available in every aplet S1fit S5fit for example are only available in the Statistics aplet Under each variable name is a list of the aplets where the variable can be used Plot view variables Area Function Contains the last value found by the Area function in Plot FCN menu Axes All Aplets Turns axes on or off From Plot Setup check or uncheck AXES or In a program type 1 X Axes to turn ax...

Page 380: ...ution between plotting in every other column faster or plotting in every column more detail From Plot Setup choose Faster or More Detail or In a program type 1 X FastRes for faster 0 X FastRes for more detail default Grid All Aplets Turns the background grid in Plot view on or off From Plot setup check or uncheck GRID or In a program type 1 X Grid to turn the grid on 0 X Grid to turn the grid off ...

Page 381: ...osshairs Inverted is useful if the background is solid From Plot Setup check or uncheck InvCross or In a program type 1 X InvCross to invert the crosshairs 0 X InvCross for solid crosshairs default Isect Function Contains the last value found by the Intersection function in the Plot FCN menu Labels All Aplets Draws labels in Plot view showing X and Y ranges From Plot Setup check or uncheck Labels ...

Page 382: ...ter on default 0 X Recenter to turn recenter off Root Function Contains the last value found by the Root function in the Plot FCN menu S1mark S5mark Statistics Sets the mark to use for scatter plots From Plot Setup for two variable statistics S1mark S5mark then choose a mark or In a program type n X S1mark where n is 1 2 3 5 SeqPlot Sequence Enables you to choose types of sequence plot Stairstep o...

Page 383: ...variable statistics plot between Histogram or Box and Whisker From Plot Setup select StatPlot then choose Histogram or BoxWhisker or In a program type 1 X StatPlot for Histogram 2 X StatPlot for Box and Whisker Umin Umax Polar Sets the minimum and maximum independent values Appears as the URNG field in the Plot Setup input form From the Plot Setup input form enter values for URNG or In a program t...

Page 384: ...turn Tracing mode on default 0 X Tracing to turn Tracing mode off Tstep Parametric Sets the step size for the independent variable From the Plot Setup input form enter values for TSTEP or In a program type n X Tstep where Xcross All Aplets Sets the horizontal coordinate of the crosshairs Only works with TRACE off In a program type n X Xcross Ycross All Aplets Sets the vertical coordinate of the cr...

Page 385: ...Xmin Xmax All Aplets Sets the minimum and maximum horizontal values of the plot screen Appears as the XRNG fields horizontal range in the Plot Setup input form From Plot Setup enter values for XRNG or In a program type X Xmin X Xmax where Ymin Ymax All Aplets Sets the minimum and maximum vertical values of the plot screen Appears as the YRNG fields vertical range in the Plot Setup input form From ...

Page 386: ...fault value is 4 Symbolic view variables Angle All Aplets Sets the angle mode From Symbolic Setup choose Degrees Radians or Grads for angle measure or In a program type 1 X Angle for Degrees 2 X Angle for Radians 3 X Angle for Grads F1 F9 F0 Function Can contain any expression Independent variable is X Example SIN X X F1 X You must put single quotes around an expression to keep it from being evalu...

Page 387: ...ve Can contain any equation or expression Independent variable is selected by highlighting it in Numeric View Example X Y X 2 Y X E1 S1fit S5fit Statistics Sets the type of fit to be used by the FIT operation in drawing the regression line From Symbolic Setup view specify the fit in the field for S1FIT S2FIT etc or In a program store one of the following constant numbers or names into a variable S...

Page 388: ...ces to use for Number format in the HOME view and for labeling axes in the Plot view From the Modes view enter a value in the second field of Number Format or In a program type n X Digits where Format All Aplets Defines the number display format to use for numeric format on the HOME view and for labeling axes in the Plot view From the Modes view choose Standard Fixed Scientific Engineering Fractio...

Page 389: ...e 0 1 2 3 4 5 6 7 8 9 NumFont Function Parametric Polar Sequence Statistics Enables you to choose the font size in Numeric view Does not appear in the Num Setup input form Corresponds to the key in Numeric view In a program type 0 X NumFont for small default 1 X NumFont for big NumIndep Function Parametric Polar Sequence Specifies the list of independent values to be used by Build Your Own Table I...

Page 390: ... From Num Setup choose Automatic or Build Your Own or In a program type 0 X NumType for Build Your Own 1 X NumType for Automatic default NumZoom Function Parametric Polar Sequence Sets the zoom factor in the Numeric view From Num Setup type in a value for NUMZOOM or In a program type n X NumZoom where StatMode Statistics Enables you to choose between 1 variable and 2 variable statistics in the Sta...

Page 391: ...ailable in Sketch view Page All Aplets Sets a page in a sketch set The graphics can be viewed one at a time using the and keys The Page variable refers to the currently displayed page of a sketch set In a program type graphicname X Page PageNum All Aplets Sets a number for referring to a particular page of the sketch set in Sketch view In a program type the page that is shown when SKETCH is presse...

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Page 393: ...g for further details Creating new aplets based on existing aplets You can create a new aplet based on an existing aplet To create a new aplet save an existing aplet under a new name then modify the aplet to add the configurations and the functionality that you want Information that defines an aplet is saved automatically as it is entered into the calculator To keep as much memory available for st...

Page 394: ... four formulas θ O H θ A H θ O A A B C 3 Decide whether you want the aplet to operate in Degrees Radians or Grads MODES Degrees 4 View the Aplet Library The TRIANGLES aplet is listed in the Aplet Library The Solve aplet can now be reset and used for other problems hp40g book Page 2 Friday December 9 2005 1 03 AM ...

Page 395: ...lect the aplet TRIANGLES 2 Choose the sine formula in E1 3 Change to the Numeric view and enter the known values 35 5 4 Solve for the missing value The length of the ladder is approximately 8 72 metres Resetting an aplet Resetting an aplet clears all data and resets all default settings To reset an aplet open the Library select the aplet and press You can only reset an aplet that is based on a bui...

Page 396: ...hematical concepts Note that you need the Graphing Calculator Connectivity Kit in order to load aplets from a PC Hewlett Packard s Calculators web site can be found at http www hp com calculators Sending and receiving aplets A convenient way to distribute or share problems in class and to turn in homework is to transmit copy aplets directly from one HP 40gs to another This can take place via a sui...

Page 397: ... aplet Highlight your selection and press If transmitting to a disk drive you have the options of sending to the current default directory or to another directory 3 Receiving calculator Open the aplet library and press The RECEIVE FROM menu appears with the following options HP39 40 USB to receive via the USB port HP39 40 SER to receive via the RS232 serial port USB DISK DRIVE to receive from a di...

Page 398: ...o keep a copy of a working environment for later use The aplet library is where you go to manage your aplets Press Highlight using the arrow keys the name of the aplet you want to act on To sort the aplet list In the aplet library press Select the sorting scheme and press Chronologically produces a chronological order based on the date an aplet was last used The last used aplet appears first and s...

Page 399: ...mands can store results in variables but do not display results Arguments are separated by semi colons such as DISP expression line expression A number variable or algebraic expression numbers plus functions that produces a value function An operation possibly with arguments that returns a result It does not store results in variables The arguments must be enclosed in parentheses and separated wit...

Page 400: ...as a set of menu key labels across the bottom of the display menu keys The top row of keys Their operations depend on the current context The labels along the bottom of the display show the current meanings note Text that you write in the Notepad or in the Note view for a specific aplet program A reusable set of instructions that you record using the Program editor sketch A drawing that you make i...

Page 401: ...r clip into the hole as far as it will go Hold it there for 1 second then remove it 3 Press If necessary press and the first and last menu keys simultaneously Note This will erase your calculator memory To erase all memory and reset defaults If the calculator does not respond to the above resetting procedures you might need to restart it by erasing all of memory You will lose everything you have s...

Page 402: ... the small hole in the back of the calculator Insert the end of a straightened metal paper clip into the hole as far as it will go Hold it there for 1 second then remove it Press the key 5 Remove the batteries see Batteries on page R 4 press and hold the key for 10 seconds and then put the batteries back in Press the key Operating details Operating temperature 0 to 45 C 32 to 113 F Storage tempera...

Page 403: ... lift it b Insert a new CR2032 lithium battery Make sure its positive side is facing up c Replace the plate and push it to the original place After installing the batteries press to turn the power on Warning It is recommended that you replace this battery every 5 years When the low battery icon is displayed you need to replace the batteries as soon as possible However avoid removing the backup bat...

Page 404: ...x Z1 Z9 Z0 Graphic G1 G9 G0 Library Function Parametric Polar Sequence Solve Statistics User named List L1 L9 L0 Matrix M1 M9 M0 Modes Ans Date HAngle HDigits HFormat Ierr Time Notepad User named Program Editline User named Real A Z θ hp40g book Page 6 Friday December 9 2005 1 03 AM ...

Page 405: ...abels Recenter Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Plot FCN Area Extremum Isect Root Slope Symbolic Angle F1 F2 F3 F4 F5 F6 F7 F8 F9 F0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum hp40g book Page 7 Friday December 9 2005 1 03 AM ...

Page 406: ... Recenter Simult Tmin Tmax Tracing Tstep Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X9 Y9 X0 Y0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum hp40g book Page 8 Friday December 9 2005 1 03 AM ...

Page 407: ...oss Labels Recenter Simult Umin Umax θstep Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle R1 R2 R3 R4 R5 R6 R7 R8 R9 R0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum hp40g book Page 9 Friday December 9 2005 1 03 AM ...

Page 408: ...s Labels Nmin Nmax Recenter SeqPlot Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle U1 U2 U3 U4 U5 U6 U7 U8 U9 U0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum hp40g book Page 10 Friday December 9 2005 1 03 AM ...

Page 409: ...s Connect Coord FastRes Grid Indep InvCross Labels Recenter Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle E1 E2 E3 E4 E5 E6 E7 E8 E9 E0 Numeric Digits Format NumCol NumRow Note NoteText Sketch Page PageNum hp40g book Page 11 Friday December 9 2005 1 03 AM ...

Page 410: ...S5mark StatPlot Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle S1fit S2fit S3fit S4fit S5fit Numeric C0 C9 Digits Format NumCol NumFont NumRow StatMode Stat One MaxΣ MeanΣ Median MinΣ NΣ Q1 Q3 PSDev SSDev PVarΣ SVarΣ TotΣ Stat Two Corr Cov Fit MeanX MeanY RelErr ΣX ΣX2 ΣXY ΣY ΣY2 Note NoteText Sketch Page PageNum hp40g book Page 12 Friday December 9 2005 1 03 AM ...

Page 411: ...ailable name Calculus TAYLOR Complex ARG CONJ IM RE Constant e i MAXREAL MINREAL π Hyperb ACOSH ASINH ATANH COSH SINH TANH ALOG EXP EXPM1 LNP1 List CONCAT ΔLIST MAKELIST πLIST POS REVERSE SIZE ΣLIST SORT Loop ITERATE RECURSE Σ hp40g book Page 13 Friday December 9 2005 1 03 AM ...

Page 412: ...TRACE TRN Polynom POLYCOEF POLYEVAL POLYFORM POLYROOT Prob COMB PERM RANDOM UTPC UTPF UTPN UTPT Real CEILING DEG RAD FLOOR FNROOT FRAC HMS HMS INT MANT MAX MIN MOD CHANGE TOTAL RAD DEG ROUND SIGN TRUNCATE XPON Stat Two PREDX PREDY Symbolic ISOLATE LINEAR QUAD QUOTE Category Available name Continued hp40g book Page 14 Friday December 9 2005 1 03 AM ...

Page 413: ...vailable name Continued Category Available name Angle Degrees Grads Radians Format Standard Fixed Sci Eng Fraction SeqPlot Cobweb Stairstep S1 5fit Linear LogFit ExpFit Power Trigonometric QuadFit Cubic Logist User Exponent StatMode Stat1Var Stat2Var StatPlot Hist BoxW hp40g book Page 15 Friday December 9 2005 1 03 AM ...

Page 414: ...ability μ0 acce gr acceleration of gravity g gravita gravitation G Quantum Plank s Plank s constant h Dirac s Dirac s hbar e charge electronic charge q e mass electron mass me q me ra q me ratio qme proton m proton mass mp mp me r mp me ratio mpme fine str fine structure α mag flux magnetic flux φ Faraday Faraday F Rydberg Rydberg Bohr rad Bohr radius a0 Bohr mag Bohr magneton μB nuc mag nuclear m...

Page 415: ...onstant e i π Diff Int DERIV DERVX DIVPC FOURIER IBP INTVX lim PREVAL RISCH SERIES TABVAR TAYLOR0 TRUNC Hyperb ACOSH ASINH ATANH COSH SINH TANH Integer DIVIS EULER FACTOR GCD IDIV2 IEGCD IQUOT IREMAINDER ISPRIME LCM MOD NEXTPRIME PREVPRIME Modular ADDTMOD DIVMOD EXPANDMOD FACTORMOD GCDMOD INVMOD MODSTO MULTMOD POWMOD SUBTMOD hp40g book Page 17 Friday December 9 2005 1 03 AM ...

Page 416: ... EXPLN EXP2POW FDISTRIB LIN LNCOLLECT POWEXPAND SINCOS SIMPLIFY XNUM XQ Solve DESOLVE ISOLATE LDEC LINSOLVE SOLVE SOLVEVX Tests ASSUME UNASSUME AND OR NOT IFTE Trig ACOS2S ASIN2C ASIN2T ATAN2S HALFTAN SINCOS TAN2CS2 TAN2SC TAN2SC2 TCOLLECT TEXPAMD TLIN TRIG TRIGCOS TRIGSIN TRIGTAN Category Function Continued hp40g book Page 18 Friday December 9 2005 1 03 AM ...

Page 417: ... GROBOR GROBXOR MAKEGROB PLOT PLOT REPLACE SUB ZEROGROB Loop FOR TO STEP END DO UNTIL END WHILE REPEAT END BREAK Matrix ADDCOL ADDROW DELCOL DELROW EDITMAT RANDMAT REDIM REPLACE SCALE SCALEADD SUB SWAPCOL SWAPROW Print PRDISPLAY PRHISTORY PRVAR Prompt BEEP CHOOSE CLRVAR DISP DISPXY DISPTIME EDITMAT FREEZE GETKEY INPUT MSGBOX PROMPT WAIT Stat One DO1VSTATS RANDSEED SETFREQ SETSAMPLE hp40g book Page...

Page 418: ... memory to continue operation Delete one or more matrices lists notes or programs using catalogs or custom not built in aplets using MEMORY Insufficient Statistics Data Not enough data points for the calculation For two variable statistics there must be two columns of data and each column must have at least four numbers Invalid Dimension Array argument had wrong dimensions Invalid Statistics Data ...

Page 419: ...ing this function OFF SCREEN Function value root extremum or intersection is not visible in the current screen Receive Error Problem with data reception from another calculator Re send the data Too Few Arguments The command requires more arguments than you supplied Undefined Name The global variable named does not exist Undefined Result The calculation has a mathematically undefined result such as...

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Page 421: ... during the warranty period HP will replace software media which does not execute its programming instructions due to such defects 3 HP does not warrant that the operation of HP products will be uninterrupted or error free If HP is unable within a reasonable time to repair or replace any product to a condition as warranted you will be entitled to a refund of the purchase price upon prompt return o...

Page 422: ...ATED ABOVE IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT SPECIAL INCIDENTAL CONSEQUENTIAL INCLUDING LOST PROFIT OR DATA OR OTHER DAMAGE WHETHER BASED IN CONTRACT TORT OR OTHERWISE Some countries States or provinces do not allow the exclusion or limitation of incidental or consequential damages so the above limitation or exclusion may not apply to you 8 The only warr...

Page 423: ... 02 75419782 Norway 47 63849309 Portugal 351 229570200 Spain 34 915 642095 Sweden 46 851992065 Switzerland 41 1 4395358 German 41 22 8278780 French 39 02 75419782 Italian Turkey 420 5 41422523 UK 44 207 4580161 Czech Republic 420 5 41422523 South Africa 27 11 2376200 Luxembourg 32 2 7126219 Other European countries 420 5 41422523 Asia Pacific Country Telephone numbers Australia 61 3 9841 5211 Sing...

Page 424: ... City 5258 9922 ROTC 01 800 472 6684 Venezuela 0800 4746 8368 Chile 800 360999 Columbia 9 800 114726 Peru 0 800 10111 Central America Caribbean 1 800 711 2884 Guatemala 1 800 999 5105 Puerto Rico 1 877 232 0589 Costa Rica 0 800 011 0524 N America Country Telephone numbers U S 1800 HP INVENT Canada 905 206 4663 or 800 HP INVENT ROTC Rest of the country hp40g book Page 4 Friday December 9 2005 1 03 ...

Page 425: ... antenna Increase the separation between the equipment and the receiver Connect the equipment into an outlet on a circuit different from that to which the receiver is connected Consult the dealer or an experienced radio or television technician for help Modifications The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved by He...

Page 426: ... sur le matériel brouilleur du Canada European Union Regulatory Notice This product complies with the following EU Directives Low Voltage Directive 73 23 EEC EMC Directive 89 336 EEC Compliance with these directives implies conformity to applicable harmonized European standards European Norms which are listed on the EU Declaration of Conformity issued by Hewlett Packard for this product or product...

Page 427: ...your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment The separate collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment For more infor...

Page 428: ...hp40g book Page 8 Friday December 9 2005 1 03 AM ...

Page 429: ... 20 1 Solve 7 1 sorting 22 6 statistics 10 1 transmitting 22 5 Triangle Solver 9 1 aplet commands CHECK 21 14 SELECT 21 14 SETVIEWS 21 17 UNCHECK 21 17 aplet variables definition 17 1 17 8 in Plot view 21 31 new 17 1 aplet views canceling operations in 1 1 changing 1 19 note 1 18 Numeric view 1 17 Plot view 1 16 sketch 1 18 split screen 1 17 Symbolic view 1 16 approximation 14 32 arc cosecant 13 2...

Page 430: ...mmands aplet 21 14 branch 21 17 definition of R 1 drawing 21 19 graphic 21 21 loop 21 23 print 21 25 program 21 4 R 19 stat one 21 29 stat two 21 30 with matrices 18 10 complex number functions 13 6 13 17 conjugate 13 7 imaginary part 13 7 real part 13 8 complex numbers 1 29 entering 1 29 math functions 13 7 storing 1 29 computer algebra system See CAS confidence intervals 11 15 CONJ 13 7 conjugat...

Page 431: ...VX 14 16 DESOLVE 14 33 determinant square matrix 18 11 DIFF menu 14 16 differential equations 14 33 14 35 14 57 differentiation 13 6 14 33 digamma function 14 67 14 68 display 21 21 adjusting contrast 1 2 annunciator line 1 2 capture 21 21 clearing 1 2 date and time 21 27 element 18 5 elements 19 4 engineering 1 10 fixed 1 10 fraction 1 10 history 1 22 line 1 23 matrices 18 5 parts of 1 2 printing...

Page 432: ... in HOME 1 19 evaluating in aplets 2 3 literal 13 18 plot 3 3 extended greatest common divisor 14 55 extremum 3 10 F FACTOR 14 12 14 47 14 56 factorial 13 13 factorization 14 12 FACTORMOD 14 53 FastRes variable 21 32 FDISTRIB 14 30 fit a curve to 2VAR data 10 17 choosing 10 12 defining your own 10 13 fixed number format 1 10 font size change 3 8 15 2 20 5 forecasting 10 20 FOURIER 14 17 fraction n...

Page 433: ...graphics copying 20 6 copying into Sketch view 20 6 storing and recalling 20 6 21 21 greatest common divisor 14 56 H HALFTAN 14 40 HERMITE 14 56 histogram 10 15 adjusting 10 16 range 10 18 setting min max values for bars 21 32 width 10 18 history 1 2 14 8 21 25 Home 1 1 calculating in 1 19 display 1 2 evaluating expressions 2 4 reusing lines 1 23 variables 17 1 17 7 R 6 home 14 7 horizontal zoom 2...

Page 434: ...e hyperbolic sine 13 9 inverse hyperbolic tangent 13 9 inverse Laplace transform 14 66 inverting matrices 18 8 INVMOD 14 53 IQUOT 14 49 IREMAINDER 14 49 isect variable 21 33 ISOLATE 14 34 ISPRIME 14 50 K keyboard editing keys 1 5 entry keys 1 5 inactive keys 1 8 list keys 19 2 math functions 1 7 menu keys 1 4 Notepad keys 20 8 shifted keystrokes 1 6 L labeling axes 2 7 parts of a sketch 20 5 LAP 1...

Page 435: ... menu 1 7 polynomial 13 11 probability 13 12 real number 13 14 symbolic 13 17 trigonometry 13 20 MATH menu 13 1 math operations 1 19 enclosing arguments 1 21 in scientific notation 1 20 negative numbers in 1 20 matrices adding rows 21 24 addition and subtraction 18 6 arguments 18 10 arithmetic operations in 18 6 assembly from vectors 18 1 changing row position 21 25 column norm 18 10 comma 19 7 co...

Page 436: ...ll R 3 organizing 17 9 out of R 21 saving 1 25 22 1 viewing 17 1 menu lists searching 1 9 minimum real number 13 8 mixed fraction format 1 11 modes angle measure 1 10 CAS 14 5 decimal mark 1 11 number format 1 10 MODSTO 14 53 modular arithmetic 14 51 multiple solutions plotting to find 7 7 multiplication 13 4 14 28 implied 1 20 MULTMOD 14 54 N name conflict R 21 naming programs 21 4 natural expone...

Page 437: ... pause 21 29 permutations 13 13 pictures attaching in Sketch view 20 3 plot analyzing statistical data in 10 19 auto scale 2 14 box and whisker 10 16 cobweb 6 1 comparing 2 5 connected points 10 17 10 19 decimal scaling 2 14 defining the independent variable 21 36 drawing axes 2 7 expressions 3 3 grid points 2 7 histogram 10 15 in Solve aplet 7 7 integer scaling 2 14 one variable statistics 10 18 ...

Page 438: ...ents of display 21 25 name and contents of variable 21 26 object in history 21 25 variables 21 26 probability functions 13 13 COMB 13 12 RANDOM 13 13 UTPC 13 13 UTPF 13 13 UTPN 13 13 UTPT 13 14 program commands 21 4 copying 21 8 creating 21 4 debugging 21 7 deleting 21 9 delimiters 21 1 editing 21 5 naming 21 4 pausing 21 29 printing 21 26 sending and receiving 21 8 structured 21 1 prompt commands...

Page 439: ... 3 calculator R 3 memory R 3 result copying to edit line 1 22 reusing 1 22 rigorous 14 6 RISCH 14 24 root interactive 3 10 nth 13 6 variable 21 34 root finding displaying 7 7 interactive 3 9 operations 3 10 variables 3 10 S S1mark S5mark variables 21 34 scaling automatic 2 14 decimal 2 10 2 14 integer 2 10 2 14 2 15 options 2 13 resetting 2 13 trigonometric 2 14 scatter plot 10 15 10 17 connected ...

Page 440: ... 6 elements in a list 19 9 spectral norm 18 13 spectral radius 18 13 square root 13 5 stack history printing 21 25 stairsteps graph 6 1 standard number format 1 10 statistics analysis 10 1 analyzing plots 10 19 angle mode 10 12 calculate one variable 21 30 calculate two variable 21 30 data set variables 21 40 data structure 21 40 define one variable sample 21 30 define two variable data set s de p...

Page 441: ...sions 3 2 syntax 13 2 syntax errors 21 7 T table navigate around 3 8 numeric values 3 7 numeric view setup 2 16 TABVAR 14 27 TAN2CS2 14 40 TAN2SC 14 41 TAN2SC2 14 41 tangent 13 4 inverse hyperbolic 13 9 Taylor polynomial 13 7 TAYLOR0 14 27 TCHEBYCHEFF 14 59 TCOLLECT 14 41 tests 14 61 TEXPAND 14 15 14 42 tickmarks for plotting 2 6 time 13 15 setting 21 27 time converting 13 15 times sign 1 20 TLIN ...

Page 442: ...ty 13 14 USB connectivity 22 5 user defined regression fit 10 13 V value recall 17 3 storing 17 2 variables aplet 17 1 CAS 14 4 categories 17 7 clearing 17 3 definition 17 1 17 7 R 2 in equations 7 10 in Symbolic view 2 3 independent 14 6 21 36 local 17 1 previous result Ans 1 23 printing 21 26 root 21 34 root finding 3 10 step size of independent 21 36 types 17 1 17 7 use in calculations 17 3 var...

Page 443: ...ptions 2 9 3 8 options within a table 2 18 out 2 9 redrawing table of numbers op tions 2 18 square 2 10 un zoom 2 11 within Numeric view 2 18 X zoom 2 9 Y zoom 2 10 hp40g book Page 15 Friday December 9 2005 1 03 AM ...

Page 444: ...hp40g book Page 16 Friday December 9 2005 1 03 AM ...

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