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Matrices

205

RREF

Reduced-Row Echelon Form. Changes a rectangular

matrix

to its reduced row-echelon form.

RREF

(

matrix

)

SCHUR

Schur Decomposition. Factors a square

matrix

into two

matrices. If

matrix

is real, then the result is

{[[

orthogonal

]],[[

upper-quasi triangular

]]}.

matrix

is complex, then the result is

{[[

unitary

]],[[

upper-triangular

]]}.

SCHUR

(

matrix

)

SIZE

Dimensions of

matrix

. Returned as a list: {rows,columns}.

SIZE

(

matrix

)

SPECNORM

Spectral Norm of

matrix

SPECNORM

(

matrix

)

SPECRAD

Spectral Radius of a square

matrix

SPECRAD

(

matrix

)

SVD

Singular Value Decomposition. Factors an

m × n

matrix

into two matrices and a vector:

{[[

m × m

square orthogonal

]],[[

n × n

square orthogonal

]],

[

real

]}.

SVD

(

matrix

)

SVL

Singular Values. Returns a vector containing the singular

values of

matrix.

SVL

(

matrix

)

TRACE

Finds the trace of a square

matrix.

The trace is equal to

the sum of the diagonal elements. (It is also equal to the

sum of the eigenvalues.)

TRACE

(

matrix

)

TRN

Transposes

matrix

. For a complex matrix, TRN finds the

conjugate transpose.

TRN

(

matrix

)

Содержание 39gII

Страница 1: ...HP 39gII graphing calculator user s guide Edition1 Part Number NW249 90001 ...

Страница 2: ...Printing History Edition 1 November 201 1 ...

Страница 3: ... library 24 App views 25 Standard app views 27 About the Symbolic view 27 Defining an expression Symbolic view 28 Evaluating expressions 29 About the Plot view 31 Plot setup 31 Exploring the graph 33 About the Numeric view 42 Setting up the table Numeric view setup 42 Exploring the table of numbers 43 Building your own table of numbers 45 BuildYourOwn table keys 46 3 Function app About the Functio...

Страница 4: ... with the Statistics 2Var app 83 Entering and editing statistical data 87 Defining a regression model 89 Computed statistics 91 Plotting 93 Plot setup 95 Trouble shooting a plot 96 Calculating predicted values 98 7 Inference app About the Inference app 99 Getting started with the Inference app 99 Importing sample statistics 102 Hypothesis tests 105 One Sample Z Test 106 Two Sample Z Test 107 One P...

Страница 5: ...134 Performing TVM calculations 135 Calculating Amortizations 136 12 Linear Solver app About the Linear Solver app 139 Getting started with the Linear Solver app 139 13 Triangle Solver app About the Triangle Solver app 143 Getting started with the Triangle Solver app 143 14 The Explorer Apps Linear Explorer App 147 Quadratic Explorer app 148 Trig Explorer app 149 15 Extending your App Library Crea...

Страница 6: ...and physical constants 179 Units 179 Physical constants 181 17 Lists Introduction 183 Create a list in the List Catalog 183 The List Editor 184 Deleting lists 186 Lists in the Home view 187 List functions 188 Finding statistical values for lists 191 18 Matrices Introduction 193 Creating and storing matrices 194 Working with matrices 195 Matrix arithmetic 198 Solving systems of linear equations 200...

Страница 7: ... defaults 311 If the calculator does not turn on 311 Batteries 312 Operating details 313 Variables 313 Home variables 313 App variables 314 Function app variables 314 Solve app variables 315 Statistics 1Var app variables 315 Statistics 2Var app variables 316 Inference app variables 317 Parametric app variables 318 Polar app variables 318 Sequence app variables 319 Finance app variables 320 Linear ...

Страница 8: ...am commands 325 Constants 326 Program constants 326 Physical Constants 327 Status messages 327 23 Appendix Product Regulatory Information Federal Communications Commission Notice i European Union Regulatory Notice iii ...

Страница 9: ...s that you access by pressing theSkey first are represented as follows SCLEAR SMODES SACOS etc Numbers and letters are represented normally as follows 5 7 A B etc Menu options that is the functions that you select using the menu keys at the top of the keypad are represented as follows Input form fields and choose list items are represented as follows Function Polar Parametric Your entries as they ...

Страница 10: ...e for any errors or for incidental or consequential damage in connection with the furnishing performance or use of this manual and the examples herein 1994 1995 1999 2000 2003 2006 2010 2011 Hewlett Packard Development Company L P The programs that control your HP 39gII are copyrighted and all rights are reserved Reproduction adaptation or translation of those programs without prior written permis...

Страница 11: ...s If you want to perform calculations or you want to quit the current activity such as an app a program or an editor pressH All mathematical functions are available in the Home view The name of the current app 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 an...

Страница 12: ...eys give you access to the menu items shown at the bottom of the display is the label for the first menu key in the figure above Press means press the F1 menu key Edit line The line of current entry History The Home display H shows up to 6 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 app is ...

Страница 13: ...essS Shift in effect for next keystroke To cancel pressSagain To activate pressA Alpha in effect for next keystroke To lock pressAagain To cancel pressAa third time To activate pressAS Lower case alpha in effect for next keystroke To lock pressA again To cancel pressAa third time To switch to upper case pressS Low battery power Busy Data is being transferred via cable ...

Страница 14: ... the menu keys current meanings App control keys The app control keys are Number Feature HP 39gII 1 256 x 128 pixel display 2 Context sensitive menu 3 F1 F6 menu keys 4 HP Apps keys 5 Modes 6 Common math and science functions 7 Shift keys 8 On cancel 9 Last Answer ANS 10 Enter key 1 1 Alphabetic entry 12 Catalogs and editors 13 Backspace Clear 14 Help key 15 Cursor keys 16 USB Connectivity Key Mea...

Страница 15: ... if the calculator is on by pressingO PressingS then OFF turns the calculator off S Accesses the function printed at the bottom left of a key A Accesses the alphabetical characters printed at the bottom right of a key PressAtwice to lock this shift so you can enter a string of characters E Enters an input or executes an operation In calculations E acts like When or is present as a menu key Eacts t...

Страница 16: ... screen for example Plot Setup SCLEAR returns all settings to their default values Moves the cursor around the display PressSfirst to move to the beginning end top or bottom SCHARS Displays a menu of all available characters To type one use the arrow keys to highlight it and press To select multiple characters select each and press then press Key Meaning Continued Key Description S PressSto access...

Страница 17: ...mplete the operation Sj256E displays 16 Math menu Pressb 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 The functions are grouped by category ranging in alphabetical order from Calculus to Trigonometry Use the up and down arrow keys to scroll through the list Use the ...

Страница 18: ...for your convenience For example ITERATE is the first item under Loop which is the eighth category With the Math menu open pressqxto insert the ITERATE function in the edit line at the cursor position If there are more than 9 items in a category the letters A B C etc are used For example the Matrix category uses the number 8 In this category the RREF command uses the letter H With the Math menu op...

Страница 19: ...ts within a category Highlight a general category in the left column then highlight an item in the right column The list in the right column changes when a different category is highlighted If there are three columns the left column shows a general category while the second column shows a useful sub category Highlight a general category then highlight a sub category of interest Finally select an i...

Страница 20: ...ut form to set the modes for Home H I N T Although the numeric setting in Modes affects only Home the angle setting controls Home and the current app The angle setting selected in Modes is the angle setting used in both Home and the current app To further configure an app you use the SETUP keys SY SP andSM PressSH Modes to enter the Home Modes input form Press F4 to enter the second page of the fo...

Страница 21: ...becomes 1 23E2 in Scientific 2 format Engineering Displays result with an exponent that is a multiple of 3 and the specified number of significant digits beyond the first one Example 123 456E7 becomes 1 23E9 in Engineering 2 format Complex If checked allows operations involving complex numbers if unchecked only real number operations are allowed Language Choose language preference for menus and in...

Страница 22: ...anges to degrees 4 PressHto return to Home H I N T Whenever an input form has a list of choices for a field you can press to cycle through them instead of using Mathematical calculations The most commonly used math operations are available from the keyboard Access to the rest of the math functions is via the Math menu b To access programming commands pressSCMDS See the chapter Programming for more...

Страница 23: ...ulate Long results If the result is too long to fit on the display line or if you want to see an expression in textbook format press to highlight it and then press Negative numbers Type to start a negative number or to insert a negative sign To raise a negative number to a power enclose it in parentheses For example 5 2 25 whereas 52 25 Scientific notation powers of 10 A number like or is written ...

Страница 24: ...B as A B 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 39gII calculates according to the order of algebraic precedence the next topic Following are some exampl...

Страница 25: ... where 10 Equals Largest and smallest numbers The HP 39gII represents 1 10 499 as well as all numbers smaller than this as zero The largest number displayed is 9 99999999999 10499 A greater result is displayed as this number Clearing numbers Cdeletes the character to the left of the cursor that is it is a backspace key CANCEL O clears the edit line SCLEAR clears all input and output in the display...

Страница 26: ...Home display into an expression ANS is a variable that is updated each time you pressE To repeat a previous line To repeat the very last line just pressE If the previous line is an expression containing ANS the calculation is repeated iteratively Example See howSANS retrieves and reuses the last result 50 andEupdates ANS from 50 to 75 to 100 50E 25 EE You can use the last result as the first expre...

Страница 27: ...e In addition to the COPY menu key that lets you copy expressions from the Home view there is a more universal copy and paste clipboard that you can use You can highlight the value or expression you want in most fields or the Home view history e g F1 x in the Function App and then paste it into the edit line or into another compatible field To copy a value or expression to the clipboard pressSl To...

Страница 28: ...the display history It s a good habit to clear the display history SCLEAR whenever you have finished working in Home It saves calculator memory to clear the display history Remember 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 using Textbook Format Display C Deletes the highlighted ...

Страница 29: ... cannot find exact ones Enter to see the decimal approximation 2 236 Press conce to see and again to see Pressingca third time will cycle back to the original decimal representation Converting decimals to degrees minutes and seconds Any decimal result can de displayed in hexagesimal that is in units subdivided into groups of 60 This includes degrees minutes and seconds as well as hours minutes and...

Страница 30: ...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 SAi or pressb or keys to select Constant to move to the right column of the menu to select i and Storing complex numbers There are ten variables available for storing complex numbers Z0 to Z9 To store a complex number in a variable Enter the complex numb...

Страница 31: ... well as notes and programs attached to the current HP App A catalog lists items which you can delete or transmit for example an app An editor lets you create or modify items and numbers for example a note or a matrix Catalog Editor Keystrokes To create and edit App library I HP Apps Info SI Info Notes attached to the current HP App List Sp List Lists Matrix St Matrix Matrices and vectors Program ...

Страница 32: ...22 Getting started ...

Страница 33: ... explore Function Real valued rectangular functions y in terms of x Example Solve Equations in one or more real valued variables Example Statistics 1Var One variable statistical data x Statistics 2Var Two variable statistical data x and y Inference Confidence intervals and Hypothesis tests based on the Normal and Students t distributions Parametric Parametric relations x and y in terms of t Exampl...

Страница 34: ...a name you give it and then use the original app for another problem or purpose See the chapter Extending Your Aplet Library for more information regarding customizing and saving HP Apps App library Apps are stored in the App library To open an app PressIto display the App library menu Select the app and press orE From within an app you can return to Home any time by pressingH Sequence Sequence fu...

Страница 35: ...al views an app may have Note that not all HP Apps provide all 7 of the standard views nor do all of them provide additional views via the Views key The scope and complexity of each app determines its view set However the views provided are based on these seven views and the additional views provided by the Views key These views are summarized below using the Function app as an example Symbolic vi...

Страница 36: ...ormat Numeric setup PressSSETUP NUM Sets parameters for building a table of numeric values Info view PressSINFO to display the HP App s Info view This note is transferred with the app if it is sent to another calculator or to a PC The Info view contains text to supplement an HP App The Views menu Besides the 7 views that all HP Apps can utilize the Views key provides access to any special views or...

Страница 37: ...om options section later in this chapter Standard app views This section examines the options and functionality of the three main views Symbolic Plot and Numeric as well as their setups for the Function Polar Parametric and Sequence apps About the Symbolic view The Symbolic view is the defining view for the Function Parametric Polar and Sequence apps The other views are derived from the symbolic e...

Страница 38: ...ssion or clear one line C or all lines SCLEAR Expressions are selected check marked on entry To deselect an expression press All selected expressions are plotted For a Function definition enter an expression to define F X The only independent variable in the expression is X For a Parametric definition enter a pair of expressions to define X T and Y T The only independent variable in the expression...

Страница 39: ... have to enter the second term if the HP 39gII is unable to calculate it automatically Typically if Ux N depends on Ux N 2 then you must enter Ux 2 Evaluating expressions In apps In the Symbolic view a variable is a symbol only and does not represent one specific value To evaluate a function in Symbolic view press If a function calls another function then resolves all references to other functions...

Страница 40: ... 9 in place of X in F4 Symb view keys The following table describes the keys that you use to work with the Symbolic view Key Meaning Copies the highlighted expression to the edit line for editing Press when done Checks unchecks the current expression or set of expressions Only checked expression s are evaluated in the Plot and Numeric views Enters the independent variable in the Function app Or yo...

Страница 41: ...the Polar app Or you can use thed key on the keyboard Enters the independent variable in the Sequence app Or you can use thedkey on the keyboard Displays the current expression in Textbook Format Resolves all references to other definitions in terms of variables a Displays a menu for entering variable names or contents of variables b Displays the menu for entering math operations SCHARS Displays s...

Страница 42: ...gs The fields in the Plot setup are Field Meaning XRNG YRNG Specifies the minimum and maximum horizontal X and vertical Y values for the plotting window TRNG Parametric app Specifies the t values T for the graph θRNG Polar app Specifies the angle θ value range for the graph NRNG Sequence app Specifies the index N values for the graph TSTEP For Parametric plots the increment for the independent var...

Страница 43: ... The following tables describe the keys that you use to work with the Plot view Field Meaning AXES Draws the axes LABELS Labels the axes with XRNG and YRNG values GRID DOTS Draws grid points using XTICK and YTICK spacing GRID LINES Draws grid lines using XTICK and YTICK spacing Cursor Choose between the Standard cursor and Inverting or Blinking cursors Method Choose between the default Adaptive me...

Страница 44: ...mps to the point on the graph that you entered Function app only displays a list of commands for analyzing functions see the chapter Function app for more details Displays the current defining expression Press to restore the menu Key Meaning Continued Key Meaning with trace mode off Moves cursor one pixel left and right respectively Moves cursor one pixel up and down respectively S S Moves cursor ...

Страница 45: ...lue To turn trace on off If the menu labels are not displayed press first Turn off trace mode by pressing Turn on trace mode by pressing Zoom within a graph One of the menu key options is Zooming redraws the plot on a larger or smaller scale It is a shortcut for changing the Plot Setup The Set Factors option enables you to set the factors by which you zoom in or zoom out and whether the zoom is ce...

Страница 46: ...ooming in results in 1 4 as many units depicted per pixel see Set Factors Out Multiplies horizontal and vertical scales by the X factor and Y factor see Set Factors X In Divides horizontal scale only using X factor X Out Multiplies horizontal scale only using X factor Y In Divides vertical scale only using Y factor Y Out Multiplies vertical scale only using Y factor Square Changes the vertical sca...

Страница 47: ...h 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 12 7 to 12 7 and YRNG 5 5 5 5 Integer Rescales horizontal axis only making each pixel 1 unit Trig Rescales horizontal axis so 1 pixel π 24 radians or 7 58 degrees rescales vertical axis so 1 pixel 0 1 unit Un zoom Re...

Страница 48: ...iews Un zoom Un zoom Note press to move to the bottom of the Zoom list Zoom Out Out Now un zoom As a shortcut presswwhile in the Plot view to zoom out X Zoom In X In Now un zoom X Zoom Out X Out Now un zoom Y Zoom In Y In ...

Страница 49: ...e area 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 ...

Страница 50: ...ve you two simultaneous views of the plot Option Meaning Plot Detail Splits the screen into the current plot and a zoom Plot Table Splits the screen into the plot and a numeric table Auto Scale Rescales the vertical axis so that the display shows a representative portion of the plot based on the current XRNG For Sequence and Statistics apps auto scale rescales both axes The auto scale process uses...

Страница 51: ...3 To un split the screen pressP The left side takes over the whole screen Plot Table The Plot Table view gives you a plot view and a table view simultaneously 1 PressV Select Plot Table and press The screen displays the plot on the left side and a table of numbers on the right side 2 To move up and down in the table use the and cursor keys These keys move the trace point left or right along the pl...

Страница 52: ...nd selecting check marking the expression or expressions that you want to explore in the Symbolic view pressMto view a table of data values for the independent and dependent variables Setting up the table Numeric view setup Press SNUM to define any of the table settings Use the Numeric Setup input form to configure the table 1 Highlight the field to edit Use the arrow keys to move from field to fi...

Страница 53: ...pendent variable s starting value NUMSTEP The size of the increment from one independent variable value to the next NUMTYPE Type of numeric table Automatic or BuildYourOwn To build your own table you must type each independent value into the table yourself NUMZOOM Sets the zoom factor for zooming in or out on a row of the table Key Meaning Displays the Zoom menu list Toggles between two character ...

Страница 54: ...When you press E the values for the dependent variable s are Option Meaning In Decreases the step value for the independent variable so a narrower range is shown Uses the NUMZOOM factor in Numeric Setup Out Increases the step value 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...

Страница 55: ...lculated and displayed Build a table 1 Start with an expression defined in Symbolic view in the app of your choice Note Function Polar Parametric and Sequence apps only 2 In the Numeric Setup SNUM choose NUMTYPE BuildYourOwn 3 Open the Numeric view M 4 Clear existing data in the table SCLEAR 5 Enter the independent values in the left hand column Type in a number and press E You do not have to ente...

Страница 56: ... specify the functions ISelect Function Sjl25 Key Meaning Puts the highlighted independent value X T θ or N into the edit line PressingEreplaces 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 pressingE Sorts the independent variable values into ascending or descending order Press and select the ascending o...

Страница 57: ...7 wdjmE Sjl25 wdjmE 2 Reset the graph setup to the default settings SSETUP PLOT SCLEAR 3 Plot the two functions P 4 Reset the numeric setup to the default settings SSETUP NUM SCLEAR 5 Display the functions in numeric form M ...

Страница 58: ...48 Apps and their views ...

Страница 59: ...particular values This chapter demonstrates the basic tools of the Function app by stepping you through an example Getting started with the Function app Throughout this chapter we will use an example involving two functions a linear and a quadratic Open the Function app 1 Open the Function app ISelect Function The Function app starts in the Symbolic view The Symbolic view is the defining view for ...

Страница 60: ... existing expression or SClear to clear all expressions 2 Enter the linear function in F1 X 1wdE 3 Enter the quadratic function in F2 X ldw 1mjw 3E N O T E You can use the menu key to assist in the entry of equations It has the same effect as pressingd Set up the plot You can change the scales of the x and y axes and the spacing of the axis tick marks 4 Display plot settings SSETUP PLOT Note for o...

Страница 61: ...our ways Press to zoom in orwto zoom out on the current cursor coordinates This method uses the zoom factors set in the Zoom menu The default for both x and y is 2 Use the Plot Setup to define XRNG and YRNG exactly as you want Use the Zoom menu to zoom in or out horizontally or vertically or both etc Use the Views menu to select a pre defined window You can also use Autoscale in either the Zoom or...

Страница 62: ...e and step value for the x column as well as the zoom factor for zooming in or out on a row of the table You can also choose the table type PressSCLEAR to reset all values to their defaults 3 Match the table settings to the pixel columns in the graph view Explore the table 4 Display the table of values M To navigate around a table 5 Move to x 12 1 6 times ...

Страница 63: ...the zoom options 7 Zoom in on X 10 by a factor of 4 Note NUMZOOM has a setting of 4 In To change font size 8 Display table numbers in smaller font To display the symbolic definition of a column 9 Display the symbolic definition for the F1 column The symbolic definition of F1 is displayed at the bottom of the screen To change column width 10 Press 3 times to toggle from showing 3 function columns t...

Страница 64: ... graph Display the Plot menu 1 Display the Plot view menu P To find a root of the quadratic function 2 Move the cursor so that it is near x 3 or to select the quadratic or to move the cursor near 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 displayed T...

Страница 65: ...e slope of the quadratic function at the intersection point Select Slope The slope value is displayed at the bottom of the screen You can use the left and right cursor keys to trace along the curve and see the slope at other points You can also use the up and down cursor keys to jump to another function and see the slope at points on that graph Press to quit and return to the Plot view To find the...

Страница 66: ...s the other boundary for the integral 9 Choose the end value for x 2 3 The cursor jumps to on the linear function and the area is shaded The shading shows plus if the area is positive and minus if negative 10 Display the numerical value of the integral to display the value to return to the plot menu x 2 3 ...

Страница 67: ... displayed at the bottom of the screen H I N T The ROOT and EXTREMUM functions return one value only even if the function has more than one root or extremum The function finds the value closest to the position of the cursor You need to re locate the cursor to find other roots or extrema that may exist The FCN Variables The results of the FCN functions are saved in the following variables Root Isec...

Страница 68: ...erivative of the current function 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 or more expressions checkmarked then you will be asked to choose the second expression from a list that includes the x axis Select a starting point then move the cursor to select an ending point The result...

Страница 69: ...riables are contained on the Vars menu To access FCN variables in the Home view Ha Select Function Results or to choose a variable You can access and use the FCN variables to define functions in the Symbolic view the same way as you do in the Home view ...

Страница 70: ...60 Function app ...

Страница 71: ...n equation for any one of its variables In addition if the equation or expression is a polynomial in a single variable and there is more than one solution for the variable then appears in the menu Pressing this menu key will display a list of all real solutions for the variable You can solve the equation as many times as you want using new values for the knowns and highlighting a different unknown...

Страница 72: ... key to assist in the entry of equations Enter known variables 3 Display the Solve numeric view screen M In the Numeric view you specify the values of the known variables V 2 U 2 2AD 1 Open the Solve app ISelect Solve The Solve app starts in the Symbolic view where you specify the expression or equation to solve You can define up to ten equations or expressions named E0 to E9 Each equation can con...

Страница 73: ...ions 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 Select A as the variable The plot view will now plot two equations 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 also a line The desired solut...

Страница 74: ... of using the Numeric view Solve option Solve app s Numeric view keys The Solve app s Numeric view keys are Key Meaning Copies the highlighted value to the edit line for editing Press when done Displays information about the nature of the solution found Displays other pages of variables if any If available displays a list of multiple solutions for the selected variable Displays the symbolic defini...

Страница 75: ...s highlighted variable to zero or deletes current character in the edit line if the edit line is active SCLEAR Resets all variable values to zero or clears the edit line if cursor is in the edit line Key Meaning Continued ...

Страница 76: ... expression where the 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 a...

Страница 77: ...s is the case Multiple solutions Consider the polynomial equation Since this equation is quadratic for x there can be and in this case are two solutions In the case of polynomials the HP 39gII offers a quick way to find multiple solutions 1 Select the Solve app and enter the equation I Select Solve AXk2w AXw1 Message Condition Bad Guess es The initial guess lies outside the domain of the equation ...

Страница 78: ... variable wherever its name is used Therefore if you have defined a value for T as in the above example in another app or even another Solve equation that value shows up in the Numeric view for 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 probl...

Страница 79: ... App variables Functions defined in other apps can also be referenced in the Solve app For example if you define F1 X X2 10 in the Function app you can enter F1 X 50 in the Solve app to solve the equation X2 10 50 ...

Страница 80: ...70 Solve app ...

Страница 81: ... of specific statistics variables The values computed in the Statistics 1Var app are saved in variables and many of these variables are listed by the function accessible from the Statistics 1Var app s Numeric view Getting started with the Statistics 1Var app The following example is about the heights of students in a classroom We will use the example to introduce the structure and function of the ...

Страница 82: ... statistics H1 H5 If data is entered in D1 H1 is automatically set to use D1 for data and the frequency of each data point is set to 1 You can select other columns of data from the Symbolic view of the app 4 Press to close the statistics window PressYto see the data set definitions The first column indicates the associated column of data for each data set definition and the second column indicates...

Страница 83: ...ting Press when done Checks unchecks the current data set Only the checkmarked data set s are computed and plotted Typing aid for the column names Displays the current expression is Textbook Format Press when done Evaluates the highlighted expression resolving any references to function expressions a Displays the menu for entering variable names or contents of variables b Displays the menu for ent...

Страница 84: ...the highlight bar into the right column of the H1 definition and enter the column variable name D2 2 6 Return to the numeric view M 7 Enter the frequency data shown in the above table 5E3E 8E 2E 1E 8 Display the computed statistics The mean height is approximately 167 63cm Height cm Frequency 160 5 165 3 170 8 175 2 180 1 ...

Страница 85: ...ing the data you must define the data set in the Symbolic view Y H I N T A data column must have at least two data points for one variable statistics You can also store statistical data values by copying lists from Home into statistics data columns For example in Home L1 D1 stores a copy of the list L1 into the data column variable D1 Statistics 1Var app s Num View keys The Statistics 1Var app s N...

Страница 86: ...uency data column accordingly Switches between larger and smaller font sizes Opens a dialog box for creating a sequence based on an expression and storing it in a data column Computes descriptive statistics for each data set specified in the Symbolic view C Deletes the currently highlighted value SCLEAR Clears the current column or all columns of data PressSCLEAR to display a menu list then select...

Страница 87: ...elect All columns and press Insert data 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 independen...

Страница 88: ...nly the last three terms 15 16 and 17 are used to calculate Q3 Statistic Definition n Number of data points Min Minimum data value in data set Q1 First quartile median of values to left of median Med Median value of data set Q3 Third quartile median of values to right of median Max Maximum data value in data set Σ Sum of data values with their frequencies Σ Sum of the squares of the data values Me...

Страница 89: ...HK the data sets you want to plot 2 Select the plot type Highlight the Plot field for your data set press the menu key and scroll to the plot type you want Press the menu key when you have made your choice 3 For any plot but especially for a histogram adjust the plotting scale and range in the Plot Setup view If you find histogram bars too fat or too thin you can adjust them by changing the HWIDTH...

Страница 90: ...sor is and the third quartile The right whisker marks the maximum data value The numbers below the plot mean that this column has a minimum of 1 2 normal probability plot The normal probability plot is used to determine whether or not sample data is more or less normally distributed The more linear the data appear the more likely that the data is normally distributed Line plot The line plot connec...

Страница 91: ... to the Statistics 1Var app are as follows 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 enables you to specify the range of values for a set of histogram bars The range runs from the left edge of the leftmost bar to the ...

Страница 92: ...ys The Plot view keys are Key Meaning SCLEAR Erases the plot V Offers additional pre defined views for splitting the screen and autoscaling the axes S S Moves cursor to far left or far right Displays the Zoom menu Turns trace mode on off The white box appears next to the option when Trace mode is active Displays the definition of the current statistical plot Toggles the menu off and on ...

Страница 93: ...stics values in Home and recall the values of specific statistics variables The values computed in the Statistics 2Var app are saved in variables and many of these variables are listed by the function accessible from the Statistics 2Var app s Numeric view Getting started with the Statistics 2Var app The following example is based on the advertising and sales data in the table below In the example ...

Страница 94: ...cs 2Var app starts in the Numeric view Enter data 2 Enter the data into the columns 2E1E 3E5E 5E4E to move to the next column 1400E920E 1 100E2265E 2890E2200E Choose data columns and fit 3 Specify the columns that hold the data you want to analyze Y You could have entered your data into columns other than C1 and C2 4 Select a fit Select Linear ...

Страница 95: ...elation r between advertising time and sales M The correlation is r 0 8995 6 Find the mean advertising time and the mean sales The mean advertising time is approximately 3 3 minutes The mean sales is approximately 1 796 Setup plot 7 Change the plotting range to ensure all the data points are plotted and select a different point mark if you wish SSETUP PLOT 100E 4000E x y x y ...

Страница 96: ...urve a curve to fit the data points This draws the regression line for the best linear fit Display the equation 10 Return to the Symbolic view Y The slope m is 425 875 The y intercept b is 376 25 Predict values Predict the sales figure if advertising were to go up to 6 minutes 1 1 Return to the Plot view P ...

Страница 97: ...o C9 After entering the data you must define the data set in the Symbolic view Y H I N T A data column must have at least four data points to provide valid two variable statistics You can also store statistical data values by copying lists from Home into Statistics data columns For example in Home L1 C1 stores a copy of the list L1 into the data column variable C1 Statistics 2Var app s NUM view ke...

Страница 98: ... edit line Sorts the specified independent data column in ascending or descending order and rearranges a specified dependent or frequency data column accordingly Switches between larger and smaller font sizes Opens a dialog box to create a column of data based on an expression Computes descriptive statistics for each data set specified in the Symbolic view C Deletes the currently highlighted value...

Страница 99: ...rt Order You can choose either Ascending or Descending 3 Specify the INDEPENDENT DEPENDENT and if applicable the FREQUENCY data columns Sorting is by the independent column For instance if Age is C1 and Income is C2 and you want to sort by Income then you make C2 the independent column for the sorting and C1 the dependent column To sort just one column choose None for the dependent column For one ...

Страница 100: ...up whether the trigonometric units are to be interpreted as degrees or radians Choose the fit 1 PressYto display the Symbolic view Highlight the Type number Type1 through Type5 you want to define 2 Press and select from the list Press when done The regression formula for the fit is displayed in the Symbolic view Fit models Eleven fit models are available Fit model Meaning Linear Default Fits the d...

Страница 101: ...see the statistics involving just the independent column or to display the statistics derived from the 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 Quadratic Fits to a quadratic curve y ax2 bx c Needs at least three points Cubic Fits to a cubic polynomial Quartic Fits to a quartic pol...

Страница 102: ... a value from 1 to 1 where 1 and 1 indicate best fits R2 The coefficient of determination which is the square of the correlation coefficient The value of this statistics is dependent on the Fit type chosen sCOV Sample covariance of independent and dependent data columns COV Population covariance of independent and dependent data columns ΣXY Sum of xy products σ Statistic Definition Mean of x indep...

Страница 103: ...sted the Plot Setup yourself you can tryVselect Auto Scale Auto Scale can be relied upon to give a good starting scale which can then be adjusted in the Plot Setup TracingaScatter Plot The numbers below the plot indicate that the cursor is at the first data point for S1 at 1 6 Press to move to the next data point and display information about it Statistic Definition Mean of y dependent values ΣY S...

Страница 104: ... to move the tracer to the graph of the fit Press and to trace along the fit and to see the equation of the fit PressYto see the equation of the fit in the Fit1 field To see the full equation highlight the fit equation and press The expression in Fit2 shows the slope m 1 98082191781 and the y intercept b 2 26575 ...

Страница 105: ...hat model is linear or not A measure of 1 indicates a perfect fit H I N T In order to access the and R 2 variables after you plot a data set you must pressMto access the numeric view and then to display the correlation values The values are stored in the variables when you access the Numeric view Stats page Plot setup The Plot Setup SSETUP PLOT sets most of the same plotting parameters as it does ...

Страница 106: ...ing range Try usingVAuto Scale instead ofP or adjust the plotting parameters in Plot Setup for the ranges of the axes Ensure that both paired columns contain data and that they are the same length Ensure that a paired column of frequency values is the same length as the data column to which it refers Exploring the graph The Plot view has menu keys for zooming tracing and coordinate display There a...

Страница 107: ...menu Turns trace mode on off The white dot 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 Enables you to specify a value on the line of best fit to jump to or a data point number to jump to Displays the equation of the regression curve or the definition of the current statistica...

Страница 108: ...jumps to the specified point on the curve and the coordinate display shows X and the predicted value of Y In the Home view Enter PREDX y value Eto find the predicted value for the independent variable given a hypothetical dependent value Enter PREDY x value to find the predicted value of the dependent variable given a hypothetical independent variable You can type PREDX and PREDY into the edit lin...

Страница 109: ...ess an input form for an 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 app This e...

Страница 110: ...an Z Int 1 μ the confidence interval for 1 mean based on the Normal distribution Z Test 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 Test 1 p the Z Test on 1 proportion Z Int 1 p the confidence interval for 1 proportion based on the Normal distribution Z Test p1 p2 the Z Test on the difference...

Страница 111: ...sent Select the inferential method 2 Select the Hypothesis Test inferential method Select Hypothesis Test 3 Define the type of test Z Test 1 μ 4 Select an alternative hypothesis μ Enter data 5 Go to the Numeric view to see the default data M The table below lists the fields in this view for our current Z Test 1 μ example μ0 Field name Definition Sample mean x ...

Страница 112: ...l Z value as well With the menu key active you can use the left and right cursor keys to decrease and increase the α level Importing sample statistics The Inference app supports the calculation of confidence intervals and the testing of hypotheses based on data in the Statistics 1Var and Statistics 2Var apps Computed statistics for a sample of data in a column in any Statistics based app can be im...

Страница 113: ... T If the Decimal Mark setting in the Modes input form Smodes is set to Comma use oinstead of Calculate statistics 3 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 confidence interval for the true mean of the population of random numbers a...

Страница 114: ... Set up the interval calculation Note The default values are derived from sample data from the on line help example M Import the data 9 Import the data from the Statistics app Note The data from D1 is displayed by default Use the App field to select the Statistics based app from which you want to import data Use the Column field to choose the column in that app where the data is stored You can vie...

Страница 115: ... in the Plot view P You can see that the mean is contained within the 90 confidence interval CI of 0 3469814 to 0 8370186 Hypothesis tests You use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or two populations The tests are based on statistics of samples of the populations The HP 39gII hypothesis tests use the Normal Z distribution or Studen...

Страница 116: ...e of the following alternative hypotheses against which to test the null hypothesis Inputs The inputs are Results The results are H1 μ μ0 H1 μ μ0 H1 μ μ0 Field name Definition Sample mean n Sample size μ0 Hypothetical population mean σ Population standard deviation α Significance level x Result Description Test Z Z test statistic Test Value of associated with the test Z value P Probability associa...

Страница 117: ... Η0 μ1 μ2 You select one of the following alternative hypotheses to test against the null hypothesis Inputs The inputs are Results The results are Critical Boundary value s of required by the α value that you supplied Result Description x x H1 μ1 μ2 H1 μ1 μ2 H1 μ1 μ2 Field name Definition Sample 1 mean Sample 2 mean n1 Sample 1 size n2 Sample 2 size σ1 Population 1 standard deviation σ2 Population...

Страница 118: ...f successes is an assumed value Η0 π π0 You select one of the following alternative hypotheses against which to test the null hypothesis Test Difference in the means associ ated with the test Z value P Probability associated with the Z Test statistic Critical Z Boundary value s of Z associ ated with the α level that you supplied Critical Difference in the means associ ated with the α level you sup...

Страница 119: ...pulations are equal Η0 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 Z Z Test statistic Test Proportion of successes in the sample P Probability associated with the Z Test statistic Critic...

Страница 120: ...lt Description Test Z Z Test statistic Test Difference between the proportions of successes in the two samples that is associated with the test Z value P Probability associated with the Z Test statistic Critical Z Boundary value s of Z associated with the α level that you supplied Critical Difference in the proportion of successes in the two samples associated with the level you supplied Δ p Δ p ...

Страница 121: ...hat the sample mean has some assumed value Η0 μ μ0 You select one of the following alternative hypotheses against which to test the null hypothesis Inputs The inputs are Results The results are H1 μ μ0 H1 μ μ0 H1 μ μ0 Field name Definition Sample mean s Sample standard deviation n Sample size μ0 Hypothetical population mean α Significance level x Result Description Test T T Test statistic Test Val...

Страница 122: ...s is that the two populations means are equal Η0 μ1 μ2 You select one of the following alternative hypotheses against which to test the null hypothesis Inputs The inputs are Critical T Boundary value s of T associated with the α level that you supplied Critical Boundary value s of required by the α value that you supplied Result Description x x H1 μ1 μ2 H1 μ1 μ2 H1 μ1 μ2 Field name Definition Samp...

Страница 123: ...μ the true mean of a population when the true population standard deviation σ is known Pooled Check this option to pool samples based on their standard deviations Field name Definition Result Description Test T T Test statistic Test Difference in the means associated with the test t value P Probability associated with the T Test statistic DF Degrees of freedom Critical T Boundary values of T assoc...

Страница 124: ...ans of two populations μ1 μ2 when the population standard deviations σ1 and σ2 are known Inputs The inputs are Field name Definition Sample mean n Sample size σ Population standard deviation C Confidence level x Result Description C Confidence level Critical Z Critical values for Z Lower Lower bound for μ Upper Upper bound for μ Field name Definition Sample 1 mean Sample 2 mean n1 Sample 1 size n2...

Страница 125: ...ample of size n has a number of successes x Inputs The inputs are Results The results are σ1 Population 1 standard deviation σ2 Population 2 standard deviation C Confidence level Field name Definition Result Description C Confidence level Critical Z Critical values for Z Lower Lower bound for μ Upper Upper bound for μ Δ Δ Field name Definition x Sample success count n Sample size C Confidence leve...

Страница 126: ... populations Inputs The inputs are Results The results are Critical Z Critical values for Z Lower Lower bound for π Upper Upper bound for π Result Description Field name Definition Sample 1 success count Sample 2 success count n1 Sample 1 size n2 Sample 2 size C Confidence level x1 x2 Result Description C Confidence level Critical Z Critical values for Z Lower Lower bound for π Upper Upper bound f...

Страница 127: ...ts are Two Sample T Interval Menu name T int μ1 μ2 This option uses the Student s t distribution to calculate a confidence interval for the difference between the means of two populations μ1 μ2 when the population standard deviations σ1and σ2 are unknown Field name Definition Sample mean s Sample standard deviation n Sample size C Confidence level x Result Description C Confidence level DF Degrees...

Страница 128: ...tandard 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 deviations x1 x2 Result Description C Confidence level DF Degrees of freedom Critical T Critical values for T Lower Lower bound for μ Upper Upper bound for μ Δ Δ ...

Страница 129: ... They take the forms and Getting started with the Parametric app 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 app 1 Open the Parametric app ISelect Parametric Like the function app the Parametric app opens in the Symbolic view x f t y g t x t 5 t y t 5 t cos sin ...

Страница 130: ...S Select Degrees Set up the plot 4 Set up the plot by displaying the graphing options SPLOT SETUP The Plot Setup input form has two fields not included in the Function app 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 ...

Страница 131: ...20 apart instead of nearly continuous and selecting Fixed Step Segments connects the points 120 apart with line segments You are able to explore the graph using the trace zoom split screen and scaling functionality available in the Function app Display the numeric view 8 Display the Numeric view M 9 With a t value selected type in a replacement value and see the table jump to that value You can al...

Страница 132: ...122 Parametric app your own table and the split screen functionality available in the Function app ...

Страница 133: ...re equations in which r is defined in terms of They take the form Getting started with the Polar app Open the Polar app 1 Open the Polar app ISelect Polar Like the Function app the Polar app opens in the Symbolic view Define the expression 2 Define the polar equation tsS zsf dny msfdmjE θ r f θ r 4π θ 2 θ 2 cos cos ...

Страница 134: ...he plot In this example we will use the default settings except for the θRNG fields SSETUP PLOT SCLEAR tSπ Plot the expression 5 Plot the expression P Explore the graph 6 Display the Plot view menu key labels The Plot view options available are the same as those found in the Function app except there is no FCN menu ...

Страница 135: ...c view 7 Display the table of values for θ and R1 in the Numeric view M 8 With a θ value selected type in a replacement value and press and see the table jump to that value You can also zoom in or zoom out on any θ value in the table ...

Страница 136: ...126 Polar app ...

Страница 137: ...etting started with the Sequence app The following example defines and then plots an expression in the Sequence app 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 al...

Страница 138: ...t two is the sum of the preceding two terms for In the Symbolic view of the Sequence app highlight the U1 1 field and begin defining your sequence 1E1E E Note You can use the and menu keys to assist in the entry of expressions Set up the plot 3 In Plot Setup set the SEQPLOT option to Stairstep and reset the default plot settings by clearing the Plot Setup view SSETUP PLOT SCLEAR 8E 8E U1 1 U2 1 Un...

Страница 139: ...cci sequence P 5 In Plot Setup set the SEQPLOT option to Cobweb SSETUP PLOT Select Cobweb P Display the numeric view 6 Display the Numeric view for this example M 7 With any n value selected type in a replacement value and see the table jump to that value ...

Страница 140: ...130 Sequence app ...

Страница 141: ...unt earns interest at a certain rate Financial calculations involving compound interest include savings accounts mortgages pension funds leases and annuities Getting Started with the Finance app Suppose you finance the purchase of a car with a 5 year loan at 5 5 annual interest compounded monthly The purchase price of the car is 19 500 and the down payment is 3 000 What are the required monthly pa...

Страница 142: ...ess E 4 With PV highlighted type 19 500 3 000 and press E 5 Leave P YR and C YR both at 12 their default values Leave End as the payment option Also leave Future Value FV 0 00 6 With PMT highlighted press to obtain a payment of 315 17 i e PMT 315 17 as shown N O T E The payment is negative to indicate it is money owed 7 To determine the maximum loan possible if the monthly payments are only 300 ty...

Страница 143: ...f view The following cash flow diagram shows a loan from the lender s point of view Present value PV Loan Money received is a positive number Money paid out is a negative number Equal periods 1 2 3 4 5 PMT Future value FV Equal payments Payment PMT Payment PMT Payment PMT Payment PMT Cash flow diagrams also specify when payments occur rela tive to the compound ing periods The diagram to the right ...

Страница 144: ...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 an investor PV is the initial investment PV always occurs at the beginning of the first period P YR ...

Страница 145: ...d for payments made at the end of each period 5 Use the arrow keys to highlight the unknown variable and press Example mortgage with balloon payment Suppose you have taken out a 30 year 150 000 house mortgage at 6 5 annual interest You expect to sell the house in 10 years repaying the loan in a balloon payment Find the size of the balloon payment the value of the mortgage after 10 years of payment...

Страница 146: ...alculates the future value of the loan as 127 164 19 N O T E The negative values indicate payments from the homeowner Calculating Amortizations Amortization calculations which also use the TVM variables determine the amounts applied towards principal and interest in a payment or a series of payments To calculate amortizations 1 Start the Finance Solver as indicated at the beginning of this section...

Страница 147: ... balloon payment calculate how much has been applied to the principal how much has been applied to the interest and the remaining balance of the loan after the first 10 years 12x10 120 payments 1 Verify and compare your data from the previous example with the figure to the right 2 Press 3 Scroll down the table to Group 10 to see the same results as shown previously After 10 years 22 835 81 has bee...

Страница 148: ...138 Finance app ...

Страница 149: ...quation and the Linear Solver app will attempt to solve for x and y and z in three equation sets The HP 39gII will alert you if no solution can be found or if there is an infinite number of solutions Getting started with the Linear Solver app The following example defines a set of three equations and then solves for the unknown variables In this example we are going to solve the following equation...

Страница 150: ...cient of x in the first equation Enter that coefficient and press orE 3 The cursor moves to the next co efficient Enter that co efficient press or E and continue doing likewise until you have defined all the equations Once you have entered enough values for the solver to be able to generate solutions those solutions appear on the display In the example at the right the solver was able to find solu...

Страница 151: ... displayed and you want to solve a two equation set press NOTE You can enter any expression that resolves to a numerical result including variables you can enter the name of a stored variable For more information on storing variables see the chapter titled Using mathematical functions ...

Страница 152: ...142 Linear Solver app ...

Страница 153: ...es and one of the angles or you could specify two angles and one length or all three lengths In each case the solver will calculate the remaining lengths or angle measures The HP 39gII will 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 Gettin...

Страница 154: ...we know the length of two sides and the angle at which those sides meet Hence if we specify the lengths of sides A and B we must enter the angle as δ since δ is the angle where A and B meet If instead we entered the lengths as B and C we would need to specify the angle as α The illustration on the display will help you determine where to enter the known values Specify the known values 2 Using the ...

Страница 155: ...Special cases The indeterminate case 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 No solution with given data If you are using the general input form and you enter more than 3 values the ...

Страница 156: ...for the Triangle Solver to be able to 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 ...

Страница 157: ...hanging the y intercept of the line For vertical translations press F3 to change the magnitude of the increment for the translation The and keys as well aswand increase and decrease the slope Press to change the sign of the slope The form of the linear function is shown at the top right of the display with the current equation that matches the graph just below it As you manipulate the graph of the...

Страница 158: ... select each parameter and set its value When you are ready press F4 to see whether or not you have correctly matched your equation to the given graph Press F5 to see the correct answer Press F6 to exit Test mode and return to Graph mode Quadratic Explorer app The Quadratic Explorer app is used to investigate the behaviour of as the values of a h and v change both by manipulating the equation and ...

Страница 159: ...n a student feels that they have correctly chosen the parameters a menu key evaluates the answer and provide feedback An menu key is provided for those who give up Trig Explorer app The Trig Explorer app is used to investigate the behaviour of the graph of as the values of a b c and d change both by manipulating the equation and seeing the change in the graph or by manipulating the graph and seein...

Страница 160: ...change the amplitude and frequency of the graph This is most easily seen by experimenting Press the F1 menu key to toggle from GRAPH to EQ In this mode the graph is controlled by the equation In the equation displayed at the top of the screen one of the parameters is highlighted Press or to increase or decrease the value of the highlighted parameter Press and to move from parameter to parameter Th...

Страница 161: ...B cable Program new apps See the chapter titled Programming for more details Creating new apps based on existing apps You can create a new app based on an existing app To create a new app save an existing app under a new name then modify the app to add the configurations and the functionality that you want Information that defines an app is saved automatically as it is entered into the calculator ...

Страница 162: ...On AHEfAX m AAnAHEgA X m AO nAAE 3 Decide whether you want the app to operate in Degrees or Radians SY Degrees 4 View the App Library The TRIANGLES app is listed in the App Library I The Solve app can now be reset and used for other problems The advantage of storing an app is to allow you to keep a copy of a working environment for later use ...

Страница 163: ... for more details Sending and receiving apps A convenient way to distribute or share problems in class and to turn in homework is to transmit copy apps directly from one HP 39gII to another Transfer of apps between calculators is done with the micro USB cable that comes with each HP 39gII You can also send apps to and receive apps from a PC via the PC Connectivity Kit A USB cable with a micro USB ...

Страница 164: ...er of all data from your PC to your HP 39gII Managing apps The app library is where you go to manage your apps PressI Highlight using the cursor keys the name of the app you want to act on To sort the app list In the app library press Select the sorting scheme and pressE Chronologically produces a chronological order based on the date an app was last used The last used app appears first and so on ...

Страница 165: ...f a key on the keyboard All the rest of the mathematical functions are found in the Math menu Keyboard functions The most frequently used functions are available directly from the keyboard Many of the keyboard functions also accept complex numbers as arguments w s n Add Subtract Multiply Divide Also accepts complex numbers lists and matrices value1 value2 etc h Natural logarithm Also accepts compl...

Страница 166: ...e COS value TAN value Example TAN 45 returns 1 Degrees mode SASIN Arc sine sin 1 x Output range is from 90 to 90 or π 2 to π 2 Inputs and outputs depend on the current angle format Also accepts complex numbers ASIN value Example ASIN 1 returns 90 Degrees mode SACOS Arc cosine cos 1x Output range is from 0 to 180 or 0 to π Inputs and outputs depend on the current angle format Also accepts complex n...

Страница 167: ...rs ATAN value Example ATAN 1 returns 45 Degrees mode j Square Also accepts complex numbers value2 Example 182 returns 324 S Square root Also accepts complex numbers value or expression Example returns 18 k Power x raised to y Also accepts complex numbers value power Example 2 8 returns 256 S Nth root Takes the nth root of x root NTHROOT value Example 3 NTHROOT 8 returns 2 324 n x n ...

Страница 168: ...pressingbopens the Math Functions menu Each of the three menus Math Functions Units and SI Constants has its own menu key The Math menu is organized by category For each category of functions on the left there is a list of function names on the right The highlighted category is the current category When you pressb you see the menu list of Math categories in the left column and the corresponding fu...

Страница 169: ... functions on the right applies to the currently highlighted category on the left Use and to switch between the category list and the function list 3 Highlight the name of the function you want and press This copies the function name and an initial parenthesis if appropriate to the edit line Function categories Calculus Complex numbers Constant Distribution Hyperbolic trigonometry Integer List Loo...

Страница 170: ...le value Example x2 x x 3 returns 5 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 variables expression variable lower upper Example x2 x x 0 3 returns 4 5 Evaluates expression where each given variable is set to the given value Defines numeric evaluation of a...

Страница 171: ...J 3 4 i returns 3 4 i IM Imaginary part y of a complex number x y i IM x y i Example IM 3 4 i returns 4 RE Real part x of a complex number x y i RE x y i Example RE 3 4 i returns 3 Constants The constants available from the Math Functions menu are mathematical constants These are described in this section The HP 39gII has two other menus of constants program constants and physical constants The ph...

Страница 172: ...al Chi square Fisher Poisson and Student s t distributions normald Normal probability density function Computes the probability density at the value x given the mean μ and standard deviation σ of a normal distribution If only a single value x is supplied assumes μ 0 and σ 1 normald μ σ x Example normald 0 5 and normald 0 1 0 5 both return 0 352065326765 normald_cdf Cumulative normal distribution f...

Страница 173: ...probability of success p Returns Comb n k if there is no third argument Note that n and k are integers with binomial n k p Example binomial 4 2 0 5 returns 0 375 binomial_cdf Cumulative binomial distribution function Returns the probability of k or fewer successes out of n trials with a probability of success p for each trial Note that n and k are integers with binomial_cdf n p k Example binomial_...

Страница 174: ...bution function Returns the value x such that the lower tail probability of x with n degrees of freedom is p chisquare_icdf n p Example chisquare_icdf 2 0 952641075609 returns 6 1 fisher Fisher or Fisher Snedecor probability density function Computes the probability density at the value x given numerator n and denominator d degrees of freedom fisher n d x Example fisher 5 5 2 returns 0 15808023109...

Страница 175: ...poisson 4 2 returns 0 14652511111 poisson_cdf Cumulative poisson distribution function Returns the probability x or fewer occurrences of an event in a given time interval given expected occurrences poisson_cdf x Example poisson_cdf 4 2 returns 0 238103305554 poisson_icdf Inverse cumulative poisson distribution function Returns the value x such that the probability of x or fewer occurrences of an e...

Страница 176: ... probability of x with n degrees of freedom is p student_icdf n p Example student_icdf 3 0 0246659214813 returns 3 2 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 sinh 1x ASINH value ATANH Inverse hyperbolic tangent tanh 1 x ATANH value COSH Hyperbolic cosin...

Страница 177: ...er ichinrem Integer Chinese Remainder Theorem for two equations Takes two lists a p and b q and returns a list of two integers r n such that x r modn In this case x is such that modp and modq also ichinrem a p b q Example ichinrem 2 7 3 5 returns 12 35 idivis Integer divisors Returns a list of all the factors of the integer a idivis a Example idivis 12 returns 1 2 3 4 6 12 iegcd Integer extended g...

Страница 178: ...e integer that is the greatest common divisor of the integers a and b igcd a b Example igcd 24 36 returns 12 iquo Euclidean quotient Returns the integer quotient when the integer a is divided by the integer b iquo a b Example iquo 46 21 returns 2 iquorem Euclidean quotient and remainder Returns the integer quotient and remainder when the integer a is divided by the integer b iquorem a b Example iq...

Страница 179: ...the next prime number after the integer a nextprime a Example nextprime 1 1 returns 13 powmod Power and modulo For the integers a n and p returns modp powmod a n p Example powmod 5 2 13 returns 12 prevprime Previous prime Returns the previous prime number before the integer a prevprime a Example prevprime 1 1 returns 7 euler Euler s phi or totient function Takes a positive integer x and returns th...

Страница 180: ...functions work on list data See the chapter Lists for details 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 variable The value for variable is updated each time starting with initialvalue ITERATE expression variable initialvalue times Example ITERATE X2 X 2 3 returns 256 Σ S...

Страница 181: ...ied roots POLYCOEF roots Example To find the polynomial with roots 2 3 4 5 POLYCOEF 2 3 4 5 returns 1 2 25 26 120 representing x4 2x3 25x2 26x 120 POLYEVAL Polynomial evaluation Evaluates a polynomial with the specified coefficients for the value of x POLYEVAL coefficients value Example For x4 2x3 25x2 26x 120 POLYEVAL 1 2 25 26 120 8 returns 3432 POLYROOT Polynomial roots Returns the roots for th...

Страница 182: ...s them individually in calculations by referring to M1 1 M1 2 etc Probability functions COMB Number of combinations without regard to order of n things taken r at a time n r n r COMB n r Example COMB 5 2 returns 10 That is there are ten different ways that five things can be combined two at a time Factorial of a positive integer For non integers Γ x 1 This calculates the gamma function value Examp...

Страница 183: ...he F distribution evaluated at value Returns the probability that a Snedecor s F random variable is greater than value UTPF numerator denominator value UTPN Upper Tail Normal Probability given mean and variance evaluated at value Returns the probability that a normal random variable is greater than value for a normal distribution Note the variance is the square of the standard deviation UTPN mean ...

Страница 184: ... initial estimate FNROOT expression variable guess Example FNROOT M 9 8 600 1 M 1 returns 61 224489796 FRAC Fractional part FRAC value Example FRAC 23 2 returns 2 HMS Hours minutes seconds to decimal Converts a number or expression in H MMSSs format time or angle that can include fractions of a second to x x format number of hours or degrees with a decimal fraction HMS H MMSSs Example HMS 8 30 ret...

Страница 185: ...eater of two values MAX value1 value2 Example MAX 210 25 returns 210 MIN Minimum The lesser of two values MIN value1 value2 Example MIN 210 25 returns 25 MOD Modulo The remainder of value1 value2 value1 MOD value2 Example 9 MOD 4 returns 1 x percent of y that is x 100 y x y Example 20 50 returns 10 CHANGE Percent change from x to y that is 100 y x x CHANGE x y Example CHANGE 20 50 returns 150 ...

Страница 186: ...s Round can also round to a number of significant digits as showed in the second example below 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 a complex number this is the unit vector in the direction of the number SIGN value SIGN x y Example SIGN 2 returns 1 SIGN 3 4 returns 6 8 TRUNCATE...

Страница 187: ...turns 1 if true 0 if false value1 value2 Not equal to Returns 1 if true 0 if false value1 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 IFT...

Страница 188: ... of them is non zero otherwise returns 0 value1 XOR value2 Trigonometry functions The trigonometry functions can also take complex numbers as arguments For SIN COS TAN ASIN ACOS and ATAN see the Keyboard category ACOT Arc cotangent ACOT value ACSC Arc cosecant ACSC value ASEC Arc secant ASEC value COT Cotangent cosx sinx COT value CSC Cosecant 1 sinx CSC value SEC Secant 1 cosx SEC value ...

Страница 189: ...on numbers without units attached except that the units are carried along with the operations The function usimplify unit simplify will simplify the results back to the simplest unit structure The units are found in the Units menu Like the Math menu the Units menu is divided into a set of categories on the left and units in each category on the right The categories are Unit categories Suppose you ...

Страница 190: ...To continue the example we divide this result by 4 seconds and convert the result to kilometers per hour n4 b to select Time to select _s E The result is shown as 8 175 cm s 4 Now convert the result to kilometers per hour b 5 times to select Functions to select convert l to select 8 175_ cm s 1ob 6 times to select Speed 4 times to select _km h The result is shown as 0 2943 kilometers per hour ...

Страница 191: ... to navigate through the options 4 While in the Physical Constants menu pressing toggles between showing the entire value of the constant and a description of the constant in the help line To attach units to the constant when you paste it into the command line keep active when you press to paste just the value without units de activate before pressing 5 To use the selected constant in a calculatio...

Страница 192: ... the mass and multiplication 5 s 2 Go to the Physical Constants menu b 3 Select the speed of light to select Physics to select c 4 Enter the speed of light into the current expression 5 Square the speed of light and evaluate the expression jE ...

Страница 193: ...in Home or in a program 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 SLIST You can also create and store lists named or unnnamed in Home List variables are identical in behavior to the columns C1 C0 in the Statistics 2Var app and the columns D1 D0 in the Statistics 1Var app You can ...

Страница 194: ... 4 When done pressSLIST to see the List catalog or pressHto return to Home List Catalog keys The list catalog keys are The List Editor Press to create or edit a list Once you press this menu key you enter the List Editor The List Editor is a special environment for entering data into lists Key Meaning Opens the highlighted list for editing or C Deletes the contents of the selected list Transmits t...

Страница 195: ...u want to edit L1 etc and press to display the list contents Key Meaning Inserts a new value before the highlighted item Copies the highlighted list item into the edit line Toggles between large and small fonts Toggles between showing 1 2 3 or 4 lists at a time or C Deletes the highlighted item from the list SCLEAR Clears all elements from the list S or Moves to the end or the beginning of the lis...

Страница 196: ... value 9 in L1 2 in the list L1 shown to the right 1 Move to the insertion point and insert the new value 9 Deleting lists To delete a list In the List catalog highlight the list name and pressC You are prompted to confirm that you want to delete the contents of the highlighted list variable PressEto delete the contents orOto cancel the deletion To delete all lists In the List catalog pressSCLEAR ...

Страница 197: ...st in the Home view type its name and pressE To display one element To display one element of a list in the Home view enter listname element For example if L2 is 3 4 5 6 then L2 2 Ereturns 4 To store one element To store a value in one element of a list in the Home view enter value listname element For example to store 148 as the second element in L2 type 148 L2 2 E To transmit a list You can send...

Страница 198: ...ns have the following syntax Functions have arguments that are enclosed in parentheses and separated by commas Example CONCAT L1 L2 An argument can be either a list variable name such as L1 or the actual list For example REVERSE 1 2 3 Common operators like and can take lists as arguments If there are two arguments and both are lists then the lists must have the same length since the calculation pa...

Страница 199: ... x2 xn xn 1 ΔLIST list1 Example In Home store 3 5 8 12 17 23 in L5 and find the first differences for the list HS 3 5 8 12 17 23S AL 5E b7 2AL 5E MAKELIST Calculates a sequence of elements for a new list Evaluates expression with respect to variable as variable takes on values from begin to end values taken at increment steps MAKELIST expression variable begin end increment The MAKELIST function g...

Страница 200: ...e 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 element POS list element Example POS 3 7 12 19 12 returns 3 REVERSE Creates a list by reversing the order of the elements in a list REVERSE list Example REVERSE 1 2 3 returns 3 2 1 SIZE Calculates the number of ele...

Страница 201: ...ts To find values such as the mean median maximum and minimum of a list use the Statistics 1Var app Example In this example use the Statistics 1Var app 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 S 88o90 o89o65 o70o89 S AL1E 2 In Home store L1 into D1 You will then be able to see the list data in the Numeric view o...

Страница 202: ...his is done in the Symbolic view Y By default H1 is defined to use D1 so nothing further remains to be done in the Symbolic view however if the data were in D2 or any column other than D1 you would have to enter the desired data column here 5 Calculate summary statistics M 6 Press when you are done See the chapter titled Statistics 1Var for the meaning of each computed statistic ...

Страница 203: ...e 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 at least one column Two dimensional matrices are represented with nested brackets for example 1 2 3 4 5 6 You can create complex matrices for example 1 2 3 4 4...

Страница 204: ...h the number of its elements You can also create and store matrices named or unnamed in Home For example the command POLYROOT 1 0 1 0 M1 stores the roots of the complex vector of length 3 into the M1 variable M1 now contains the three roots of Matrix Catalog keys The table below lists the operations of keys in the Matrix Catalog x 3 x 0 Key Meaning Opens the highlighted matrix for editing orC Clea...

Страница 205: ... of zeros to the left of the highlighted cell You are prompted to choose row or column WIDTHn Toggles between showing 1 2 3 or 4 columns at a time in the Matrix Editor Switches between larger and smaller font sizes A three way toggle for cursor advancement in the Matrix editor advances to the right advances downward and does not advance at all C Deletes the highlighted cell replacing it with a zer...

Страница 206: ...e the direction of the highlight bar by pressing The menu key toggles between the following options specifies that the cursor moves to the cell below the current cell when you pressE specifies that the cursor moves to the cell to the right of the current cell when you pressE specifies that the cursor stays in the current cell when you pressE 5 When done pressSMATRIX to see the Matrix catalog or pr...

Страница 207: ...the matrix and it will be evaluated To display a matrix In Home enter the name of the matrix variable and pressE To display one element In Home enter matrixname row column For example if M2 is 3 4 5 6 then M2 1 2 Ereturns 4 To store one element In Home enter value matrixname row column For example to change the element in the first row and second column of M5 to 728 then display the resulting matr...

Страница 208: ... Press 5 The transfer will occur immediately 6 Open the List Catalog on the receiving calculator to see the new list 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 example...

Страница 209: ...d for the previous example press the following keys AM1sAM2 E 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...

Страница 210: ...uivalent to M2 1 M1 To divide the two matrices M1 and M2 that you created for the previous example press the following keys AM1nAM2 E To invert a matrix You can invert a square matrix in Home by typing the matrix or its variable name and pressingSx 1 E Or you can use the matrix INVERSE command 1 from the Matrix category of the Math menu To negate each element You can change the sign of each elemen...

Страница 211: ...vector of the constants in the linear system 5 E7E 1 E 3 Return to the Matrix Catalog SMATRIX In this example the vector you created is listed as M1 4 Create a new matrix C 5 Enter the equation coefficients 2E3E 4E 1E1E 1E4E 1E2E In this example the matrix you created is listed as M2 ...

Страница 212: ...me as well as in programs Functions always produce and display a result They do not change any stored variables such as a matrix variable Functions have arguments that are enclosed in parentheses and separated by commas for example CROSS vector1 vector2 The matrix input can be either a matrix variable name such as M1 or the actual matrix data inside brackets For example CROSS M1 1 2 About commands...

Страница 213: ... 1 norm column norm of a square matrix COND matrix CROSS Cross Product of vector1 with vector2 CROSS vector1 vector2 DET Determinant of a square matrix DET matrix DOT Dot Product of two arrays matrix1 and matrix2 DOT matrix1 matrix2 EIGENVAL Displays the eigenvalues in vector form for matrix EIGENVAL matrix EIGENVV Eigenvectors and Eigenvalues for a square matrix Displays a list of two arrays The ...

Страница 214: ...KEMAT Make Matrix Creates a matrix of dimension rows columns using expression to calculate each element If expression contains the variables I and J then the calculation for each element substitutes the current row number for I and the current column number for J MAKEMAT expression rows columns Example MAKEMAT 0 3 3 returns a 3 3 zero matrix 0 0 0 0 0 0 0 0 0 QR QR Factorization Factors an m n mat...

Страница 215: ...ZE matrix SPECNORM Spectral Norm of matrix SPECNORM matrix SPECRAD Spectral Radius of a square matrix SPECRAD matrix SVD Singular Value Decomposition Factors an m n matrix into two matrices and a vector m m square orthogonal n n square orthogonal real SVD matrix SVL Singular Values Returns a vector containing the singular values of matrix SVL matrix TRACE Finds the trace of a square matrix The tra...

Страница 216: ...en they are not equal Transposing a Matrix The TRN function swaps the row column and column row elements of a matrix For instance element 1 2 row 1 column 2 is swapped with element 2 1 element 2 3 is swapped with element 3 2 and so on For example TRN 1 2 3 4 creates the matrix 1 3 2 4 Reduced Row Echelon Form The following set of equations can be written as the augmented matrix which can then be s...

Страница 217: ...ill also work with inconsistent matrices resulting from systems of equations which have no solution or infinite solutions For example the following set of equations has an infinite number of solutions The final row of zeros in the reduced row echelon form of the augmented matrix indicates an inconsistent system with infinite solutions x y z 5 2x y 7 x 2y z 2 ...

Страница 218: ...208 Matrices ...

Страница 219: ...app When you save the app or send it to another calculator this note is saved or sent as well The Notes Catalog Subject to available memory you can store as many notes as you want in the Note Catalog These notes are independent of any app The Note Catalog lists the existing entries by name The list does not include notes that were created in any apps Info view but these can be copied and pasted us...

Страница 220: ...key to exit the Note Editor Your work is automatically saved To access your new note return to the Note Catalog While you are in the Note Catalog you can use the following keys Notes 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 39gII or PC orC Deletes the selected note SCLEAR Deletes all notes in the ca...

Страница 221: ... are in the Note or Info Editors you can use the following keys Key Meaning Opens the text formatting menu See Formatting options later in this chapter Space key for text entry Moves from page to page in a multi page note Starts text selection Use the arrow keys to select existing text for formatting C Backspaces cursor and deletes character E Starts a new line SCLEAR Erases the entire note a Menu...

Страница 222: ...h cases for one keystroke by pressingS to switch cases and lock pressSA Text formatting You can format text in any Note or Info To format existing text follow these steps 1 Open the Note or Info view 2 Move the cursor to the beginning of the text you wish to format 3 Press SCHARS Displays special characters To type one highlight it and press To copy a character without closing the Chars menu press...

Страница 223: ... formatting option on the right 6 Use and to select the formatting category Use to switch to the right column and then use and again to select the formatting option you wish to apply to the selected text 7 Press to apply or to cancel Formatting Options The formatting options are listed in the table below Category Options Align Text alignment Left Center Right Font Font size Small Large FG Color Fo...

Страница 224: ...e cursor to the beginning of the text you wish to copy and begin text selection 3 Move the cursor to the end of the text you wish to format 4 Copy the selected text to the clipboard SCOPY 5 Open the app s Info view ISelect Function SINFO 6 Move the cursor to the location where you want the copied text to be pasted and open the clipboard SPASTE Bullets Level 1 Level 2 Level 3 Style Font style Under...

Страница 225: ... and highlight the name of the variable G1 etc 4 Press to recall the contents of the graphic variable and then press To transmit a note You can send notes between calculators just as you can send apps programs matrices and lists 1 Connect the two HP 39gII calculators with the micro USB cable provided with the calculators and turn both calculators on 2 Open the Notes Catalog on the sending calculat...

Страница 226: ...216 Notes and Info ...

Страница 227: ...object that you create in memory to hold data The HP39gII has three types of variables Home variables App variables and User variables Home variables are available in all apps For example you can store real numbers in variables A to Z and complex numbers in variables Z0 to Z9 These can be numbers you have entered or the results of calculations These variables are available within all apps and with...

Страница 228: ...r Engineering A displayed number has only the precision that is displayed If you copy it from the Home view display history you obtain only the precision 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 In the Home view enter a value expression or object followed by the Store command H5 2 Enter ...

Страница 229: ...re 3 Copy the result to the edit line 4 Store the result AA E The results of a calculation can also be stored directly to a variable For example 2 k l5n3 m ABE To recall a value To recall a variable s value type the name of the variable and pressE AAE To use variables in calculations You can use variables in calculations The calculator substitutes the variable s value in the calculation 65 AAE ...

Страница 230: ...y For each variable category in the left column there is a list of variables in the right column You select a category and then select a variable in the category 1 Open the Vars menu and press a 2 Use the cursor keys or press the number of the category 1 5 to select a variable category In the figure to the right the Matrix category has been selected 3 Move the highlight to the variables column 4 U...

Страница 231: ...ace the contents 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 SLIST to select L1 2 Enter the data fo...

Страница 232: ...he List Catalog to create L2 SLIST to select L2 4 Enter data for L2 55 48 86 90 77 5 PressHto access Home 6 Open the variable menu and select L1 a 7 Copy it to the command line 8 Insert the operator and select the L2 variable from the List variables a ...

Страница 233: ...es You can create up to ten matrices and you can store these in variables M0 to M9 You cannot store matrices in variables other than M0 to M9 Category Available names Complex numbers Z0 to Z9 To store a complex number enter it in the form For example Z1 Lists L0 to L9 For example 1 2 3 L1 Matrices M0 to M9 Store matrices and vectors in these variables See the chapter Matrices for more information ...

Страница 234: ...e 1 Open the app that contains the variable you want ISelect Function 2 Go to where you want to paste the variable H 3 Open the Vars menu and switch to the App Vars menu V to select App Vars 4 Use the cursor keys to select the view and then the variable you want to select Plot to select Ymax 5 To copy the variable name to the edit line press to copy the variable contents press and You can qualify ...

Страница 235: ...ll as declaring them local or global see the chapter Programming Memory Manager Use the Memory Manager to view the amount of available memory and organize it If the available memory is low use the Memory Manager to determine which variables you might delete to free up memory You can also use the Memory manager to send sets of variables to another HP 39gII or to clone your entire memory to another ...

Страница 236: ...e and the total memory used by the variables of that type 2 Select a category and press Memory Manager opens the selected catalog or library so you can edit delete or clear variables of a selected type To delete variables in a category PressCto delete the selected variable PressSCLEAR to delete all variables in the selected category C Deletes the contents of all variables of the selected type SC D...

Страница 237: ...fer will occur immediately 6 Open the Memory Manager on the receiving calculator to see the new variables To clone your HP 39gII You can clone the entire memory of your HP 39gII to another HP 39gII calculator effectively copying your HP 39gII to another HP 39gII This is helpful if you want to backup your calculator s memory or in settings where calculators in a classroom or in a group require simi...

Страница 238: ...228 Variables and memory management ...

Страница 239: ... separated by a semicolon Commands that take multiple arguments have those arguments enclosed in parentheses and separated by a comma For example PIXON xposition yposition Sometimes arguments to a command are optional If an argument is omitted a default value is used in its place In the case of the PIXON command a third argument could be used that specifies the color of the pixel PIXON xposition y...

Страница 240: ...each of which is a function or procedure Subroutines start with a heading consisting of the name followed by parentheses that contain a list of parameters or arguments separated by commas The body of a subroutine is a sequence of statements enclosed within a BEGIN END pair For example the body of a simple program called MYPROGRAM could look like this EXPORT MYPROGAM BEGIN PIXON 1 1 END Comments Wh...

Страница 241: ... the active app This entry is the app program for the active app if such a program exists See the section on App Programming Before starting to work with programs you should take a few minutes to become familiar with the Program Catalog menu keys You can use any of the following keys both menu and keyboard to perform tasks in the Program Catalog Program catalog keys The program catalog keys are Ke...

Страница 242: ...EXPORT MYPROGRAM and a BEGIN END pair that blocks off the statements for the function H I N T A program name can contain only alphanumeric characters letters and numbers and the underscore character The first character must be a letter For example GOOD_NAME and Spin2 are valid program names while HOT STUFF no space allowed and 2Cool starts with number and no are not valid S or S Moves to the begin...

Страница 243: ... menu The Program Templates menu contains structures that control execution flow such as IF THEN statements and FOR loops Use the cursor keys to highlight a command and press to paste the command into the program at the cursor position 3 Insert a FOR loop Select Loop Select FOR Again a template is inserted Use the keyboard to fill in the missing parts of the command then position the cursor on the...

Страница 244: ...ommand that you want and press to paste the command into the program You can also use keyboard shortcuts indicated in the menu title bar in the Program Commands menu to quickly select a command 4 Insert the MSGBOX Message Box command SCMDS or enter 5 Select I O switch columns or enter 6 Select MSGBX 5 Fill in the arguments to the MSGBOX command and type a semicolon at the end of the command ...

Страница 245: ... program with open and closing parentheses after it If the program takes any arguments insert these in the parentheses separated by commas Press E From the Program Catalog highlight the program you want to run and press When a program is executed from the catalog the system looks for a function named START no parameters If it finds one that function is executed Otherwise it looks for a function wi...

Страница 246: ...ng the key the HP 39gII returns you to the Program catalog when the program ends Debug a Program You cannot run a program that contains syntax errors You must first correct all the syntax errors before executing the program If there is an error detected at run time such as division by zero the program will stop and you will see an error message If the program does not do what you expect it to do o...

Страница 247: ...ext command F3 Step in F4 Continue F5 Stop program execution F6 Display Help 2 Execute the first command 2 The FOR loop starts and the pointer moves to Line 2 3 Execute Line 2 2E The message box appears Note that when each message box is displayed you still have to dismiss the message box by pressing E Press 2and Erepeatedly to execute the program step by step When the next instruction to be execu...

Страница 248: ...The name of your program appears in the title bar of the display You can use the following keys to edit your program Editing Keys Keys Meaning Inserts the STORE character at the cursor location Checks the current program for errors Displays previous page of the program Displays next page of the program Displays the catalog of program commands Select a command and press Eto insert the command into ...

Страница 249: ...Backspace SCLEAR Erases the entire program a Displays menus for selecting variable names contents of variables functions names and constants b Displays menus for selecting mathematical functions units and constants SCMDS Displays menus for selecting program conmmands SCHARS Displays all characters To type one highlight it and press To enter several characters in a row while in the Chars menu Keys ...

Страница 250: ... highlighted as you move the cursor 6 When all the commands you want are highlighted press SCOPY to copy the selected commands to the clipboard 7 Return to the Program Catalog and open the target program 8 Move the cursor to the line where you wish to insert the copied commands 9 Press SPASTE and the clipboard will open Your commands will be first in the list and highlighted already so just press ...

Страница 251: ... calculators and turn both calculators on 2 Open the Program Catalog on the sending calculator 3 Highlight the name of the program to send 4 Press 5 The transfer will occur immediately 6 Open the Program Catalog on the receiving calculator to see the new list The HP 39gII Programming Language Variables and visibility Variables in an HP 39gII program can be used to store numbers lists matrices grap...

Страница 252: ...pter Variables and programs Within a program you can declare variables for use only within a particular function This is done using a LOCAL declaration The use of LOCAL variables allows the programmer to declare and use variables that will not affect the rest of the calculator LOCAL variables declared by the programmer are not bound to a particular type That is you can store floating point numbers...

Страница 253: ...ogram you could reference that variable using the name of the program followed by the two colons and the variable name Variables declared in a program should have descriptive names For example a variable used to store the radius of a circle can be named RADIUS If such a variable is needed after the program executes it can be exported from the program using the EXPORT command To do this the first c...

Страница 254: ...the same way that this is done for variables This feature makes the HP39gII an incredibly powerful programming platform In this section we will create a small set of programs each illustrating some aspect of programming on the HP 39gII Each of these programs will be used as a building block for a custom app described in the next section App Programs Here is a program that defines a function called...

Страница 255: ...are stored into the list L2 so that L2 1 shows the number of times the dies came up with a 1 L2 2 shows the frequency of 2 s etc L2 1 should be 0 as a result Program ROLLMANY EXPORT ROLLMANY n sides BEGIN LOCAL k roll initialize list of frequencies MAKELIST 0 X 1 2 sides 1 L2 FOR k FROM 1 TO n DO ROLLDIE sides ROLLDIE sides roll L2 roll 1 L2 roll END END This program uses a FOR loop explained in t...

Страница 256: ...could be returned as the result of calling ROLLMANY instead of being stored directly into the global list variable L2 This way if the user wanted to store the results elsewhere it could be done easily EXPORT ROLLMANY n sides BEGIN LOCAL k roll results MAKELIST 0 X 1 2 sides 1 results FOR k FROM 1 TO n DO ROLLDIE sides ROLLDIE sides roll results roll 1 results roll END RETURN results END On the Hom...

Страница 257: ...views in the Views menu Using dedicated program functions There is a set of special program names which run the named programs if they exist These programs are run on the keyboard events shown in the table below These program functions are designed to be used in the context of an app Program Name Keystrokes Symb Symbolic view Y SymbSetup Symbolic Setup SY Plot Plot view P PlotSetup Plot Setup SP N...

Страница 258: ...custom app A useful procedure for customizing an app is illustrated below 1 Decide on the HP app that you want to customize For example you could customize the Function app or the Statistics 1Var app The customized app inherits all the properties of the HP app Go to the apps Catalog and save the customized app with a unique name 2 Customize the new app if you need to by configuring the settings fo...

Страница 259: ...app This app creates an environment to simulate the rolling of a pair of dice each with a number of sides specified by the user The results are tabulated and can be viewed either in a table or graphically The app is based on the Statistics 1Var app 1 Save the Statistics 1Var app with a unique name Iselect Statistics 1Var 2 Name the app DiceSimulation and press the OK menu key AAD SAice A A AS SAim...

Страница 260: ...pecify number of times to roll the dice RESET start over The START option will initialize the app and display a note embedded in the app containing instructions for the user The user will also interact with the app through the Numeric view and the Plot view These views will be activated by pressing Mand P but the functions Num and Plot in our app program will actually launch those views after doin...

Страница 261: ...IEWS Roll Dice ROLLMANY BEGIN LOCAL k roll MAKELIST X 1 X 1 2 SIDES 1 1 D1 MAKELIST 0 X 1 2 SIDES 1 1 D2 FOR k FROM 1 TO ROLLS DO Roll ROLLDIE SIDES ROLLDIES SIDES D2 roll 1 1 D2 roll 1 END 1 Xmin MAX D1 1 Xmax 0 Ymin MAX D2 1 Ymax STARTVIEW 1 1 END VIEWS Set Sides SETSIDES BEGIN REPEAT INPUT SIDES Die Sides N Enter num sides 2 FLOOR SIDES SIDES ...

Страница 262: ...X You must enter a number 1 END UNTIL ROLLS 1 END Plot BEGIN 1 Xmin MAX D1 1 Xmax 0 Ymin MAX D2 1 Ymax STARTVIEW 1 1 END The ROLLMANY routine is another adaptation from a program presented previously in this chapter Since you cannot pass parameters into a program called through a selection from a custom Views menu the exported variables SIDES and ROLLS are used in place of the parameters that were...

Страница 263: ...CESIMVARS Store it into a new user program The program DICESIMVARS EXPORT ROLLS SIDES EXPORT DICESIMVARS BEGIN 10 ROLLS 6 SIDES END Press Vto see the custom app menu Here you can set the number of sides of the dice the number of rolls and execute a simulation After running a simulation press Pto see a histogram of your simulation results ...

Страница 264: ...pp STARTVIEW Syntax STARTVIEW draw Starts the nth view of the current app If draw is true non 0 it will force an immediate redrawing of the screen for that view The view numbers are as follows Symbolic 0 Plot 1 Numeric 2 Symbolic Setup 3 Plot Setup 4 Numeric Setup 5 App Info 6 Views Menu 7 First special view Split Screen Plot Detail 8 Second special view Split Screen Plot Table 9 Third special vie...

Страница 265: ...ands The block commands determine the beginning and end of a sub routine or function There is also a Return command to recall results from sub routines or functions BEGIN END Syntax BEGIN stmt1 stm2 stmtN END A command list is a list of single statements enclosed within a BEGIN END pair Command lists appear as the body of a function RETURN Syntax RETURN expression Returns the current value of expr...

Страница 266: ... Syntax IF test THEN command s 1 ELSE command s 2 END Evaluate test If test is true non 0 execute command s 1 otherwise execute command s 2 IFTE Syntax IFTE test true_xpr false_xpr Evaluates test If test is true non 0 return true_xpr otherwise return false_xpr IFERR THEN END IFERR commands1 THEN commands2 ELSE commands3 END Executes sequence of commands1 If an error occurs during execution of comm...

Страница 267: ...variables Thirteen of them work based on Cartesian coordinates using the Cartesian plane defined in the current app by the variables Xmin Xmax Ymin and Ymax in the plot setup menu Thirteen of them work on pixel coordinates where the pixel 0 0 is the top left pixel of the GROB and 255 126 is the bottom right This second set of function has a _P suffix on the function name PIXON and PIXON_P Syntax P...

Страница 268: ...1 y1 are optional The default values represent the top left of the graphic x2 y2 are optional The default values represent the bottom right of the graphic edgecolor and fillcolor can be 1 to 3 1 transparent 0 black 1 dark gray 2 light gray 3 white edgecolor is optional The default is white fillcolor is optional The default is edgecolor Note To erase a GROB execute RECT G To clear the screen execut...

Страница 269: ...RT_P G x1 y1 x2 y2 Inverts a rectangle on G between points x1 y1 and x2 y2 This means that every black pixel becomes white and vice versa In the same way Light gray and dark gray are inverted G can be any of the graphic variables and is optional The default is G0 x2 y2 are optional and if not specified will be the bottom right of the graphic x1 y1 are optional and if not specified will be the top ...

Страница 270: ...G0 c can be 0 to 3 0 black 1 dark gray 2 light gray 3 white c is optional The default is black TEXTOUT and TEXTOUT_P Syntax TEXTOUT text G x y font c1 width c2 TEXTOUT_P text G x y font c1 width c2 Draws text using color c1 on graphic G at position x y using font Do not draw text more than width pixels wide and erase the background before drawing the text using color c2 G can be any of the graphic...

Страница 271: ...TEXTOUT_P N 0 0 TEXTOUT_P PI APPROX 0 30 REPEAT A sign 4 2 K 1 A TEXTOUT_P K 35 0 2 0 100 3 TEXTOUT_P A 90 30 2 0 100 3 sign 1 sign K 1 K UNTIL 0 END The program executes until the user presses Oto terminate The spaces after K the number of the term and A the current approximation in the TEXTOUT_P commands are there to overwrite the previously displayed value BLIT and BLIT_P Syntax BLIT trgtGRB dx...

Страница 272: ...tGRB c can be 0 to 3 0 black 1 dark gray 2 light gray 3 white c is optional If not specified all pixels from G2 will be copied N O T E Using the same variable for trgtGRB and srcGRB can be unpredictable when the source and destination overlap DIMGROB and DIMBROB_P Syntax DIMGROB G w h c or DIMGROB G line_1 line_2 line_h DIMGROB G w h c or DIMGROB G line_1 line_2 line_h Sets the dimensions of GROB ...

Страница 273: ...variables except G0 x2 y2 are optional and if not specified will be the bottom right of srcGRB x1 y1 are optional and if not specified will be the top left of srcGRB N O T E SUBGROB G1 G4 will copy G1 in G4 GROBH and GROBH_P Syntax GROBH G GROBH_P G Returns the height of G G can be any of the graphic variables and is optional The default is G0 GROBW and GROBW_P Syntax GROBW G GROBW_P G Returns the...

Страница 274: ...ntax INPUT var title label help default Starts a dialog box with the title text title with one field named label displaying help at the bottom and using the default value Updates the variable var if the user presses and returns 1 If the user presses it does not update the variable and returns 0 Example EXPORT SIDES EXPORT GETSIDES BEGIN INPUT SIDES Die Sides N Enter num sides 2 END PRINT Syntax PR...

Страница 275: ...le on the terminal EXPORT AREACALC BEGIN LOCAL radius INPUT radius Radius of Circle r Enter radius 1 PRINT The area is radius 2 END Notice the use of the LOCAL variable for the radius and the naming convention that uses lower case letters for the local variable Adhering to such a convention will improve the readability of your programs GETKEY Syntax GETKEY Returns the ID of the first key in the ke...

Страница 276: ...and false 0 if it is not MSGBOX Syntax MSGBOX expression or string ok_cancel Displays a message box with the value of the given expression or string If ok_cancel is true displays and menu keys otherwise only displays the key Default value for ok_cancel is false Returns true non zero if the user presses false 0 if the user presses ...

Страница 277: ...en title and containing the choose items If the user selects an object the variable whose name is provided will be updated to contain the number of the selected object an integer 1 2 3 or 0 if the user presses Returns true non zero if the user selects an object otherwise return false 0 Example CHOOSE N Pick Hero Euler Gauss Newton IF N 1 PRINT You picked Euler END ELSE IF N 2 PRINT You picked Gaus...

Страница 278: ...s than or equal to finish executes the sequence of commands and then adds 1 increment to var Example 1 This program determines which integer from 2 to N has the greatest number of factors EXPORT MAXFACTORS N BEGIN LOCAL cur max k result 1 max 1 result FOR k FROM 2 TO N DO SIZE idivis k cur IF cur max THEN cur max k result END END MSGBOX Max of max factors for result In Home enter MAXFACTORS 100 Ex...

Страница 279: ...FLOOR X 2 Y 2 MOD 4 PIXON X Y color END END FREEZE END REPEAT UNTIL Syntax REPEAT commands UNTIL test Repeats the sequence of commands until test is true non 0 This code prompts for a positive value for SIDES modifying an earlier program in this chapter Example EXPORT SIDES EXPORT GETSIDES BEGIN REPEAT INPUT SIDES Die Sides N Enter num sides 2 UNTIL SIDES 0 END WHILE DO END Syntax WHILE test DO co...

Страница 280: ...number because 6 1 2 3 This function returns true when its argument is a perfect number Example EXPORT ISPERFECT n BEGIN LOCAL d sum 2 d 1 sum WHILE sum n AND d n DO IF irem n d 0 THEN sum d sum END d 1 d END RETURN sum n END This program displays all the perfect numbers up to 1000 EXPORT PERFECTNUMS BEGIN LOCAL k FOR k FROM 2 TO 1000 DO IF ISPERFECT k THEN MSGBOX k is perfect press OK END END END...

Страница 281: ...alues must be separated by commas and the number of values must be the same as the number of rows in the matrix name ADDROW Syntax ADDROW name value1 valuen row_number Add Row Inserts values into a row before row_number in the specified matrix You enter the values as a vector these are not optional arguments The values must be separated by commas and the number of values must be the same as the nu...

Страница 282: ...tart for a matrix is a list containing two numbers for a vector it is a single number REPLACE also works with lists and graphics SCALE Syntax SCALE name value rownumber Multiplies the specified row_number of the specified matrix by value SCALEADD Syntax SCALEADD name value row1 row2 Multiplies the specified row1 of the matrix name by value then adds this result to the second specified row2 of the ...

Страница 283: ...DRAW returns QUICKDRAW Example 2 32 X X X returns X 32 asc Syntax asc str Returns a vector containing the ASCII codes of string str Example asc AB returns 65 66 char Syntax char vector or int Returns the string corresponding to the character codes in vector or the single code int Examples char 65 returns A char 82 77 72 returns RMH dim Syntax dim str Returns the number of characters in string str ...

Страница 284: ... string representation of the object The result varies depending on the type of object For example string 2 3 results in string 2 3 Examples inString Syntax inString str1 str2 Returns the index of the first occurrence of str2 in str1 Returns 0 if str2 is not present in str1 Note that the first character in a string is a position 1 Examples inString vanilla van returns 1 inString banana na returns ...

Страница 285: ...yntax rotate str n Permutation of characters in string str If 0 n dim str shifts n places to left If dim str n 1 shifts n spaces to right If n dim str or n dim str returns str Examples rotate 12345 2 returns 34512 rotate 12345 1 returns 51234 rotate 12345 6 returns 12345 Test Commands The Test commands include both Boolean and relational operations Boolean and relational expressions evaluate to tr...

Страница 286: ...bject2 Example 3 1 4 returns 1 Greater than Syntax object1 object2 Example 3 1 4 returns 0 or Greater than or equal to Syntax object1 object2 Example 3 1 4 returns 1 or or Not equal to Syntax object1 object2 Example 3 1 4 returns 0 Boolean expressions AND or Logical And Syntax expr1 AND expr2 Example 3 1 4 AND 4 5 returns 1 OR or Logical Or Syntax expr1 OR expr2 Example 3 1 4 OR 8 5 returns 1 ...

Страница 287: ...Local Syntax LOCALvar1 var2 varn Makes the variables var1 var2 etc local to the program in which they are found Variables and Programs The HP 39gII has three types of variables Home variables App variables and User variables You use the Variable menu a to retrieve Home app or User variables Home variables are used for real numbers complex numbers graphics lists and matrices among other things Home...

Страница 288: ...st of the variables are used in common by the Function Parametric Polar Sequence Solve Statistics 1Var and Statistics 2Var apps If a variable is not available in all of these apps or is available only in some other apps then a list of the apps where the variable can be used appears under the variable name The following sections list the app variables by the view in which they are used Plot view va...

Страница 289: ... default 0 GridLines to turn the grid lines off Hmin Hmax Statistics 1Var Defines minimum and maximum values for histogram bars From Plot Setup for one variable statistics set values for HRNG Or in a program type Hmin Hmax where Hwidth Statistics 1Var Sets the width of histogram bars From Plot Setup for one variable statistics set a value for Hwidth Or in a program type Hwidth Indep Defines the va...

Страница 290: ...check Recenter Or in a program type 1 Recenter to turn recenter on default 0 Recenter to turn recenter off S1mark S5mark Statistics 2Var Sets the mark to use for scatter plots From Plot Setup for two variable statistics highlight one of S1mark S5mark and choose a mark Or in a program type S1mark where is 1 2 3 5 SeqPlot Sequence Enables you to choose types of sequence plots Stairstep or Cobweb Fro...

Страница 291: ...nd maximum independent variable values Appears as the TRNG field in the Plot Setup input form From Plot Setup enter values for TRNG Or in a program type Tmin Tmax where Tracing Turns tracing on or off in the Plot view From the Plot view press then to toggle tracing off or on Or in a program type 1 Tracing to turn Tracing mode on default 0 Tracing to turn Tracing mode off Tstep Parametric Sets the ...

Страница 292: ...value Or in a program type Ycross Xtick Sets the distance between tick marks for the horizontal axis From Plot Setup input enter a value for Xtick Or in a program type Xtick where Ytick Sets the distance between tick marks for the vertical axis From Plot Setup enter a value for Ytick Or in a program type Ytick where Xmin Xmax Sets the minimum and maximum horizontal values of the plot screen Appear...

Страница 293: ...up P press then Scroll to Set Factors select it and press Enter the value for XZOOM Or in a program type XZOOM where The default value is 4 Yzoom From Plot setup P press then Scroll to Set Factors select it and press Enter the value for YZOOM and press Or in a program type YZOOM The default value is 4 Symbolic view variables AltHyp Inference Determines the alternative hypothesis used for a hypothe...

Страница 294: ...a 1 variable statistical analysis For example H1 n returns the nth value in the data set for the H1 analysis H1Type H5Type Sets the type of plot used to graphically represent the statistical analyses H1 through H5 From the Symbolic setup specify the type of plot in the field for Type1 Type 2 etc Or in a program store one of the following constant integers or names into the variables H1Type H2Type ...

Страница 295: ...be used by the FIT operation in drawing the regression line From Symbolic Setup view specify the fit in the field for Type1 Type2 etc Or in a program store one of the following constant integers or names into a variable S1Type S2Type etc 1 Linear 2 Logarithmic 3 Exponential 4 Power 5 Exponent 6 Inverse 7 Logistic 8 Quadratic 9 Cubic 10 Quartic 11 User Defined Example Cubic S2fit or 9 S2fit Type In...

Страница 296: ... Test 4 T Test 1 5 T Test With Method 1 the constant values and their meanings are as follows 0 Z Int 1 1 Z Int 2 Z Int 1 3 Z Int 4 T Int 1 5 T Int X0 Y0 X9 Y9 Parametric Can contain any expression Independent variable is T Example SIN 4 T Y1 2 SIN 6 T X1 U0 U9 Sequence Can contain any expression Independent variable is N Example RECURSE U U N 1 N 1 2 U1 μ μ1 μ2 π π1 π2 μ μ1 μ2 μ μ1 μ2 π π1 π2 μ μ...

Страница 297: ...IST is either a list or the name of a list NumCol Function Parametric Polar Sequence Sets the column to be highlighted in the Numeric view Or in a program type NumCol where n can be 0 1 2 3 4 5 6 7 8 9 NumFont Enables you to choose the font size in the Numeric view Does not appear in the Num Setup input form Corresponds to in the Numeric view Or in a program type 0 NumFont for small 1 NumFont for ...

Страница 298: ...r a value for NUMSTART Or in a program type NumStart NumStep Function Parametric Polar Sequence Sets the step size increment value for an independent variable in Numeric view From Num Setup enter a value for NUMSTEP Or in a program type NumStep where NumType Function Parametric Polar Sequence Sets the table format From Num Setup enter 0 or 1 Or in a program type 0 NumType for BuildYourOwn 1 NumTyp...

Страница 299: ...he value of Conf Or in a program type Conf where Mean1 Sets the value of the mean of a sample for a 1 mean hypothesis test or confidence interval For a 2 mean test or interval sets the value of the mean of the first sample From the Numeric view set the value of Mean1 Or in a program type Mean1 Mean2 For a 2 mean test or interval sets the value of the mean of the second sample From the Numeric view...

Страница 300: ... Sets the assumed proportion of successes for the One proportion Z test From the Numeric view set the value of Or in a program type where Pooled Determine whether or not the samples are pooled for tests or intervals using the Student s T distribution involving two means From the Numeric view set the value of Pooled Or in a program type 0 Pooled for not pooled default 1 Pooled for pooled s1 Sets th...

Страница 301: ...f σ1 Or in a program type σ1 σ2 For a test or interval involving the difference of two means or two proportions sets the population standard deviation of the second sample From the Numeric view set the value of σ2 Or in a program type σ2 x1 Sets the number of successes for a one proportion hypothesis test or confidence interval For a test or interval involving the difference of two proportions set...

Страница 302: ... the Finance app Check or uncheck END Or in a program type 1 END for compounding at the end of the period Default 0 END for compounding at the beginning of the period FV Future value Sets the future value of an investment From the Numeric view of the Finance app enter a value for FV Or in a program type FV Note positive values represent return on an investment or loan IPYR Interest per year Sets t...

Страница 303: ... in a program type PPYR where PV Present value Sets the present value of an investment From the Numeric view of the Finance app enter a value for PV Or in a program type PV Note negative values represent an investment or loan GSize Group size Sets the size of each group for the amortization table From the Numeric view of the Finance app enter a value for Group Size Or in a program type GSize Linea...

Страница 304: ...es are used by the Triangle Solver app They correspond to the fields in the app s Numeric view SideA The length of Side A Sets the length of the side opposite the angle A From the Triangle Solver Numeric view enter a positive value for A Or in a program type SideA where SideB The length of Side B Sets the length of the side opposite the angle B From the Triangle Solver Numeric view enter a positiv...

Страница 305: ...here AngleC The measure of angle C Sets the measure of angle C The value of this variable will be interpreted according to the angle mode setting Degrees or Radians From the Triangle Solver Numeric view enter a positive value for C Or in a program type AngleC where RECT Corresponds to the status of in the Numeric view of the Triangle Solver app Determines whether a general triangle solver or a rig...

Страница 306: ...ces to use for Number format in the Home view and for labelling axes in the Plot view From the Modes view enter a value in the second field of Number Format Or in a program type ADigits where AFormat Defines the number display format used for number display in the Home view and to label axes in the Plot view From the Modes view choose Standard Fixed Scientific or Engineering in the Number Format f...

Страница 307: ... FCN menu Slope Contains the last value found by the Slope function in the Plot FCN menu The following Results variable stores calculations from the Linear Solver app These calculations correspond to the solution to a 2x2 or 3x3 linear system LSolution Contains a vector with the last solution found by either the Linear Solver app or the LSolve app function The following Results variables store cal...

Страница 308: ...tandard error of the data set in the current 1 variable analysis H1 H5 The following Results variables store calculations from the Statistics 2Var app These calculations are performed when is pressed in the Numeric view or the Do2VarStats command is executed Corr Contains the correlation coefficient from the latest calculation of summary statistics This value is based on the linear fit only regard...

Страница 309: ...eanY Contains the mean of the dependent values Y of the current 2 variable statistical analysis S1 S5 ΣY Contains the sum of the dependent values Y of the current 2 variable statistical analysis S1 S5 ΣY2 Contains the sum of the squares of the dependent values Y of the current 2 variable statistical analysis S1 S5 sY Contains the sample standard deviation of the dependent values Y of the current 2...

Страница 310: ...l of the HP Apps to perform common calculations For example in the Function app the Plot view FCN menu has a function called SLOPE that calculates the slope of a given function at a given point The SLOPE function can be used from the Home view or a program etc to give the same results as if you were in the Function app Plot view App functions can be used to get the same results in a program or the...

Страница 311: ...sest to the X value guess ROOT Fn guess Example ROOT 3 X2 2 returns 1 732 SLOPE Slope of a function Returns the slope of the function Fn at the X value if value exists SLOPE Fn value Example SLOPE 3 X2 2 returns 4 Solve app functions The Solve app has a single function that solves a given equation or expression for one of its variables En may be an equation or expression or it may be the name of o...

Страница 312: ... based on one of the statistical analyses H1 H5 defined in the Symbolic view of the Statistics 1Var app Do1VStats Performs the same calculations as pressing in the Statistics 1Var app s Numeric view and stores the results in the appropriate Statistics 1Var app results variables Hn must be one of the Statistics 1Var app Symbolic view variables H1 H5 Do1VStats Hn SETFREQ Set frequency Sets the frequ...

Страница 313: ...results in the appropriate Statistics 2Var app results variables Sn must be one of the Statistics 2Var app Symbolic view variables S1 S5 Do2VStats Sn PredX Predict X Uses the fit from the first active analysis S1 S5 found to predict an x value given the y value value PredX value PredY Predict Y Uses the fit from the first active analysis S1 S5 found to predict a y value given the x value value Pre...

Страница 314: ...s an expression only in N then term1 and term2 are optional RECURSE Un nthterm term1 term2 Examples RECURSE U1 N defines the sequence U1 to be the sequence of counting numbers RECURSE U2 U2 N 1 N 1 defines U2 to create a factorial calculating sequence U2 5 for example will return 120 RECURSE U3 U3 N 2 U3 N 1 1 1 defines U3 to be the Fibonacci sequence Finance app functions The Finance app has a si...

Страница 315: ...complete triangle from the input of 3 consecutive parts of the triangle The names of these commands use A to signify an angle and S to signify a side length To use these commands enter 3 inputs in the specified order given by the command name AAS AAS angle angle side ASA ASA angle side angle SAS SAS side angle side SSA SSA side side angle SSS SSS side side side Returns a list of three results that...

Страница 316: ...Var Parametric Polar Sequence CHECK Checks the Symbolic view variable Symbn Symbn can be any of the following F0 F9 for the function app E0 E9 for the Solve app H1 H5 for the Statistics 1Var app S1 S5 for the Statistics 2Var app X0 Yo X9 Y9 for the parametric app R0 R9 for the Polar app U0 U9 for the Sequence app CHECK Symbn Example CHECK F1 checks the Function app Symbolic view variable F1 The re...

Страница 317: ...ecks the Symbolic view variable Symbn UNCHECK Symbn Example UNCHECK R1 unchecks the Polar app Symbolic view variable R1 The result is that R1 θ is not drawn in the Plot view and does not appear in the Numeric view of the Polar app ...

Страница 318: ...308 Programming ...

Страница 319: ...oblem It is reusable like a program but easier to use and it records all your settings and definitions command An operation for use in programs Commands can store results in variables but do not display results 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 resul...

Страница 320: ...ey 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 Note Editor or the Info view of an app program A reusable set of instructions that you record using the Program editor variable The name of a number list matrix or graphic that is...

Страница 321: ...ove resetting procedures you might need to restart it by erasing all of memory You will lose everything you have stored All factory default settings are restored 1 Press and holdO 1 and6 simultaneously 2 Release all keys in the reverse order If the calculator does not turn on If the HP 39gII does not turn on follow the steps below until the calculator turns on You may find that the calculator turn...

Страница 322: ... the battery annunciator indicates that the batteries are low you need to replace the batteries as soon as possible Please install the batteries according to the following procedure 1 Turn off the calculator 2 Slide up the battery compartment cover 3 Insert 4 new AAA LR03 batteries into the compartment 4 Make sure each battery is inserted in the indicated direction 5 After installing the batteries...

Страница 323: ...azardous chemicals Operating details Operating temperature 0 to 45 C 32 to 113 F Storage temperature 20 to 65 C 4 to 149 F Operating and storage humidity 90 relative humidity at 40 C 104 F maximum Avoid getting the calculator wet Battery operates at 6 0V dc 80mA maximum Variables Home variables The Home variables are Category Available names Complex Z1 Z9 Z0 Graphic G1 G9 G0 Library Function Solve...

Страница 324: ...cs 1Var Statistics 2Var Inference Parametric Polar Sequence Finance Linear Solver Triangle Solver User named programs Real A Z θ Category Available names Continued Category Available names Results Area Extremum Isect Root Slope Symbolic F1 F2 F3 F4 F5 F6 F7 F8 F9 F0 Plot Axes Cursor GridDots GridLines Labels Method Recenter Tracing Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom ...

Страница 325: ...NumZoom Modes AAngle AComplex ADigits AFormat Category Available names Continued Category Available names Symbolic E1 E2 E3 E4 E5 E6 E7 E8 E9 E0 Plot Axes Cursor GridDots GridLines Labels Method Recenter Tracing Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom Modes AAngle AComplex ADigits AFormat Category Available names Results NbItem Min Q1 Med Q3 Max ΣX ΣX2 MeanX sX σX serrX ...

Страница 326: ...Dots GridLines Labels Method Recenter Tracing Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom Numeric D1 D2 D3 D4 D5 D6 D7 D8 D9 D0 Modes AAngle AComplex ADigits AFormat Category Available names Continued Category Available names Results NbItem Corr CoefDet sCov σCov ΣXY MeanX ΣX ΣX2 sX σX serrX MeanY ΣY ΣY2 sY σY serrY Symbolic S1 S2 S3 S4 S5 S1Type S2Type S3Type S4Type S5Type ...

Страница 327: ...zoom Ymax Ymin Ytick Yzoom Numeric C1 C2 C3 C4 C5 C6 C7 C8 C9 C0 Modes AAngle AComplex ADigits AFormat Category Available names Continued Category Available names Results Result TestScore TestValue Prob DF CritScore CritVal1 CritVal2 Symbolic AltHyp Method Type Numeric Alpha Conf Mean1 Mean2 n1 n2 μ0 π0 Pooled s1 s2 σ1 σ2 x1 x2 Modes AAngle AComplex ADigits AFormat ...

Страница 328: ...y Available names Symbolic X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X9 Y9 X0 Y0 Plot Axes Cursor GridDots GridLines Labels Method Recenter Tracing Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom Numeric NumStart NumStep NumType NumZoom Modes AAngle AComplex ADigits AFormat Category Available names Symbolic R1 R2 R3 R4 R5 R6 R7 R8 R9 R0 ...

Страница 329: ...Ytick Yzoom Numeric NumStart NumStep NumType NumZoom Modes AAngle AComplex ADigits AFormat Category Available names Continued Category Available names Symbolic U1 U2 U3 U4 U5 U6 U7 U8 U9 U0 Plot Axes Cursor GridDots GridLines Labels Method Recenter Tracing Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom Functions NumStart NumStep NumType NumZoom Modes AAngle AComplex ADigits AFormat ...

Страница 330: ...e Solver app variables The Triangle solver app variables are Category Available names Numeric CPYR END FV GSize IPYR NbPmt PMT PPYR PV Category Available names Results LSolution Numeric LSystem Size Modes AAngle AComplex ADigits AFormat Category Available names Numeric AngleA AngleB AngleC Rect SideA SideB SideC Modes AAngle AComplex ADigits AFormat ...

Страница 331: ...rer app variables The Quadratic Explorer app variables are Trig Explorer app variables The Trig Explorer app variables are Category Available names Modes AAngle AComplex ADigits AFormat Category Available names Modes AAngle AComplex ADigits AFormat Category Available names Modes AAngle AComplex ADigits AFormat ...

Страница 332: ...ld_icdf binomial binomial_cdf binomial_icdf chisquare chisquare_cdf chisquare_icdf fisher fisher_cdf fisher_icdf poisson poisson_cdf poisson_icdf student student_cdf student_icdf Hyperbolic ACOSH ASINH ATANH COSH SINH TANH ALOG EXP EXPM1 LNP1 Integer ichinrem idivis iegcd ifactor ifactors igcd iquo iquorem irem isprime ithprime nextprime powmod prevprime euler numer denom List CONCAT ΔLIST MAKELIS...

Страница 333: ...AT QR RANK ROWNORM RREF SCHUR SIZE SPECNORM SPECRAD SVD SVL TRACE TRN Polynom POLYCOEF POLYEVAL 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 Tests AND IFTE NOT OR XOR Category Available functions Continued ...

Страница 334: ...uess SLOPE Fn value Solve SOLVE En var guess Statistics 1Var Do1VStats Hn SETFREQ Hn Dn or SETFREQ Hn value SETSAMPLE Hn Dn Statistics 2Var Do2VStats Sn PredX value PredY value SetDepend Sn Cn SetIndep Sn Cn Inference DoInference Sequence RECURSE Un nthterm term1 term2 Finance DoFinance TVMVar Linear Solver LinSolve matrix Triangle Solver AAS angle angle side ASA angle side angle SAS side angle si...

Страница 335: ...RECT_P INVERT INVERT_P ARC ARC_P LINE LINE_P TEXTOUT TEXTOUT_P BLIT BLIT_P DIMGROB DIMGROB_P SUBGRB SUBGROB_P FREEZE GROBH GROBH_P GROBW GROBW_P I O CHOOSE EDITMAT GETKEY ISKEYDOWN INPUT MSGBOX PRINT WAIT debug Loop FOR FROM TO STEP END DO UNTIL WHILE REPEAT BREAK CONTINUE Matrix ADDCOL ADDROW DELCOL DELROW EDITMAT RANDMAT REDIM REPLACE SCALE SCALEADD SUB SWAPCOL SWAPROW Strings asc char expr stri...

Страница 336: ...ilable names Angle Degrees Radians H1Type H5Type Hist BoxW NormalProb LineP BarP ParetoP Format Standard Fixed Sci Eng SeqPlot Cobweb Stairstep S1Type S5Type Linear LogFit ExpFit Power Inverse Exponent Logistic QuadFit Cubic Quartic Trig User Stat1VPlot Hist BoxW NormalProb LineP BarP ParetoP ...

Страница 337: ...ttivity Σ0 permeability μ0 acceleration of gravity g gravitation G Quantum Planck h Dirac h electronic charge q electron mass me q me ratio qme proton mass mp mp me ratio mpme fine structure α magnetic flux Φο Faraday F Rydberg Bohr radius a0 Bohr magneton μB nuclear magneton μN photon wavelength λ0 photon frequency f0 Compton wavelength λc R Message Meaning Bad Argument Type Incorrect input for t...

Страница 338: ...ensions Invalid Statistics Data Need two columns with equal numbers of data values Invalid Syntax The function or command you entered does not include the proper arguments or order of arguments The delimiters parentheses commas periods and semi colons must also be correct Look up the function name in the index to find its proper syntax Name Conflict The where function attempted to assign a value t...

Страница 339: ...ts than you supplied Undefined Name The global variable named does not exist Undefined Result The calculation has a mathematically undefined result such as 0 0 Out of Memory You must recover a lot of memory to continue operation Delete one or more matrices lists notes or programs using catalogs or custom not built in apps usingSMEMORY Message Meaning Continued ...

Страница 340: ...330 Reference information ...

Страница 341: ...rmined by turning the equipment off and on the user is encouraged to try to correct the interference by one or more of the following measures Reorient or relocate the receiving 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 t...

Страница 342: ...o Hewlett Packard Company P O Box 692000 Mail Stop 5301 13 Houston TX 77269 2000 For questions regarding this FCC declaration write to Hewlett Packard Company P O Box 692000 Mail Stop 510101 Houston TX 77269 2000 or call HP at 281 514 3333 To identify your product refer to the part series or model number located on the product Canadian Notice This Class B digital apparatus meets all requirements o...

Страница 343: ...product or product family and available in English only either within the product docu mentation or at the following web site www hp eu cer tificates type the product number in the search field The compliance is indicated by one of the following con formity markings placed on the product Please refer to the regulatory label provided on the prod uct The point of contact for regulatory matters is He...

Страница 344: ...uipment 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 information about where you can drop off your waste ...

Страница 345: ... with legal requirements such as REACH Regulation EC No 1907 2006 of the European Parliament and the Council A chemical information report for this product can be found at http www hp com go reach Perchlorate Material special handling may apply This calculator s Memory Backup battery may contain perchlorate and may require special handling when recycled or disposed in California ...

Страница 346: ...vi Product Regulatory Information ...

Страница 347: ...ng the app list 154 Statistics 1Var 71 Statistics 2Var 83 Triangle Solver 143 app functions Common 306 Finance 304 Function 300 Inference 303 Linear Solver 305 Sequence 304 Statistics 1Var 302 Statistics 2Var 303 Triangle Solver 305 app variables Mode 295 Numeric view 287 Plot view 278 Results 297 Symbolic view 283 app views Info 26 Numeric setup 42 Numeric view 42 43 Plot setup 26 31 Plot view 26...

Страница 348: ... 326 copying copy and paste 16 17 notes 214 programs 240 the display 15 correlation coefficient 95 covariance 92 critical value s displayed 102 D data set definition 74 84 debugging programs 236 decimal scaling 40 42 decreasing display contrast 2 define your own fit 91 definite integral definition of 160 deleting an app 154 characters 15 lists 186 matrices 194 notes 210 programs 232 statistical da...

Страница 349: ...f 309 syntax 160 Function app 49 Function app functions 300 Function app variables results 297 summary 314 functions analyze with FCN tools 54 area 55 definition of 49 entering 50 extremum 57 intersection point 54 Math menu 322 slope 55 tracing 51 G glossary 309 graph auto scale 40 axes 33 bar 80 box and whisker 80 cobweb 127 comparing 31 connected points 33 exploring with menu keys 96 grid lines ...

Страница 350: ... T Test 112 Two Sample Z Test 107 Two Sample Z Interval 114 Inference app 99 Inference app variables Numeric view 289 Results 300 summary 317 infinite result 328 input forms resetting default values 10 setting Modes 12 insufficient memory 328 insufficient statistics data 328 integer functions 167 170 integer scaling 40 42 integral definite 160 invalid dimension 328 statistics data 328 syntax 328 i...

Страница 351: ...addition and subtraction 198 arithmetic operations in 198 column norm 203 commands 271 272 condition number 203 create identity 206 creating 196 deleting 194 deleting columns 195 deleting rows 195 determinant 203 displaying 197 displaying matrix elements 197 dividing by a square matrix 200 dot product 203 editing 196 functions 202 205 inverting 200 matrix calculations 193 multiplying and dividing ...

Страница 352: ...ng 44 setup 42 Numeric view app variables 278 O off automatic 1 power 1 on cancel 1 One Proportion Z Interval 115 One Proportion Z Test 108 One Sample T Interval 117 One Sample T Test 111 One Sample Z Interval 113 One Sample Z Test 106 order of precedence 14 P π 162 Parametric app 119 define the expression 120 exploring the graph 121 parametric app variables 318 parentheses to close arguments 14 t...

Страница 353: ...206 regression 89 resetting app 153 calculator 311 memory 311 result copying to edit line 15 reusing 15 root nth 157 S scale 36 scaling automatic 40 decimal 40 integer 37 40 42 options 40 trigonometric 40 scientific notation 13 scientific number format 11 scrolling move between relations in Trace mode 35 searching menu lists 9 speed search 8 sending apps 153 lists 187 matrices 198 notes 215 progra...

Страница 354: ...r plot 93 troubleshooting plots 96 zooming and tracing in plots 96 Statistics 2Var app 83 Statistics 2Var app variables Results 298 summary 316 storing a value in Home view 218 list element 187 matrix elements 197 subtract 155 Symbolic setup 25 Symbolic view 29 syntax of functions 160 T table automatic 45 build your own 45 numeric view setup 42 tangent 156 tickmarks for plotting 32 time hexagesima...

Страница 355: ... 91 variables 243 V value recall 219 storing 17 variable definition of 310 variables App 278 categories 217 223 Home 223 in equations 68 in Symbolic view 29 Modes 295 Numeric view 287 Plot view 278 Results 297 300 Symbolic view 283 286 types of in programming 277 use in calculations 219 User 278 Vars menu 220 vectors definition of 193 310 views definition of 310 W warning symbol 8 Where command 16...

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