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Solving

C–5

File name 32sii-Manual-E-0424
Printed Date : 2003/4/24 Size : 17.7 x 25.2 cm

Keys: Display: Description:

{

Selects Equation mode.

%:-%.

Enters the equation.

{

)

Checksum and length.

Cancels Equation mode.

Now, solve the equation to find its positive and negative roots:

Keys: Display: Description:

X 10

Your initial guesses for the
positive root.

{

%:-%.

Selects Equation mode;
displays the equation.

{

%/)

Calculates the positive root
using guesses 0 an 10.

)

Final two estimates are they
same.

{

)

f(x)

= 0.

X 10

Your initial guesses for the
negative root.

{

%:-%.

Redisplays the equation.

{

%/.)

Calculates negative root
using guesses 0 and –10.

{

)

f(x)

= 0.

Certain cases require special consideration:

If the function's graph has a discontinuity that crosses the

–axis, then the

SOLVE operation returns a value adjacent to the discontinuity (see figure
a, below). In this case,

f(x)

may be: relatively large.

Values of

f(x)

may be approaching infinity at the location where the

graph changes sign (see figure b, below). This situation is called a

pole

Since the SOLVE operation determines that there is a sign change

Содержание 32SII

Страница 1: ...File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm HP 32SII RPN Scientific Calculator Owner s Manual HP Part No 00032 90068 Printed in Singapore Edition 5 ...

Страница 2: ... or use of this manual or the examples contained herein Hewlett Packard Co 1990 1991 1992 1993 All rights reserved Reproduction adaptation or translation of this manual is prohibited without prior written permission of Hewlett Packard Company except as allowed under the copyright laws The programs that control your calculator are copyrighted and all rights are reserved Reproduction adaptation or t...

Страница 3: ... Highlights of the Keyboard an Display 1 1 Shifted Keys 1 1 Alpha Keys 1 2 Backspacing and Clearing 1 2 Using Menus 1 4 Exiting Menus 1 7 Annunciator 1 7 Keying in Numbers 1 9 Making Numbers Negative 1 10 Exponent of Ten 1 10 Understanding Digit Entry 1 11 Range Number and OVERFLOW 1 12 Doing Arithmetic 1 12 One Number Functions 1 12 Two Number Functions 1 13 Controlling the Display Format 1 14 Pe...

Страница 4: ... of Memory 1 20 2 The Automatic Memory Stack What the Stack Is 2 1 The X Register Is in the Display 2 2 Clearing the X Register 2 2 Reviewing the stack 2 3 Exchanging the X and Y Registers in the Stack 2 4 Arithmetic How the Stack Does It 2 4 How ENTER Works 2 5 How CLEAR x Works 2 7 The LAST X Register 2 8 Correcting Mistakes with LAST X 2 9 Reusing Numbers with LAST X 2 10 Chain Calculations 2 1...

Страница 5: ...Variables 3 4 Storage Arithmetic 3 4 Recall Arithmetic 3 5 Exchanging x with Any Variable 3 6 The Variable i 3 7 4 Real Number Functions Exponential and Logarithmic Functions 4 1 Power Functions 4 2 Trigonometry 4 3 Entering π 4 3 Setting the Angular Mode 4 3 Trigonometric Functions 4 4 Hyperbolic Functions 4 5 Percentage Functions 4 5 Conversion Functions 4 7 Coordinate Conversions 4 7 Time Conve...

Страница 6: ...Indicators 5 3 Longer Fractions 5 4 Changing the Fraction Display 5 5 Setting the Maximum Denominator 5 5 Choosing Fraction Format 5 6 Examples of Fraction Displays 5 7 Rounding Fractions 5 8 Fractions in Equations 5 9 Fractions in Programs 5 10 6 Entering and Evaluating Equations How You Can Use Equations 6 1 Summary of Equation Operations 6 3 Entering Equations into the Equation List 6 4 Variabl...

Страница 7: ... Responding to Equation Prompts 6 14 The Syntax of Equations 6 15 Operator Precedence 6 15 Equation Function 6 17 Syntax Errors 6 20 Verifying Equations 6 20 7 Solving Equations Solving an Equation 7 1 Understanding and Controlling SOLVE 7 5 Verifying the Result 7 6 Interrupting a SOLVE Calculation 7 7 Choosing Initial Guesses for SOLVE 7 7 For More Information 7 11 8 Integrating Equations Integra...

Страница 8: ...ion of Numbers 10 4 Negative Numbers 10 4 Range of Numbers 10 5 Windows for Long Binary Numbers 10 6 SHOWing Partially Hidden Numbers 10 6 11 Statistical Operations Entering Statistical Data 11 1 Entering One Variable Data 11 2 Entering Two Variable Data 11 2 Correcting Errors in Data Entry 11 3 Statistical Calculations 11 4 Mean 11 4 Sample Standard Deviation 11 6 Population Standard Deviation 11...

Страница 9: ...s 12 4 Data Input and Output 12 4 Entering a Program 12 5 Keys That Clear 12 6 Function Names in Programs 12 7 Running a Program 12 8 Executing a Program XEQ 12 9 Testing a Program 12 9 Entering and Displaying Data 12 11 Using INPUT for Entering Data 12 11 Using VIEW for Displaying Data 12 14 Using Equations to Display Messages 12 14 Displaying Information without Stopping 12 17 Stopping or Interr...

Страница 10: ...de in a Program 12 24 Numbers Entered in Program Lines 12 24 Polynomial Expressions and Horner s Method 12 25 13 Programming Techniques Routines in Programs 13 1 Calling Subroutines XEQ RTN 13 2 Nested Subroutines 13 3 Branching GTO 13 5 A Programmed GTO Instruction 13 5 Using GTO from the Keyboard 13 6 Conditional Instructions 13 7 Tests of Comparison x y x 0 13 8 Flags 13 9 Loops 13 16 Condition...

Страница 11: ...ng a Program 14 7 Using Integration in a Program 14 9 Restrictions o Solving and Integrating 14 10 15 Mathematics Programs Vector Operations 15 1 Solutions of Simultaneous Equations 15 12 Polynomial Root Finder 15 20 Coordinate Transformations 15 31 16 Statistics Programs Curve Fitting 16 1 Normal and Inverse Normal Distributions 16 11 Grouped Standard Deviation 16 18 17 Miscellaneous Programs and...

Страница 12: ...r Operation A 4 The Self Test A 5 Limited One Year Warranty A 6 What Is Covered A 6 What Is Not Covered A 6 Consumer Transaction in the United Kingdom A 7 If the Calculator Requires Service A 7 Service Charge A 8 Shipping Instructions A 8 Warranty on Service A 8 Service Agreements A 9 Regulatory Information A 9 B User Memory and the Stack Managing Calculator Memory B 1 Resetting the Calculator B 3...

Страница 13: ...ster B 6 C More about Solving How SOLVE Finds a Root C 1 Interpreting Results C 3 When SOLVE Cannot Find Root C 8 Round Off Error C 14 Underflow C 15 D More about Integration How the Integral Is Evaluated D 1 Conditions That Could Cause Incorrect Results D 2 Conditions That Prolong Calculation Time D 8 E Messages F Operation Index Index ...

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Страница 15: ...File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Part 1 Basic Operation ...

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Страница 17: ...formation you ve stored You can also press z to turn the calculator off To conserve energy the calculator turns itself off after 10 minutes of no use If you see the low power indicator in the display replace the batteries as soon as possible See appendix A for instructions Adjusting Display Contrast Display contrast depends on lighting viewing angle and the contrast setting To increase or decrease...

Страница 18: ...ator remains on until you press the next key To cancel a shift key and turn off its annunciator press the same shift key again Alpha Keys Menu name Shifted function Letter for alphabetic key Most keys have a letter written next to them as shown above Whenever you need to type a letter for example a variable or a program label the A Zannunciator appears in the display indicating that the alpha keys...

Страница 19: ...Equation entry mode Erases the character immediately to the left of the equation entry cursor If a number entry in your equation is complete a erases the entire number If the number is not complete a erases the character immediately to the left of _ the number entry cursor _ changes back to when number entry is complete a also clears error messages and deletes the current program line during progr...

Страница 20: ...r decision before erasing all your programs During equation entry either keyboard equations or equations in program lines the menu is displayed so you can verify your decision before erasing the equation If you are viewing a completed equation the equation is deleted with no verification Using Menus There is a lot more power to the HP 32SII than what you see on the keyboard This is because 12 of t...

Страница 21: ...rmutations seed and random number 4 L R º ˆ T P E Linear regression curve fitting and linear estimation 11 x y º º Arithmetic mean of statistical x and y values weighted mean of statistical x values 11 s σ Uº U σº σ Sample standard deviation population standard deviation 11 SUMS Q º º º Statistical data summations 11 BASE Base conversions decimal hexadecimal octal and binary 11 Programming Instruc...

Страница 22: ...ALL display formats I CLEAR Functions to clear different portions of memory refer to z b in the table on page 1 4 1 3 6 12 The following example shows you how to use a menu function Example How many permutations n different arrangements are possible from 28 items taken four r at a time Keys Display Description 28 4 _ Displays r PROB FQ8T Q8T Displays the probability menu Q8T 8 Displays the result ...

Страница 23: ...ut executing a function you have three options Pressing a backs out of the 2 level CLEAR or MEM menu one level at a time Refer to z b in the table on page 1 4 Pressing a or cancels any other menu Keys Display 123 _ PROB Q8T Q8T a or Pressing another menu key replaces the old menu with the new one Keys Display 123 _ PROB Q8T Q8T z b Annunciator The symbols along the top and bottom of the display sh...

Страница 24: ...or slightly greater than its true value If neither part of ST is on the exact value of the fraction is being displayed 5 Left shift is active 1 Right shift is active 1 PRGM Program entry is active Blinks while program is running 12 EQN Equation entry mode is active or the calculator is evaluating an expression or executing an equation 6 0 1 2 3 Indicates which flags are set flags 4 through 11 have...

Страница 25: ...nunciators may appear simultaneously in the display indicating that there are more characters to the left and to the right Press either of the indicated menu keys or 6 to see the leading or trailing characters 1 6 A Z The alphabetic keys are active 3 Attention Indicates a special condition or an error 1 Battery power is low A Keying in Numbers You can key in a number that has up to 12 digits plus ...

Страница 26: ... the exponent such as A number whose magnitude is too large or too small for the display format will automatically be displayed in exponential form For example in FIX 4 format for four decimal places observe the effect of the following keystrokes Keys Display Description 000062 _ Shows number being entered Rounds number to fit the display format 000042 Automatically uses scientific notation becaus...

Страница 27: ... calculator displays Other Exponent Functions To calculate an exponent of ten the base 10 antilogarithm use z To calculate the result of any number raised to a power exponentiation use 0 see chapter 4 Understanding Digit Entry As you key in a number the cursor _ appears in the display The cursor shows you where the next digit will go it therefore indicates that the number is not complete Keys Disp...

Страница 28: ...mallest number available on the calculator is 1 10 499 The largest number is 9 99999999999 10499 displayed as because of rounding If a calculation produces a result that exceeds the largest possible number 9 99999999999 10499 is returned and the warning message appears If a calculation produces a result smaller that the smallest possible number zero is returned No warning message appears Doing Ari...

Страница 29: ...148 84 Square root of 148 84 z Square of 12 2 _ Negation of 148 8400 The one number functions also include trigonometric logarithmic hyperbolic and parts of numbers functions all of which are discussed in chapter 4 Two Number Functions To use a two number function such as y p 0 or S 1 Key in the first number 2 Press to separate the first number from the second 3 Key in the second number Do not pre...

Страница 30: ...t answer without re typing them by pressing Z to swap the order of the numbers on the stack Then press the intended function key This is explained in detail in chapter 2 under Exchanging the X and Y Registers in the Stack Controlling the Display Format Periods and Commas in Numbers To exchange the periods and commas used for the decimal point radix mark and digit separators in a number 1 Press z t...

Страница 31: ...mal places to be displayed For 10 or 11 places press 0 or 1 For example in the number 8 the 7 0 8 and 9 are the decimal digits you see when the calculator is set to FIX 4 display mode Any number teat is too large or too small to display in the current decimal place setting will automatically be displayed in scientific format Scientific Format SCI format displays a number in scientific notation one...

Страница 32: ...ficant digit you see when the calculator is set to ENG 4 display mode The 3 following the E is the multiple of 3 exponent of 10 123 46x 103 ALL Format ALL format displays a number as precisely as possible 12 digits maximum If all the digits don t fit in the display the number is automatically displayed in scientific format 123 456 SHOWing Full 12 Digit Precision Changing the number of displayed de...

Страница 33: ...u release Fractions The HP 32SII allows you to type in and display fractions and to perform math operations on them Fractions are real numbers of the form a b c where a b and c are integers 0 b c and the denominator c must be in the range 2 through 4095 Entering Fractions Fractions can be entered onto the stack at any time 1 Key in the integer part of the number and press The first separates the i...

Страница 34: ... the number _ The key is interpreted in the normal manner 3 _ Enters the numerator of the fraction the number is still displayed in decimal form _ The calculator interprets the second as a fraction and separates the numerator from denominator 8 _ Appends the denominator of the fraction Terminates digit entry displays the number in the current display format If the number you enter has no integer p...

Страница 35: ... characters as you key them in Adds the numbers in the X and Y registers displays the result as a fraction z Switches to current decimal display format Refer to chapter 5 Fractions for more information about using fractions Messages The calculator responds to certain conditions or keystrokes by displaying a message The symbol comes on to call your attention to the message To clear a message press ...

Страница 36: ...enu key displays the catalog of variables see Reviewing Variables in the VAR Catalog in chapter 3 Pressing the menu key displays the catalog of programs 1 To enter the catalog of variables press to enter the catalog of programs press 2 To review the catalogs press z or z 3 To delete a variable or a program press z b while viewing it in its catalog 4 To exit the catalog press Clearing All of Memory...

Страница 37: ...Getting Started 1 21 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm which safeguards against the unintentional clearing of memory 2 Press yes ...

Страница 38: ......

Страница 39: ...without parentheses The key to automatic storage is the automatic RPN memory stack HP s operating logic is based on an unambiguous parentheses free mathematical logic known as Polish Notation developed by the Polish logician Jan Łukasiewicz 1878 1956 While conventional algebraic notation places the operators between the relevant numbers or variables Łhukasiewicz s notation places them before the n...

Страница 40: ... program line is being displayed You might have noticed that several function names include an x or y This is no coincidence these letters refer to the X and Y registers For example z raises ten to the power of the number in the X register the displayed number Clearing the X Register Pressing z b º always clears the X register to zero it is also used to program this instruction The key in contrast...

Страница 41: ...they started T 1 4 3 2 1 Z 2 1 4 3 2 Y 3 2 1 4 3 X 4 9 3 9 2 9 1 9 4 What was in the X register rotates into the T register the contents of the T register rotate into the Z register etc Notice that only the centents of the registers are rolled the registers themselves maintain their positions and only the X register s contents are displayed Rµ Roll Up The 8 roll up key has a similar function to 9 ...

Страница 42: ...nates in the X and Y registers into polar coordinates in the X and Y registers To swap the order of numbers in a calculation For example one way to calculate 9 13 8 Press 13 8 y 9 Z p The keystrokes to calculate this expression from left to right are 9 13 8 y p Note Always make sure that there are no more than four numbers in the stack at any given time the contents of the T register the top regis...

Страница 43: ...register and that the former contents of the T register are lost You can see therefore that the stack s memory is limited to four numbers Because of the automatic movements of the stack you do not need to clear the X register before doing a new calculation Most functions prepare the stack to lift its contents when the next number enters the X register See appendix B for lists of functions that dis...

Страница 44: ...es over the copy of the first number left in the X register The effect is simply to separate two sequentially entered numbers You can use the replicating effect of clear the stack quickly press 0 All stack registers now contain zero Note however that you don t need to clear the tech before doing calculations Using a Number Twice in a Row You can use the replicating feature of to other advantages T...

Страница 45: ...n 3 Calculates the population after 1 day 4 Calculates the population after 2 days 5 Calculates the population after 3 days How CLEAR x Works Clearing the display X register put zero in the X register The next number you key in or recall writes over this zero There are three ways to clear the contents of the X register that is to clear x 1 Press 2 Press a 3 Press z b º Mainly used during program e...

Страница 46: ...correct your error T Z Y 1 1 1 1 X 1 1 2 0 3 1 2 3 4 5 1 Lifts the stack 2 Lift the stack and replicates the X register 3 Overwrites the X register 4 Clears x by overwriting it with zero 5 Overwrites x replaces the zero The LAST X Register The LAST X register is a companion to the stack it holds the number that was in the X register before the last numeric function was executed A numeric function ...

Страница 47: ...mistake You don t have to start over To find the correct result press z Mistakes with a Two number operation If you make a mistake with a two number operation y p 0 or you can correct it by using z and inverse of the two number function or p or y or 0 1 Press z to recover the second number x just before the operation 2 Execute the inverse operation This returns the number that was originally first...

Страница 48: ...e Correction 16 19 Wrong function z z y 15 19 y Wrong first number 16 z y 16 18 y Wrong second number z p 19 y Reusing Numbers with LAST X You can use z to reuse a number such as a constant in a calculation Remember to enter the constant second just before executing the arithmetic operation so that the constant is the last number in the X register and therefore can be saved and retrieved with z Ex...

Страница 49: ...Y 149 0987 z z X 52 3947 p 2 8457 LAST X 52 3947 52 3947 Keys Display Description 96 704 Enters first number 52 3947 Intermediate result z Brings back display from before p Final result Example Two close stellar neighbors of Earth are Rigel Centaurus 4 3 light years away and Sirius 8 7 light years away Use c the speed of light 9 5 1015 meters per year to convert the distances from the Earth to the...

Страница 50: ...The automatic lifting and dropping of the stack s contents let you retain intermediate results without storing or reentering them and without using parentheses Work from the Parentheses Out For example solve 12 3 7 If you were working out this problem on paper you would first calculate the intermediate result of 12 3 12 3 15 then you would multiply the intermediate result by 7 15 7 105 Solve the p...

Страница 51: ...ate subsequent numbers and save intermediate results The last result saved is the first one retrieved as needed to carry out the calculation Calculate 2 3 10 Keys Display Description 3 10 Calculates 3 10 first 2 Z p Puts 2 before 13 so the division is correct 2 13 Calculate 4 14 7 3 2 Keys Display Description 7 3 y Calculates 7 3 14 2 Calculates denominator 4 Z Puts 4 before 33 in preparation for ...

Страница 52: ...ntermediate answers the calculator remembers them for you Keys Display Description 3 4 First adds 3 4 5 6 Then adds 5 6 y Then multiplies the intermediate answers together for the final answer Exercises Calculate 0000 181 05 0 5 3805 16 x Solution 16 3805 5 y 05 p Calculate 5743 21 9 8 7 6 5 4 3 2 Solution 2 3 4 5 y 6 7 8 9 y Calculate 10 5 17 12 4 0 2500 Solution 17 12 4 y 10 5 Z p or 10 5 17 12 ...

Страница 53: ...takes one additional keystroke Notice that the first intermediate result is still the innermost parentheses 7 3 The advantage to working a problem left to right is that you don t have to use Z to reposition operands for nomcommutaiive functions and p However the first method starting with the innermost parentheses is often preferred because It takes fewer keystrokes It requires fewer registers in ...

Страница 54: ...result 2 Intermediate result p Final result More Exercises Practice using RPN by working through the following problems Calculate 14 12 18 12 9 7 78 0000 A Solution 14 12 18 12 y 9 7 p Calculate 232 13 9 1 7 412 1429 A Solution 23 z 13 9 y 7 3 Calculate 5961 0 7 0 5 12 8 0 4 5 3 Solution 5 4 8 y 7 3 0 12 5 Z p or 5 4 8 y 12 5 7 3 0 p Calculate 5728 4 01 2 71 1 75 2 15 3 3 4 32 0 46 7 33 8 2 5 4 33...

Страница 55: ...The Automatic Memory Stack 2 17 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 4 5 2 8 33 y z 7 46 0 32 y p 3 15 2 75 4 3 y 1 71 2 01 y p ...

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Страница 57: ...Cursor prompts for variable 2 Indicates letter keys are active 3 Letter keys Each white letter is associated with a key and a unique variable The letter keys are automatically active when needed The A Z annunciator in the display confirms this Note that the variables X Y Z and T are different storage locations from the X register Y register Z register and T register in the stack Storing and Recall...

Страница 58: ...y Viewing a Variable without Recalling It The function shows you the contents of a variable without putting that number in the X register The display is labeled for the variable such as If the number is too large to fit completely in the display with its label it is rounded and the rightmost digits are dropped An exponent is displayed in full To see the full mantissa press In Fraction display mode...

Страница 59: ...nd display the desired variable Note the TS annunciator indicating that the left shifted and keys are active If Fraction display mode is active TS does not indicate accuracy To see all the significant digits of a number displayed in the catalog press If it is a binary number with more than 12 digits use the and 6 keys to see the rest 3 To copy a displayed variable from the catalog to the X registe...

Страница 60: ...o do calculations with a number stored in a variable without recalling the variable into the stack A calculation uses one number from the X register and one number from the specified variable Storage Arithmetic Storage arithmetic uses H H H y or H p to do arithmetic in the variable itself and to store the result there It uses the value in the X register and does riot affect the stack New value of ...

Страница 61: ...ter using a recalled number and to leave the result in the display Only the X register is affected New x Previous x Variable For example suppose you want to divide the number in the X register 3 displayed by the value in A 12 Press K p A Now x 0 25 while 12 is still in A Recall arithmetic saves memory in programs using K A one instruction uses half as much memory as K A two instructions A 12 A 12 ...

Страница 62: ...D H E H F Add 1 to D E And F D Displays the current value of D E F Clears the VIEW display displays X register again Suppose the variables D E and F contain the values 2 3 and 4 from the last example Divide 3 by D multiply it by E and add F to the result Keys Display Description 3 K p D Calculates 3 D K y E 3 D E K F 3 D E F Exchanging x with Any Variable The Y key allows yon to exchange the conte...

Страница 63: ... 3 T t T t Z z Z z Y y Y y X 3 Y X 12 The Variable i There is a 27th variables that you can access directly the variable i The key is labeled i and it means i whenever the A Z annunciator is on Although it stores numbers as other variables do i is special in that it can be used to refer to other variables including the statistics registers using the i function This is a programming technique calle...

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Страница 65: ...ons for coordinates angles and units Probability functions Parts of numbers number altering functions Arithmetic functions and calculations were covered in chapters 1 and 2 Advanced numeric operations root finding integrating complex numbers base conversions and statistics are described in later chapters All the numeric functions are on keys except for the probability and parts of numbers function...

Страница 66: ...ey in x and press z To calculate a power x of 10 key in x and press z To calculate a number y raised to a power x key in y x then press 0 For y 0 x can be any rational number for y 0 x must be are integer for y 0 x must be positive To Calculate Press Result 152 15 z 106 6 z 8 8 54 5 4 0 2 1 4 2 1 4 _ 0 1 4 3 1 4 _ 3 0 To calculate a root x of a number y the xth root of y key in y x then press z Fo...

Страница 67: ...ot exactly represent π since π is an irrational number Setting the Angular Mode The angular rode specifies which unit of measure do assume for angles used in trigonometric functions The mode does not convert numbers already present see Conversion Functions later in this chapter 360 degrees 2π radians 400 grads To set an angular mode press z A menu will be displayed from which you can select an opt...

Страница 68: ...pressed exactly by the 12 digit internal precision of the calculator This is particularly noticeable in trigonometry For example the calculated sin π radians is not zero but 2 0676 10 13 a very small number close to zero Example Show that cosine 5 7 π radians and cosine 128 57 are equal to four significant digits Keys Display Description z Sets Radians mode RAD annunciator on 5 7 5 7 in decimal fo...

Страница 69: ...his chapter Hyperbolic Functions With x in the display To Calculate Press Hyperbolic sine of x SINH z 7 N Hyperbolic cosine of x COSH z 7 Q Hyperbolic tangent of x TANH z 7 T Hyperbolic arc sine of x ASINH z 7 z L Hyperbolic arc cosine of x ACOSH z 7 z O Hyperbolic arc tangent of x ATANH z 7 z R Percentage Functions The percentage functions are special compared with y and p because they preserve t...

Страница 70: ... Display Description z 2 Rounds display to two decimal places 15 76 6 P Calculates 6 tax Total cost base price 6 tax Suppose that the 15 76 item cost 16 12 last year What is the percentage change from last year s price to this year s Keys Display Description 16 12 15 76 S This year s price dropped about 2 2 from last year s price z 4 Restores FIX 4 format Note The order of the two numbers is impor...

Страница 71: ...asured as shown in the illustration The angle θ uses units set by the current angular mode A calculated result for θ will be between 180 and 180 between π and π radians or between 200 and 200 grads x y r θ To convert between rectangular and polar coordinates 1 Enter the coordinates in rectangular or polar form that you want to convert The order is y x or θ r 2 Execute the conversion you want press...

Страница 72: ...θ θ Example Polar to Rectangular Conversion In the following right triangles find sides x and y in the triangle on the left and hypotenuse r and angle θ in the triangle on the right y 10 30o x r 4 3 θ Keys Display Description z Sets Degrees mode 30 10 r Calculates x Z Displays y 4 3 z q Calculates hypotenuse r Z Displays θ ...

Страница 73: ...e converted to rectangular coordinates the x value yields R in ohms the y value yields XC in ohms R C R X c _36 5o 77 8 ohms θ Keys Display Description z Sets Degrees mode 36 5 _ Enters θ degrees of voltage lag 77 8 _ Enters r ohms of total impedance r Calculates x ohms resistance R Z Displays y ohms reactance XC For more sophisticated operations with vectors addition subtraction cross product and...

Страница 74: ... are there in 1 7 of an hour Use FIX 6 display format Keys Display Description z 6 Sets FIX 6 display format 1 7 1 7 as a decimal fraction t Equals 8 minutes and 34 29 seconds z 4 Restores FIX 4 display format Angle Conversions When converting to radians the number in the x register is assumed to be degrees when converting to degrees the number in the x register is assumed to be radians To convert...

Страница 75: ... lb kg 1 z kilograms 1 kg lb 1 pounds 32 ºF ºC 32 z C 100 ºC ºF 100 F 1 in cm 1 z centimeters 100 cm in 100 inches 1 gal l 1 z liters 1 l gal 1 gallons Probability Functions Factorial To calculate the factorial of a displayed positive integer x o x 253 press z 1 the left shifted 3 key Gamma To calculate the gamma function of a noninteger x Γ x key in x 1 and press 1 The x function calculates Γ x 1...

Страница 76: ...ly Calculates the number of possible arrangements of n items taken r at a time No item occurs more than once in an arrangement and different orders of the same r items are counted separately SD Seed Stores the number in x as a new seed for the random number generator R Random number generator Generates a random number in the range 0 x 1 The number is part of a uniformly distributed pseudo random n...

Страница 77: ...tal number of combinations possible If employees are chosen at random what is the probability that the committee will contain six women To find the probability of an event divide the number of combinations for that event by the total number of combinations Keys Display Description 14 6 _ Fourteen worriers grouped six at a time PROB Q T 8 Number of combinations of six women on the committee Z 8 Bri...

Страница 78: ... part of x and replaces it with zeros For example the fractional part of 14 2300 is 0 2300 Absolute value Replaces x with its absolute value The RND function z I rounds x internally to the number of digits specified by the display format The internal number is represented by 12 digits Refer to chapter 5 for the behavior of RND in Fraction display mode Names of Function You might have noticed that ...

Страница 79: ...isplay goes back to the previous display format FIX SCI ENG and ALL also turn off Fraction display mode Functions work the same with fractions as with decimal numbers except for RND which is discussed later in this chapter This chapter gives more information about using and displaying fractions Entering Fractions You can type almost any number as a fraction on the keyboard including an improper fr...

Страница 80: ...ee chapter 10 for information about changing the number base Fractions in the Display In Fraction display mode numbers are evaluated internally as decimal numbers then they re displayed using the most precise fractions allowed In addition accuracy annunciators show the direction of any inaccuracy of the fraction compared to its 12 digit decimal value Most statistics registers are exceptions they r...

Страница 81: ...6 18 5 9 60000000000 34 12 2 83333333333 T 15 8192 183105468750 S 12345678 12345 3 Illegal entry 16 3 16384 Illegal entry Accuracy Indicators The accuracy of a displayed fraction is indicated by the S and T annunciators at the top of the display The calculator compares the value of the fractional part of the internal 12 digit number with the value of the displayed fraction If no indicator is lit t...

Страница 82: ...a little above 3 If you press z X to view the VAR catalog the ST annunciator doesn t indicate accuracy it means you can use and to move through the list of variables The accuracy isn t shown Sometimes an annunciator is lit when you wouldn t expect it to be For example if you enter 2 2 3 you see S even though that s the exact number you entered The calculator always compares the fractional part of ...

Страница 83: ... three fraction formats The next few topics show how to change the fraction display Setting the Maximum Denominator For any fraction the denominator is selected based on a value stored in the calculator If you think of fractions as a b c then c corresponds to the value that controls the denominator The c value defines only the maximum denominator used in Fraction display mode the specific denomina...

Страница 84: ... with fractions you might want any denominator to be possible c value is 4095 This is the default fraction format Factors of denominator Fractions have only denominators that are factors of the c value and they re reduced as much as possible For example if you re calculating stock prices you might want to see and c value is 8 Or if the c value is 12 possible denominators are 2 3 4 6 and 12 Fixed d...

Страница 85: ...s and type the flag number such as 8 To clear a flag press and type the flag number To see if a flag is set press and type the flag number Press or a to clear the or response Examples of Fraction Displays The following table shows how the number 2 77 is displayed in the three fraction formats for two c values How 2 77 Is Displayed Fraction Format c 4095 c 16 Most precise 2 77 100 2 7700 S2 10 13 2...

Страница 86: ...of 16 Example Suppose a stock has a current value of 48 1 4 If it goes down 2 5 8 what would be its value What would then be 85 percent of that value Keys Display Description x 8 x 9 Sets flag 8 clears flag 9 for factors of denominator format 8 Sets up fraction format for 1 8 increments 48 1 4 Enters the starting value 2 5 8 Subtracts the change 85 P S Finds the 85 percent value to the nearest 1 8...

Страница 87: ...ach section assuming you can conveniently measure 1 16 inch increments What s the cumulative roundoff error Keys Display Description 16 Sets up fraction format for 1 16 inch increments Flags 8 and 9 should be the same as for the previous example 56 3 4 H D Stores the distance in D 6 p S The sections are a bit wider than 9 7 16 inches z I Rounds the width to this value 6 y Width of six sections K D...

Страница 88: ... converted to its decimal value All numeric values in a program are shown as decimal values Fraction display mode is ignored When you re running a program displayed values are shown using Fraction display mode if it s active If you re prompted for Values by INPUT instructions you may enter fractions regardless of the display mode A program can control the fraction display using the c function and ...

Страница 89: ... determine the volume of a straight section of pipe The equation is V 25 π d2 l There d is the inside diameter of the pipe and l is its length You could key in the calculation over and over for example 25 M y 2 5 z y 16 y calculates the volume of 16 inches of 2 1 2 inch diameter pipe 78 5398 cubic inches However by storing the equation you get the HP 32SII to remember the relationship between diam...

Страница 90: ...s o f the left side of the display ºπº º Terminates and displays the equation shows that part of the equation doesn t fit in the display and above 6 means you can press 6 to see characters in that direction Shows the checksum and length for the equation so you can check your keystrokes By comparing the checksum and length of your equation with those in the example you can verify that you ve entere...

Страница 91: ... 2 1 2 inches as a fraction f value Stores D prompts for L value is current value of L 16 f Stores L calculates V in cubic inches and stores the result in V Summary of Equation Operations All equations you create are saved in the equation list This list is visible whenever you activate Equation mode You use certain keys to perform operations involving equations They re described in more detail lat...

Страница 92: ...uation for the unknown variable you specify See chapter 7 Integrates the displayed equation with respect to the variable you specify See chapter 8 a Begins editing the displayed equation subsequent presses delete the rightmost function or variable z b Deletes the displayed equation from the equation list z or z Steps up or down through the equation list Shows the displayed equation s checksum veri...

Страница 93: ...ng If you press instead the equation is saved but Equation mode is turned off You can make an equation as long as you want you re limited only by the amount of memory available Equations can contain variables numbers functions and parentheses they re described in the following topics The example that follows illustrates these elements Variables in Equations You can use any of the calculator s 28 v...

Страница 94: ...ations In an equation certain functions are normally shown between its arguments such as and For such infix operators enter them in an equation in the same order Other functions normally have one or more arguments after the function name such as COS and LN For such prefix functions enter them in an equation where the function occurs the key you press puts a left parenthesis after the function name...

Страница 95: ... Display Description G ºπº º Shows the last equation used in the equation list K R c Starts a new equation with variable R 2 _ Enters a number changing the cursor to _ y K C y º º Enters infix operators Q º º 1 Enters a prefix function with a left parenthesis K T K A º º 1 2 Enters the argument and right parenthesis This final parenthesis is optional º º 1 Terminates the equation and displays it S...

Страница 96: ...re characters to the right The annunciator over 6 means scrolling is turned on 2 Press 6 to scroll the equation one character at a time showing characters to the right Press to show characters to the left and turn off if there are no more characters to the left or right Press SCRL to turn scrolling off and on When scrolling is turned off the left end of the equation is displayed the annunciators a...

Страница 97: ...rs in the number the calculator switches back to the equation entry cursor If the equation entry cursor is on pressing a deletes the entire rightmost number or function 2 Retype the rest of the equation 3 Press or to save the equation in the equation list To edit a saved equation 1 Display the desired equation See Displaying and Selecting Equations above 2 Press a once only to start editing the eq...

Страница 98: ...ove the optional right parenthesis in the equation from the previous example Keys Display Description G º º 1 Shows the current equation in the equation list a º º 1 2 Turns on Equation entry mode and shows the cursor at the end of the equation a º º 1 Deletes the right parenthesis 6 6 º º 1 Shows the end of edited equation in the equation list Leaves Equation mode Types of Equations The HP 32SII ...

Страница 99: ...what enables you to calculate result from an equation It also enables you to solve and integrate equations as described in chapters 7 and 8 Because many equations have two sides separated by the basic value of an equation is the difference between the values of the two sides For this calculation in an equation essentially treated as _ The value is a measure of lour well the equation balances The H...

Страница 100: ...tion prompts for a value for each variable needed If you ve changed the number base it s automatically changed back to base 10 3 For each prompt enter the desired value If the displayed value is good press f If you want a different value type the value and press f Also see Responding to Equation Prompts later in this chapter The evaluation of an equation takes no values from the stack it uses only...

Страница 101: ... is returned to the X register Example Evaluating an Equation with ENTER Use the equation from the beginning of this chapter to find the volume of a 35 mm diameter pipe that s 20 meters long Keys Display Description G z as required ºπº º Displays the desired equation Starts evaluating the assignment equation so the value will be stored in V Prompts for variables on the right hand side of the equat...

Страница 102: ...illimeters Keys Display Description G ºπº º Displays the desired equation W 8 8 Starts evaluating the equation to find its value Prompts for all variables f Keeps the same V prompts for D 35 5 f 8 store new D Prompts for L f 8 Keeps the same L calculates the value of the equation the imbalance between the left and right sides 6 p Changes cubic millimeters to liters The value of the equation is the...

Страница 103: ...alue for the variable remains in the X register If you press during digit entry it clears the number to zero Press again to cancel the prompt To display digits hidden by the prompt press Each prompt puts the variable value in the X register and disables stack lift If you type a number at the prompt it replaces the value in the X register When you press f stack lift is enabled so the value is retai...

Страница 104: ...Divide º ª 5 Add and Subtract 6 Equality So for example all operations inside parentheses are performed before operations outside the parentheses Examples Equations Meaning º a b3 c 1 º 2 a b 3 c ª a b c 12 1 2ª a b c 12 0 1 2 CHG t 12 a 6 2 You can t use parentheses for implied multiplication For example the expression p 1 f must be entered as º1 2 with the º operator inserted between P and the l...

Страница 105: ...ence prefix type functions which require one or two arguments display a left parenthesis when you enter them The prefix functions that require two arguments are CHG XROOT Cn r and Pn r Separate the two arguments with a space In an equation the XROOT function takes its arguments in the opposite order from RPN usage For example 8 3 to is equivalent to 1 2 All other two argument functions take their ...

Страница 106: ...differ from their equivalent RPN operations RPN Operation Equation function x2 SQ ex EXP 10x ALOG 1 x INV X y X ROOT yx Example Perimeter of a Trapezoid The following equation calculates the perimeter of a trapezoid This is how the equation might appear in a book Perimeter a b h φ θ sin 1 sin 1 b a h φ θ The following equation obeys the syntax rules for HP 32SII equations ...

Страница 107: ...P A B Hx 1 SIN T 1 SIN F The next equation also obeys the syntax rules This equation uses the inverse function 1 1 22 instead of the fractional form ª 1 2 Notice that the SIN function is nested inside the INV function INV is typed by 3 º1 1 1 22 1 1 1 222 Example Area of a Polygon The equation for area of a regular polygon with n sides of length d is Area n sin cos 4 1 π π n n d 2 d 2 n π You can ...

Страница 108: ... equation to correct the error See Editing and Clearing Equations earlier in this chapter By not checking equation syntax until evaluation the HP 32SII lets you create equations that might actually be messages This is especially useful in programs as described in chapter 12 Verifying Equations When you re viewing an equation not while you re typing an equation you can press to show you two things ...

Страница 109: ...nd length of the equation you type in an example should match the values shown in this manual Example Checksum and Length of an Equation Find the checksum and length for the pipe volume equation at the beginning of this chapter Keys Display Description G z as required ºπº º Displays the desired equation hold Display equation s checksum and length release ºπº º Redisplays the equation Leaves Equati...

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Страница 111: ...e If you know any two of these variables then SOLVE can calculate the value of the third When the equation has only one variable or when known values are supplied for all variables except one then to solve for x is to find a root of the equation A root of an equation occurs where an equality or assignment equation balances exactly or where an expression equation equals zero This is equivalent to t...

Страница 112: ...ion at the root which should be zero For some complicated mathematical conditions a definitive solution cannot he found and the calculator displays See Verifying the Result later in this chapter and Interpreting results and When SOLVE Cannot Find Root in appendix C For certain equations it helps t provide one or two initial guesses for the unknown variable before solving the equation This can spee...

Страница 113: ...s starting from rest Since Equation mode is turned on and the desired equation is turn on and the desired is already in the display you can start solving for D Keys Display Description _ Prompts for unknown known variable D value Selects D prompts for V 0 f value Stores 0 in V prompts for T 5 f value Stores 5 in T prompts for G 9 8 f Stores 9 8 in G prompts for D Try another calculation using the ...

Страница 114: ...le K and T is temperature Kelvins K C 273 1 Enter the equation Keys Display Description G K P y º Selects Equation mode and starts the equation K V c K N y K R y K T º º º º º º Terminates and displays the equation Checksum and length A 2 liter bottle contains 0 005 moles of carbon dioxide gas at 24 C Assuming that the gas behaves as an ideal gas calculate its pressure Since Equation mode is turne...

Страница 115: ... Stores 05 in P prompts for V 5 f Stores 5 in V prompts for H f Retains previous R prompts for T 18 273 1 Calculates T Kelvins f Stores 291 1 in T solves for N 28 y Calculates mass in grams N 28 K V p Calculates density in grams per liter Understanding and Controlling SOLVE SOLVE uses an iterative repetitive procedure to solve for the unknown variable The procedure starts by evaluating the equatio...

Страница 116: ...tion root for the unknown that is the value that makes the evaluation of the equation equal to zero The Y register press 9 contains the previous estimate for the root This number should be the same as the value in the X register If it is not then the root returned was only an approximation and the values in the X and Y registers bracket the root These bracketing numbers should be close together Th...

Страница 117: ... guesses whether you enter guesses or not If you enter only one guess and store it in the variable the second guess will be the same value since the display also holds the number you just stored in the variable If such is the case the calculator changes one guess slightly so that it has two different guesses Entering your own guesses has the following advantages By narrowing the range of search gu...

Страница 118: ...unknown guesses can prevent these values from occurring For example y t log x results in an error if x 0 messages 1 2 or 1 2 In the following example the equation has more than one root but guesses help find the desired root Example Using Guesses to Find a Root Using a rectangular piece of sheet metal 40 cm by 80 cm form an open top box having a volume of 7500 cm3 You need to find the height of th...

Страница 119: ...H 1 2 y 20 K H 2º1 2 y 4 y K H º1 2º º 1 2º1 Terminates and displays the equation Checksum and length It seems reasonable that either a tall narrow box or a short flat box could be formed having the desired volume Because the taller box is preferred larger initial estimates of the height are reasonable However heights greater than 20 cm are not physically possible because the metal sheet is only 4...

Страница 120: ... cm If you ignored the upper limit on the height 20 cm and used initial estimates of 30 and 40 cm you would obtain a height of 42 0256 cm a root that is physically meaningless If you used small initial estimates such as 0 and 10 cm you would obtain a height of 2 9774 cm producing an undesirably short flat box If you don t know what guesses to use you can use a graph to help the behavior of the equ...

Страница 121: ...0 50 H _10 For More Information This chapter gives you instructions for solving for unknowns or roots over a wide range of applications Appendix C contains more detailed information about how the algorithm for SOLVE works how to interpret results what happens when no solution is found and conditions that can cause incorrect results ...

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Страница 123: ...nterval of integration is a to b then the integral can be expressed mathematically as b a dx x f I f x b x a I The quantity I can be interpreted geometrically as the area of a region bounded by the graph of the function f x the x axis and the limits x a and x b provided that f x is nonnegative throughout the interval of integration The operation operation FN integrates the current equation with re...

Страница 124: ... equation list press z or z to display the desired equation 4 Select the variable of integration Press variable This starts the calculation uses far more memory than any other operation in the calculator If executing causes a message refer to appendix B You can halt a running integration calculation by pressing or f However no information about the integration is available until the calculation fi...

Страница 125: ...uation start over from step 1 with an equation that defines the integrated Example Bessel Function The Bessel function of the first kind of order 0 can be expressed as π π 0 0 sin cos 1 dt t x J Find the Bessel function for x values of 2 and 3 Enter the expression that defines the integrand s function cos x sin t Keys Display Description z b ALL Y Clears memory G Current equation or Selects Equati...

Страница 126: ...Prompts for value of X 2 f x 2 Starts integrating calculates result for π 0 t f M p The final result for J0 2 Now calculate J0 3 with the same limits of integration You must respecify the limits of integration 0 π since they were pushed off the stack by the subsequent division by π Keys Display Description 0 M Enters the limits of integration lower limit first G 1 º 1 2 Displays the current equati...

Страница 127: ...at x 0 the lower limit of integration an error would result However the integration algorithm normally does not evaluate functions at either limit of integration unless the endpoints of the interval of integration are extremely close together or the number of sample points is extremely large Keys Display Description G The current equation or Selects Equation mode N K X 1 Starts the equation 1 2 Th...

Страница 128: ...s of functions that can cause problems as well as techniques for dealing with them are discussed in appendix D Specifying Accuracy The display format s setting FIX SCI ENG or ALL determines the precision of the integration calculation the greater the number of digits displayed the greater the precision of the calculated integral and the greater the time required to calculate it The fewer the numbe...

Страница 129: ... specifying that the function is accurate to two decimal places 9 9 Rolls down the limits of integration frown the Z and T registers into the X and Y registers G 1 2ª Displays the current Equation X The integral approximated to two decimal places Z The uncertainty of the approximation of the integral The integral is 1 61 0 00100 Since the uncertainty would not affect the approximation until its th...

Страница 130: ...e display 9 9 Rolls down the limits of integration from the Z and T registers into the X and Y registers G 1 2ª Displays the current equation X Calculates the result Z Note that the uncertainty is about 1 100 as large as the uncertainty of the SCI 2 result calculated previously z 4 Restores FIX 4 format z Restores Degrees mode This uncertainty indicates that the result might be correct to only fou...

Страница 131: ...er gives you instructions for using integration in the HP 32SII over a wide range of applications Appendix D contains more detailed information about how the algorithm for integration works conditions that could cause incorrect results conditions that prolong calculation time and obtaining the current approximation to an integral ...

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Страница 133: ...complex number 1 Type the imaginary part 2 Press 3 Type the real part Complex numbers in the HP 32SII are handled by entering each part imaginary and real of a complex number as a separate entry To enter two complex numbers you enter four separate numbers To do a complex operation press z F before the operator For example to do 2 i 4 3 i 5 press 4 2 5 3z F The result is 5 i 9 Press Z to see the im...

Страница 134: ...nd stored separately you can easily work with or alter either part by itself y1 Z1 x1 Complex function y2 y imaginary part Z2 x2 x real part Complex input z or z1 and z2 Complex result z Always enter the imaginary part the y part of a number first The real portion of the result zx is displayed press Z to view the imaginary portion zy For two number operations the first complex number z1 is replica...

Страница 135: ...do real operations but precede the operator with z F To do an operation with one complex number 1 Enter the complex number z composed of x i y by keying in y x 2 Select the complex function Functions for One Complex Number z To Calculate Press Change sign z z F _ Inverse 1 z z F 3 Natural log ln z z F Natural antilog ez z F Sin z z F N Cos z z F Q Tan z z F T ...

Страница 136: ...z2 second 3 Select the arithmetic operation Arithmetic With Two Complex Numbers z1 and z2 To Calculate Press Addition z1 z2 z F Subtraction z1 z2 z F Multiplication z1 z2 z F y Division z1 z2 z F p Power function 2 1 z z z F 0 Examples Here are some examples of trigonometry and arithmetic with complex numbers Evaluate sin 2 i 3 Keys Display Description 3 2 z F N Real part of result Z Result is 9 1...

Страница 137: ...complex operations when calculating just one part of a complex number Keys Display Description 2 5 _ Enters imaginary part of first complex number as a fraction 4 Enters real part of first complex number 2 3 _ Enters imaginary part of second complex number as a fraction 3 z F y Completes entry of second number and then multiplies the two complex numbers Z Result is 11 7333 i 3 8667 Evaluate 2 z e ...

Страница 138: ...eal numbers in polar form or polar notation These forms use pairs of numbers as do complex numbers so you can do arithmetic with these numbers by using the complex operations Since the HP 32SII s complex operations work on numbers in rectangular form convert polar form to rectangular form using r before executing the complex operation then convert the result back to polar form a i b r cos θ i sin ...

Страница 139: ... the polar coordinates to rectangular coordinates y 185 lb 62 o 100 lb 261 o 170 lb 143 o L 1 L 2 L 3 x Keys Display Description z Sets Degrees mode 62 185 r Enters L1 and converts it to rectangular form 143 170 r Eaters and converts L2 z F Adds vectors 261 100 r Enters and converts L3 z F Adds LI L2 L3 z q Converts vector hack to polar form displays r Z Displays θ ...

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Страница 141: ... base 16 uses integers only The top row keys become digits through Octal mode OCT annunciator on Converts numbers to base 8 uses integers only The and unshifted top row keys are inactive Binary mode BIN annunciator on Converts numbers to base 2 uses integers only Digit keys other than and and the unshifted top row functions are inactive If a number is longer than 12 digits then the outer top row k...

Страница 142: ... Use the 6 key to type F z w The entire binary number does riot fit The annunciator indicates that the number continues to the left the annunciator Points to Displays the rest of the number The full number is 100100111111112 6 Displays the first 12 digits again z w 8 Restores base 10 Arithmetic in Bases 2 8 and 16 You can perform arithmetic operations using y and p in any base The only function ke...

Страница 143: ...he displayed number and not the number in the X register arithmetic does alter the number in the X register If the result of an operation cannot be represented in 36 bits the display shows and then shows the largest positive or negative number possible Example Here are some examples of arithmetic in Hexadecimal Octal and Binary modes 12F16 E9A16 Keys Display Description z w Sets base 16 HEX annunc...

Страница 144: ... calculations When a number appears in hexadecimal octal or binary base it is shown as a right justified integer with up to 36 bits 12 octal digits or 9 hexadecimal digits Leading zeros are riot displayed but they are important because they indicate a positive number For example the binary representation of 12510 is displayed as 11111101 which is the same as these 36 digits 00000000000000000000000...

Страница 145: ...imal 9 digits octal 12 digits and binary bases 36 digits and the range of decimal numbers 11 digits that can be converted to these other bases Range of Numbers for Base Conversions Base Positive Integer of Largest Magnitude Negative Integer of Largest Magnitude Hexadecimal 7FFFFFFFF 800000000 Octal 377777777777 400000000000 Binary 011111111111111111111 111111111111111 100000000000000000000 0000000...

Страница 146: ...r can have 36 digits three times as many digits as fit in the display Each 12 digit display of a long number is called a window 36 bit number Highest window Lowest window displayed When a binary number is larger than the 12 digits the or annunciator or both appears indicating in which direction the additional digits lie Press the indicated key or 6 to view the obscured window 10 7B Picture SHOWing...

Страница 147: ... E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Press to view the digits obscured by the or label Keys Display Description z w 123456712345 _ Enters a large octal number H A A Drops leftmost three digit s hold Shows all digits z w 8 8 8 Restores Decimal mode ...

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Страница 149: ...y Weighted mean x weighted by y A Summation statistics n Σx Σy Σx2 Σy2 and Σxy L R x y r m b x y x w x y n x y x y xy 2 2 sx sy x y σ σ s σ SUMS Entering Statistical Data One and two variable statistical data are entered or deleted in similar fashion using the 6 or z 4 key Data values are accumulated as summation statistics in six statistic s registers 28 through 33 whose names are displayed ire t...

Страница 150: ...ave entered an unequal number of x and y values No error occurs but the results are obviously not meaningful To recall a value to the display immediately after it has been entered press z Entering Two Variable Data When your data consist of two variables x is the independent variable and y is the dependent variable Remember to enter an x y pair in reverse order y x so that y ends up in the Y regis...

Страница 151: ...e correct value s using 6 If the incorrect values were the ones just entered press z to retrieve them then press z 4 to delete them The incorrect y value was still in the Y register and its T value was saved in the LAST X register Example Key in the x y values on the left these make the corrections shown on the right Initial x y Corrected x y 20 4 20 5 400 6 40 6 Keys Display Description z b Clear...

Страница 152: ...ey Description L R The linear regression menu linear estimation º ˆ and curve fitting T P E See Linear Regression later in this chapter x y z The mean menu º º See Mean below s σ z 2 The standard deviation menu Uº U σº σ See Sample Standard Deviation and Population Standard Deviation later in this chapter SUMS z 5 The summation menu Q º º º See Summation Statistics later in this chapter Mean Mean ...

Страница 153: ... all data as x values Keys Display Description z b Clears the statistics registers 15 5 6 Enters the first time 9 25 6 10 6 12 5 6 12 6 8 5 6 Enters the remaining data six data points accumulated º Calculates the mean time to complete the process Example Weighted Mean Two Variables A manufacturing company purchases a certain part four times a year Last year s purchases were Price per Part x 4 25 4...

Страница 154: ...e standard deviation of x values Press 2 U for the standard deviation of y values The σº and σ keys in this menu are described in the next section Population Standard Deviation Example Sample Standard Deviation Using the same process times as in the above mean example May Kitt now wants to determine the standard deviation time sx of the process 15 5 9 25 10 0 12 5 12 0 8 5 Calculate the standard d...

Страница 155: ...pulation standard deviation of the y values Example Population Standard Deviation Grandma Tinkle has four grown sons with heights of 170 173 174 and 180 cm Find the population standard deviation of their heights Keys Display Description z b Clears the statistics registers 170 6 173 6 174 6 180 6 Enters data 2 σº Four data points accumulated Calculates the population standard deviation Linear regre...

Страница 156: ...alculated line fits the data P Slope of the calculated line E y intercept of the calculated line To find an estimated value for x or y key in a given hypothetical value for y or x then press º or ˆ To find the values that define the line that best fits your data press followed by T P or E Example Curve Fitting The yield of a new variety of rice depends on its rate of fertilization with nitrogen Fo...

Страница 157: ...03 4 24 Size 17 7 x 25 2 cm data 4 63 0 6 5 78 20 6 6 61 40 6 7 21 60 6 Enters data displays n 7 78 80 6 Five data pairs entered º ˆ T P E Displays linear regression menu T Correction coefficient data closely approximate a straight line z P Slope of the line z E y intercept ...

Страница 158: ...g of nitrogen fertilizer were applied to the rice field Predict the grain yield based on the above statistics Keys Display Description 70 _ Enters hypothetical x value ˆ The predicted yield in tons per hectare Limitations on Precision of Data Since the calculator uses finite precision 12 to 15 digits it follows that there are limitations to calculations due to rounding Here are two examples ...

Страница 159: ...e sure to supply an x value that is less 7777000 Similar inaccuracies can result if your x and y values have greatly different magnitudes Again scaling the data can avoid this problem Effect of Deleted Data Executing z 4 does not delete any rounding errors that might have been generated in the statistics registers by the original data values This difference is not serious unless the incorrect data...

Страница 160: ...tics Registers Use 6 to store data pairs 1 2 and 3 4 in the statistics registers Then view the stored statistical values Keys Display Description z b Clears the statistics registers 2 1 6 Stores the first data pair 1 2 4 3 6 Stores the second data pair 3 4 z X º Displays VAR catalog and views Σxy register z Views Σy2 register z º Views Σx2 register z Views Σy register z º Views Σx register z Q Vie...

Страница 161: ... in the following table Statistics Registers Register Number Description n 28 Number of accumulated data pairs Σx 29 Sum of accumulated x values Σy 30 Sum of accumulated y values Σx2 31 Sum of squares of accumulated x values Σy2 32 Sum of squares of accumulated y values Σxy 33 Sum of products of accumulated x and y values You can load a statistics register with a summation by storing the numb r 28...

Страница 162: ...Statistics Programs File name 32sii Manual E 0424Page 14 162 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Part 2 Programming ...

Страница 163: ...put or output control or more intricate logic A program lets you repeat operations and calculations in the precise manner you want In this chapter you will learn how to program a series of operations In the next chapter Programming Techniques you will learn about subroutines and conditional instructions Example A Simple Program To find the area of a circle with a radius of 5 you would use the form...

Страница 164: ...tes Program entry mode PRGM annunciator on z U Resets program pointer to PRGM TOP z º Radius 2 M π y º Area πx2 z d Exits Program entry mode Try running this program to find the area of a circle with a radius of 5 Keys Display Description z U This sets the program to its beginning 5 f The answer We will continue using the above program for the area of a circle to illustrate programming concepts an...

Страница 165: ...annot assign the same label more than once this causes the message but a label can use the same letter that a variable uses It is possible to have one program the top one in memory without any label However adjacent programs need a label between them to keep them distinct Program Line Numbers Line numbers are preceded by the letter for the label such as If one label s routine has more than 99 line...

Страница 166: ...nd read Execute a bit faster Can automatically prompt When a program executes a line containing an equation the equation is evaluated in the same way that W evaluates an equation in the equation list For program evaluation in an equation is essentially treated as There s no programmable equivalent to for an assignment equation other than writing the equation as an expression then using STO to stor...

Страница 167: ...te Program entry mode 2 Press z U to display This sets the program pointer to a known spot before any other programs As you enter program lines they are inserted before all other program lines If you don t need any other programs that might be in memory clear program memory by pressing z b To confirm that you want all programs deleted press after the message 3 Give the program a label a single let...

Страница 168: ...ion does not become part of the equation list After you ve entered an equation you can press to see its checksum and length Hold the key to keep the values in the display For a long equation the and annunciators show that scrolling is active for this program line You can use 6 and to scroll the display Press SCRL to turn off and to use the top row keys to enter program instructions Keys That Clear...

Страница 169: ...as you hold down the key the name is displayed Example Entering a Labeled Program The following keystrokes delete the previous program for the area of a circle and enter a new one that includes a label and a return instruction If you make a mistake during entry press a to delete the current program line then reenter the line correctly Keys Display Description z d Activates Program entry mode PRGM ...

Страница 170: ...s Display Description z d z U Activates Program entry mode sets pointer to top of memory z E Labels this program routine E for equation H R Stores radius in variable R G M y K R 0 2 πº Selects Equation entry mode enters the equation returns to Program entry mode Checksum and length of equation Ends the program z X Displays label E and the length of the program in bytes Cancels program entry Runnin...

Страница 171: ... area is displayed 2 5 W E Calculates area of the second circle using program E 2 M y W A Calculates area of the third circle Testing a Program If you know there is an error in a program but are not sure where the error is then a good way to test the program is by stepwise execution It is also a good idea to test a long or complicated program before relying on it By stepping through its execution ...

Страница 172: ...l you find an error an incorrect result occurs or reach the end of the program If Program entry mode is active then z or z simply changes the programs pointer without executing lines Holding down an arrow key during program entry makes the lines roll by automatically Example Testing a Program Step through the execution of the program labeled A Use a radius of 5 for the test data Check that Program...

Страница 173: ...riables that already have values stored From automatic equation prompting if enabled by flag 11 set This is also handy if you re using equations In a program you can display information in these ways With a VIEW instruction which shows the name and value of a variable This is the most handy technique On the stack only the value in the X register is visible You can use PSE for a 1 second look at th...

Страница 174: ...radius which we can assign to R 2 In the beginning of the program insert an INPUT instruction for each variable whose value you will need Later in the program when you write the part of the calculation that needs a given value insert a K variable instruction to bring that value back into the stack Since the INPUT instruction also leaves the value you just entered in the X register you don t have t...

Страница 175: ...pt you for that variable such as The value displayed and the contents of the X register will be the current contents of R To leave the number unchanged just press f To change the number type the new number and press f This new number writes over the old value in the X register You can enter a number as a fraction if you want If you need to calculate a number use normal keyboard calculations then p...

Страница 176: ...you don t want the program to stop see Displaying Information without Stopping below For example see the program for Normal and Inverse Normal Distributions in chapter 16 Lines T15 and T16 at the end of the T routine display the result for X Note also that this VIEW instruction in this program is preceded by a RCL instruction The RCL instruction is not necessary but it is convenient because it bri...

Страница 177: ...tors turn on when the message is displayed You can then use 6 and to scroll the display You can press SCRL to turn off and make the top row keys perform their normal functions If you don t want the program to stop see Displaying Information without Stopping below Example INPUT VIEW and Messages in a Program Write an equation to find the surface area and volume of a cylinder given its radius and he...

Страница 178: ... y K R K H ºπº º 1 Calculates the surface area Checksum and length of equation H S Stores the surface area in S x 0 Sets flag 10 to display equations G K V K O K L o o K A K R K E K A Displays message in equations x 0 Clears flag 10 V Displays volume S Displays surface area Ends program z X Displays label C and the length of the program in bytes Checksum and length of program Cancels program entry...

Страница 179: ...splays a variable with VIEW or displays an equation message You normally have to press f to resume execution If you want you can make the program continue while the information is displayed If the next program line after a VIEW instruction or a viewed equation contains a PSE pause instruction the information is displayed and execution continues after a 1 second pause In this case no scrolling or k...

Страница 180: ...nstruction or an equation that s displayed flag 10 set the variable or equation is displayed instead and the display remains after the 1 second pause Interrupting a Running Program You can interrupt a running program at any time by pressing or f The program completes its current instruction before stopping Press f run stop to resume the program If you interrupt a program and then press W z U or yo...

Страница 181: ...a The pointer then moves to the preceding line If you are deleting more than one consecutive program line start with the last line in the group 3 Key in the new instruction if any This replaces the one you deleted 4 Exit program entry or d To insert a program line 1 Locate and display the program line that is before the spot where you would like to insert a line 2 Key in the new instruction it is ...

Страница 182: ... active there are three ways to change the program pointer the displayed line Use the arrow keys z and z Pressing z at the last line wraps the pointer around to while pressing z at wraps the pointer around to the last program line To move more than one line at a time scrolling continue to hold the or key Press U to move the program pointer to Press U label nn to move to a labeled line number less ...

Страница 183: ...he Catalog of Programs MEM The catalog of programs is a list of all program labels with the number of bytes of memory used by each label and the lines associated with it Press z X to display the catalog and press z or z to move within the list You can use this catalog to Review the labels in program memory and the memory cost of each labeled program or routine Execute a labeled program Press W or ...

Страница 184: ... all programs The Checksum The checksum is a unique hexadecimal value given to each program label and its associated lines until the next label This number is useful for comparison with a known checksum for an existing program that you have keyed into program memory If the known checksum and the one shown by your calculator are the same then you have correctly entered all the lines of the program ...

Страница 185: ...an equation in a program line earlier in this chapter Nonprogrammable Functions The following functions of the HP 32 II are not programmable z b z U z b z U label nn a z X z z z d G z Programming with BASE You can program instructions to change the base mode using z w These settings work in programs just as they do as functions executed from the keyboard This allows you to write programs that acce...

Страница 186: ...affect the program lines as you enter them Equation evaluation SOLVE and FN automatically set Decimal mode Numbers Entered in Program Lines Before starting program entry set the base mode The current setting for the base mode determines the base of the numbers that are entered into program lines The display of these numbers changes when you change the base mode Program line numbers always appear i...

Страница 187: ...ver would be to use a stack which has been filled with the constant see Filling the Stack with a Constant in chapter 2 Rorer s Method is a useful means of rearranging polynomial expressions to cut calculation steps and calculation time It is especially expedient with SOLVE and FN two relatively complex operations that use subroutines This method involves rewriting a polynomial expression in a nest...

Страница 188: ... º 5x 2 5x 2 y º 5x 2 x y º 5x 2 x2 y º 5x 2 x3 z X Displays label P which takes 19 5 bytes z Checksum and length Cancels program entry Now evaluate this polynomial x 7 Keys Display Description W P value Prompts for x 7 f 8 Result A more general form of this program for any equation Ax B C D E would be ...

Страница 189: ...Simple Programming 12 27 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm º º º º Checksum and length E93F 028 5 ...

Страница 190: ......

Страница 191: ...ith counters to execute a set of instructions a certain number of times Using indirect addressing to access different variables using the same program instruction Routines in Programs A program is composed of one or more routines A routine is a functional unit that accomplishes something specific Complicated programs need routines to group and separate tasks This makes a program easier to write re...

Страница 192: ... it can call other subroutines XEQ must branch to a label LBL for the subroutine It cannot branch to a line number At the very next RTN encountered program execution returns to the line after the originating XBQ For example routine Q in the Normal and Inverse Normal Distributions program in chapter 16 is a subroutine to calculate Q x that is called from routine D by line Routine Q ends with a RTN ...

Страница 193: ...ine can call another subroutine and that subroutine can call yet another subroutine This nesting of subroutines the calling of a subroutine within another subroutine is limited to a stack of subroutines seven levels deep not counting the topmost program level The operation of nested subroutines is as shown below MAIN program top level End of program Attempting to execute a subroutine nested more t...

Страница 194: ...lation in a larger program The subroutine calls upon another subroutine a nested subroutine labeled Q to do the repetitive squaring and addition This saves memory by keeping the program shorter than it would be without the subroutine Starts subroutine here Enters A Enters B Enters C Enters D Recalls the data º 1 A2 2 3 A2 B2 4 5 A2 B2 C2 6 2 2 2 2 D C B A Returns to main routine 135 Nested subrout...

Страница 195: ...ific line number during a program A Programmed GTO Instruction The GTO label instruction press z U label transfers the execution of a running program to the program line containing that label wherever it may be The program continues running from the new location and never automatically returns to its point of origination so GTO is not used for subroutines For example consider the Curve Fitting pro...

Страница 196: ...n start here 1 Branches to Z 1 Branch to here Using GTO from the Keyboard You can use z U to move the program pointer to a specified label or line number without starting program execution To z U To a line number z U label nn nn 100 For example z U A05 To a label z U label but only if program entry is not active no program lines displayed PRGM off For example z U A ...

Страница 197: ...f the X register does not contain zero then the program skips the next line thereby branching to line A07 This rule is commonly known as Do if true Do next if true º 2 Skip next if false 1 2 1 The above example points out a common technique used with conditional tests the line immediately after the test which is only executed in the true case is a branch to another label So the net effect of the t...

Страница 198: ...e number in the Y register These do not compare the variables X and Y Select the category of comparison then press the menu key for the conditional instruction you want The Test Menus x y x 0 for x y for x 0 for x y for x 0 for x y for x 0 for x y for x 0 for x y for x 0 for x y for x 0 If you execute a conditional test from the keyboard the calculator will display or Example The Normal and Invers...

Страница 199: ... flag is clear Meanings of Flags The HP 32SII has 12 flags numbered 0 through 11 All flags can be set cleared and tested from the keyboard or by a program instruction The default state of all 12 flags is clear The three key memory clearing operation described in appendix B clears all flags Flags are not affected by z b Flags 0 1 2 3 and 4 have no preassigned meanings That is their states will mean...

Страница 200: ...ult Fraction display off display real numbers in the current display format Fraction denominators not greater than the c value Reduce fractions to smallest form Set Fraction display on display real numbers as fractions Fraction denominators are factors of the c Value No reduction of fractions Used only if flag 8 is set Flag 10 controls program execution of equations When flag 10 is clear the defau...

Страница 201: ...occurs only once regardless of the number of times the variable appears in the equation When solving no prompt occurs for the unknown when integrating no prompt occurs for the variable of integration Prompts halt execution Pressing f resumes the calculation using the value for the variable you keyed in or the displayed current value of the variable if f is your sole response to the prompt Flag 11 ...

Страница 202: ...ustrated under Conditional Instructions earlier in this chapter If you test a flag from the keyboard the calculator will display or It is good practice in a program to make sure that any conditions you will be testing start out in a known state Current flag settings depend on how they have been left by earlier programs that have been run You should not assume that any given flag is clear for insta...

Страница 203: ...f both the X and Y inputs for a Power model curve Note that lines S03 S04 L04 and E03 clear flags 0 and 1 to ensure that they will be set only as required for the four curve models Program Lines Description Clears flag 0 the indicator for In X Clears flag 1 the indicator for In Y Sets flag 0 the indicator for In X Clears flag 1 the indicator for In Y Clears flag 0 the indicator for In X Sets flag ...

Страница 204: ...flag 10 are used Messages in this program are listed a MESSAGE and are entered as equations 1 Set Equation entry mode by pressing G the EQN annunciator turns on 2 Press K letter for each alpha character in the message press o the f key for each space character 3 Press to insert the message in the current program line and end Equation entry mode Program Lines Description Begins the fraction program...

Страница 205: ...gth 10C3 102 0 Use the above program to see the different forms of fraction display Keys Display Description W F value Executes label F prompts for a fractional number V 2 53 f value Stores 2 53 in V prompts for denominator D 16 f Stores 16 as the c value Displays message then the decimal number f d Message indicates the fraction format denominator is no greater than 16 then shows the fraction d i...

Страница 206: ... program on page 15 31 in chapter 15 is an example of an infinite loop It is used to collect the initial data prior to the coordinate transformation After entering the three values it is up to the user to manually interrupt this loop by selecting the transformation to be performed pressing W N for the old to new system or W O for the new to old system Conditional Loops GTO When you want to perform...

Страница 207: ... DSE ISG When you want to execute a loop a specific number of times use the z k increment skip if greater than or m decrement skip if less than or equal to conditional function keys Each time a loop function is executed in a program it automatically decrements or increments a counter value stored in a variable It compares the current counter value to a final counter value then continues or exits t...

Страница 208: ...e changes with loop execution fff is the final counter value must be three digits This value does not change as the loop runs ii is the interval for incrementing and decrementing must be two digits or unspecified This value does not change An unspecified value for ii is assumed to be 01 increment decrement by 1 Given the loop control number ccccccc fffii DSE decrements ccccccc to ccccccc ii compar...

Страница 209: ...value final value continue loop If current value final value exit loop For example the loop control number 0 050 for ISG means start counting at zero count up to 50 and increase the number by 1 each loop The following program uses ISG to loop 10 times The loop counter 0000001 01000 is stored in the variable Z Leading and trailing zeros can be left off Press Z to see that the loop control number is...

Страница 210: ... a variable whose contents can refer to another variable or label It holds a number just like any other variable A through Z is a programming function that directs Use the number in i to determine which variable or label to address This is an indirect address A through Z are direct addresses Both and are used together to create an indirect address See the examples below By itself i is just another...

Страница 211: ...iable Z or label Z 27 variable i 28 n register 29 Σx register 30 Σy register 31 Σx2 register 32 Σy2 register 33 Σxy register 34 or 34 or 0 error 6L5 Only the absolute value of the integer portion of the number in i is used for addressing The INPUT i and VIEW i operations label the display with the name of the indirectly addressed variable or register The SUMS menu enables you to recall values from...

Страница 212: ... an index holding the address of the variable that contains the loop control number for the functions DSE and ISG See the second example below Example Choosing Subroutines With i The Curve Fitting program in chapter 16 uses indirect addressing to determine which model to use to compute estimated values for x and y Different subroutines compute x and y for the different models Notice that i is stor...

Страница 213: ... model 8 LBL H Compute x for logarithmic model 9 LBL I Compute x for exponential model 10 LBL J Compute x for power model Example Loop Control With i An index value in i is used by the program Solutions of Simultaneous Equations Matrix Inversion Method in chapter 15 This program uses the looping instructions L and L in conjunction with the indirect instructions 1L2 and 1L2 to fill and manipulate a...

Страница 214: ...s the final counter value execution branches back to A Label J is a loop that completes the inversion of the 3 3 matrix Program Lines Description This routine completes inverse by dividing by determinant ª1L2 Divides element L Decrements index value so it points closer to A Loops for next value Returns to the calling program or to Equations with i You can use i in an equation to specify a variable...

Страница 215: ...6 L Stores counter Initializes sum Checksum and length EA5F 017 0 Program Lines Description Starts summation loop 1L2 Equation to evaluate the ith square Press G to start the equation Ckecksum and length of equation 48AD 006 0 Adds ith square to sum L Tests for end of loop Branches for next variable Ends program Checksum and length of program 19A8 013 5 ...

Страница 216: ......

Страница 217: ...m that defines the function See To write a program for SOLVE below 2 Select the program to solve press V label You can skip this step if you re re solving the same program 3 Solve for the unknown variable press variable Notice that FN is required if you re solving a programmed function but not if you re solving an equation from the equation list To halt a calculation press or f The current best es...

Страница 218: ...he solution If your equation is f x g x your program should calculate f x g x 0 is implied A function programmed as an equation can be any type of equation equality assignment or expression The equation is evaluated by the program and its value goes to zero at the solution If you want the equation to prompt for variable values instead of including INPUT instructions make sure flag 11 is set 4 End ...

Страница 219: ...scription z d z U Sets Program mode Type in the program Program Lines Description Identifies the programmed function Stores P Stores V Stores N Stores R Stores T Pressure º Pressure volume Number of moles of gas º Moles gas constant º Moles gas constant temp _ P V N R T Ends the program Checksum and length 053B 019 5 Press to cancel Program entry mode Use program G to solve for the pressure of 0 0...

Страница 220: ...f Stores 297 1 in T solves for P Pressure is 0 0610 atm Example Program Using Equation Write a program that uses an equation to solve the Ideal Gas Law Keys Display Description z d z U Selects Program entry mode Moves program pointer to top of the list of programs z H Labels the program x 1 Enables equation prompting G K P y K V K N y K R y K T º º º Evaluates the equation clearing flag 11 Checksu...

Страница 221: ...7 1 in T solves for new P K L Calculates pressure change of the gas when temperature drops from 297 1 K to 287 1 K negative result indicates drop in pressure Using SOLVE in Program You can use the SOLVE operation as part of a program If appropriate include or prompt for initial guesses into the unknown variable and into the X register before executing the SOLVE variable instruction The two instruc...

Страница 222: ...ot finding a root such as by choosing new initial estimates or changing an input value Example SOLVE in a Program The following excerpt is from a program that allows you to solve for x or y by pressing W X or Y Program Lines Description Setup for X Index for X Branches to main routine Checksum and length CCEC 004 5 Setup for Y Index for Y Branches to main routine Checksum and length 2E48 004 5 Mai...

Страница 223: ...imit and press then key in the upper limit 4 Select the variable of integration and start the calculation press variable Notice that FN is required if you re integrating a programmed function but riot if you re integrating an equation from the equation list You can halt a running integration calculation by pressing or f However no information about the integration is available until the calculatio...

Страница 224: ...ion is usually included as an expression specifying the integrand though it can be any type of equation If you want the equation to prompt for variable values instead of including INPUT instructions make sure flag 11 is set 4 End the program with a RTN Program execution should end with the value of the function in the X register Example Program Using Equation The sine integral function in the exam...

Страница 225: ...cution time are controlled by the display format at the time the program runs The two integration instructions appear in the program as label G variable The programmed FN instruction does not produce a labeled display value since this might riot be the significant output for your program that is you might want to do further calculations with this number before displaying it If you do want this res...

Страница 226: ...le and FN d variable instructions cannot call a routine that contains another SOLVE or FN instruction That is neither of these instructions can be used recursively For example attempting to calculate a multiple integral will result in an 1 2 error Also SOLVE and FN cannot call a routine that contains an label instruction if attempted a or error will be returned SOLVE cannot call a routine that con...

Страница 227: ...thematics Programs Vector Operations This program performs the basic vector operations of addition subtraction cross product and dot or scalar product The program uses three dimensional vectors and provides input and output in rectangular or polar form Angles between vectors can also be found Y P X T R Z ...

Страница 228: ... 2 2 2 Z Y X Y R sin P sin T T arctan Y X Z R cos P P arctan 2 2 Y X Z Vector addition and subtraction v1 v2 X U i Y V j Z W k v2 v1 U X i V Y j W Z k Cross product v1 v2 YW ZV i ZU XW j XV YU k Dot Product D XU YV ZW Angle between vectors γ G arccos 2 1 R R D where v1 X i Y j Z k and v2 U i V j W k The vector displayed by the input routines LBL P and LBL R is V1 Program Listing ...

Страница 229: ...6 0 Defines beginning of rectangular to polar conversion process 8º θ8T Calculates Y X 2 2 and arctan Y X º65 Saves T arctan Y X Gets Y X 2 2 back 8º θ8T Calculates Z Y X 2 2 2 and P Saves R º65 Saves P Checksum and length 3D28 018 0 Defines the beginning of the polar input display routine Displays or accepts input of R Displays or accepts input of T Displays or accepts input of P θ8T 8º Calculate...

Страница 230: ...ength D518 022 5 Defines the beginning of the vector enter routine Copies values in X Y and Z to U V and W respectively Loops back for polar conversion and display input Checksum and length 1032 012 0 Defines beginning of vector exchange routine Exchanges X Y and Z with U V and W respectively 65 65 65 Loops back for polar conversion and display input Checksum and length DACE 016 5 Defines beginnin...

Страница 231: ...back for polar conversion and display input Checksum and length 641B 016 5 Defines the beginning of the vector subtraction routine Multiplies X Y and Z by 1 to change the sign º º º Goes to the vector addition routine Checksum and length D051 017 0 Defines the beginning of the cross product routine º º Calculates YW ZV which is the X component º º Calculates ZU WX which is the Y component º ...

Страница 232: ...nent Stores Y component Stores X component Loops back for polar conversion and display input Checksum and length FEB2 033 0 Defines beginning of dot product and vector angle routine º º º Stores the dot product of XU YV ZW Displays the dot product ª Divides the dot product by the magnitude of the X Y Z vector 8º θ8T º65 8º θ8T Calculates the magnitude of the U V W vector º65 ...

Страница 233: ...rs as 1 followed by it will require only 3 bytes To do this you can press 1 _ The terms polar and rectangular which refer to two dimensional systems are used instead of the proper three dimensional terms of spherical and Cartesian This stretch of terminology allows the labels to be associated with their function without confusing conflicts For instance if LBL C had been associated with Cartesian c...

Страница 234: ... form press W P then press f repeatedly to see the individual elements 8 Optional to review v1 in rectangular form press W R then press f repeatedly to see the individual elements 9 If you added subtracted or computed the cross product v1 has been replaced by the result v2 is not altered To continue calculations based on the result remember to press W E before keying in a new vector 10 Go to step ...

Страница 235: ...the direction to the transmitter N y S W E x Antenna Transmitter 7 3 15 7 Keys Display Description z W R value Sets Degrees mode 7 3 f value Starts rectangular input display routine 15 7 f value Sets X equal to 7 3 Sets Y equal to 15 7 76 _ f Sets Z equal to 0 76 and calculates R the radius f Calculates T the angle in the x y plane f Calculates P the angle from the z axis ...

Страница 236: ...at is the angle between the resultant of the force vectors and the lever Z X Y 125 o 63 o F 17 T P 17 1 215 o o F 23 T 80 P 74 2 o o 1 07m First add the force vectors Keys Display Description W P value Starts polar input routine 17 f value Sets radius equal to 17 215 f value Sets T equal to 215 17 f Sets P equal to 17 W E Enters vector by copying it into v2 23 f Sets radius of v1 equal to 23 80 f ...

Страница 237: ...the vector representing the lever and take the cross product Keys Display Description 1 07 f Sets R equal to 1 07 125 f Sets T equal to 125 63 f Sets P equal to 63 W C Calculates cross product and displays R of result f Displays T of cross product f Displays P of cross product W R Displays rectangular form of cross product f f The dot product can be used to resolve the force still in v2 along the ...

Страница 238: ... equations in two or three unknowns It does this through matrix inversion and matrix multiplication A system of three linear equations AX DY GZ J BX EY HZ K CX FY IZ L can be represented by the matrix equation below L K J Z Y X I F C H E B G D A The matrix equation may be solved for X Y and Z by multiplying the result matrix by the inverse of the coefficient matrix Z Y X L K J I F C H E B G D A Sp...

Страница 239: ...rol value in index variable Checksum and length 9F76 012 5 Starts the input loop 1L2 Prompts for and stores the variable addressed by i L Adds one to i If i is less than 13 goes back to LBL L and gets the next value Returns to LBL A to review values Checksum and length 8356 007 5 This routine inverts a 3 3 matrix Calculates determinant and saves value for the division loop J º º Calculates E deter...

Страница 240: ...03 4 24 Size 17 7 x 25 2 cm Program Lines Description º Calculates H determinant BG AH º º L Calculates I determinant AE BD º º Calculates A x determinant EI FH º º Calculates B determinant CH BI º º Calculates C determinant BF CE Stores B º º Calculates D determinant FG DI ...

Страница 241: ...e to point to last element of matrix Recalls value of determinant Checksum and length 4C14 105 0 This routine completes inverse by dividing by determinant ª1L2 Divides element L Decrements index value so it points closer to A Loops for next value Returns to the calling program or to Checksum and length 9737 007 5 This routine multiplies a column matrix and a 3 3 matrix Sets index value to point to...

Страница 242: ...ctor Recalls K from column vector Recalls L from column vector º1L2 Multiplies by last element in row Multiplies by second element in row and adds Multiplies by first element in row and adds Sets index value to display X Y or Z based on input row L Gets result back 1L2 Stores result 1L2 Displays result Returns to the calling program or to Checksum and length 4E9D 021 0 This routine multiples and a...

Страница 243: ...on Checksum and length 4E79 012 0 This routine calculates the determinant º º Calculates A E I º º Calculates A E I D H C º º Calculates A E I D H C G F B º º A E I D H C G F B G E C º º A E I D H C G F B G E C A F H º º A E I D H C G F B G E B A F H D B I Returns to the calling program or to Checksum and length 44B2 037 5 ...

Страница 244: ...3 matrix 6 Optional press W A and repeatedly press f to review the values of the inverted matrix 7 Press W M to multiply the inverted matrix by the column vector and to see the value of X Press f to see the value of Y then press f again to see the value of Z 8 For a new case go back to step 2 Variables Used A through I Coefficients of matrix J through L Column vector values W Scratch variable used...

Страница 245: ...ription W A value Starts input routine 23 f value Sets first coefficient A equal to 23 8 f value Sets B equal to 8 4 f value Sets C equal to 4 15 f value Sets D equal to 15 Continues entry for E through L 14 f Returns to first coefficient entered W I 8 Calculates the inverse and displays the determinant W M Multiplies by column vector to compute X f Calculates and displays Y f Calculates and displ...

Страница 246: ...rm xn an 1xn 1 a1x a0 0 where n 2 3 4 or 5 The coefficient of the highest order term an is assumed to be 1 If the leading coefficient is not 1 you should make it I by dividing all the coefficients in the equation by the leading coefficient See example 2 The routines for third and fifth order polynomials use SOLVE to find one real root of the equation since every odd order polynomial must have at l...

Страница 247: ... solving these two quadratic polynomials A quadratic equation x2 a1x a0 0 is solved by the formula 0 2 1 1 2 1 2 2 a a a x If the discriminant d a1 2 2 ao 0 the roots are real if d 0 the roots are complex being d i a iv u 2 1 Program Listing Program Lines Description Defines the beginning of the polynomial root finder routine Prompts for and stores the order of the polynomial L Uses order as loop ...

Страница 248: ...gth B85F 006 0 Starts the Horner s method loop Saves synthetic division coefficient º Multiplies current sum by next power of x 1L2 Adds new coefficient L Counts down the loop Repeats until done Checksum and length 139C 010 5 Starts solver setup routine Stores location of coefficients to use First initial guess Second initial guess Specifies routine to solve Solves for a real root Gets synthetic d...

Страница 249: ...mplex roots d d Stores imaginary part if complex root Complex roots Returns if complex roots Calculates a1 2 d Calculates a1 2 d Checksum and length E454 034 5 Starts second order solution routine Gets L Gets M Calculates and displays two roots Checksum and length 52B9 006 0 Starts third order solution routine Indicates cubic polynomial to be solved Solves for one real root and puts a0 and a1 for ...

Страница 250: ...order solution routine Indicates fifth order polynomial to be solved Solves for one real root and puts three synthetic division coefficients for fourth order polynomial on stack Discards polynomial function value Stores coefficient Stores coefficient Stores coefficient Calculates a3 Stores a3 Displays real root of fifth order polynomial Checksum and length 0FE9 019 5 Starts fourth order solution r...

Страница 251: ...fficients Solves for real root and puts a0 and a1 for second order polynomial on stack Discards polynomial function value Solves for remaining roots of cubic and stores roots Gets real root of cubic Stores real root Complex roots Calculate four roots of remaining fourth order polynomial If not complex roots determine largest real root y0 º6 º65 º6 º65 Stores largest real root of cubic Checksum and...

Страница 252: ...ª K y0 2 º Creates 10 9 as a lower bound for M2 K º K2 M2 K2 a0 º6 º If M2 10 9 use 0 for M2 M 0 2 a K Stores M J º JK a1 ª a1 2 JK a1 2 º Use 1 if JK a1 2 0 Stores 1 or JK a1 2 ª Calculates sign of C J º J2 J2 a2 J2 a2 y0 C 0 2 2 y a J º Stores C with proper sign J J L K K M Calculate and display two roots of the fourth order ...

Страница 253: ...the second real root or imaginary part of complex root Were there any complex roots Displays complex roots if any Stores second real root Displays second real root Returns to calling routine Checksum and length BE87 015 0 Starts routine to display complex roots L Stores the imaginary part of the first complex root L Displays the imaginary part of the first complex root Displays the real part of th...

Страница 254: ...omial by one order by factoring out x The order and the coefficients are not preserved by the program Because of round off error in numerical computations the program may produce values that are not true roots of the polynomial The only way to confirm the roots is to evaluate the polynomial manually to see if it is zero at the roots For a third or higher order polynomial if SOLVE cannot find a rea...

Страница 255: ...nter the coefficients the first root is calculated A real root is displayed as real value A complex root is displayed as real part Complex roots always occur in pairs of the for u i v and are labeled in the output as real part and i imaginary part which you ll see in the next step 7 Press f repeatedly to see the other roots or to see i imaginary part the imaginary part of a complex root The order ...

Страница 256: ...ts for B 100 f value Stores 100 in B prompts for A 100 _ f Stores 100 in A calculates the first root f Calculates the second root f Displays the third root f Displays the fourth root f L Displays the fifth root Example 2 Find the roots of 4x4 8x3 13x2 10x 22 0 Because the coefficient of the highest order term must be 1 divide that coefficient into each of the other coefficients Keys Display Descri...

Страница 257: ...part of the fourth root f L Displays the imaginary part of the fourth root The third and fourth roots are 1 00 1 00 i Example 3 Find the roots of the following quadratic polynomial x2 x 6 0 Keys Display Description W P value Starts the polynomial root finder prompts for order 2 f value Stores 2 its F prompts for B 1 f value Stores 4 its B prompts for A 6 _f Stores 6 its A calculates the first root...

Страница 258: ... P from the Cartesian coordinate pair x y in the old system to the pair u v in the new translated rotated system u x m cosθ y n sinθ v y n cos θ y n sinθ The inverse transformation is accomplished with the formulas below x u cosθ v sinθ m y u sinθ v cosθ n The HP 32SII complex and polar to rectangular functions make these computations straightforward ...

Страница 259: ...P u y v θ Program Listing Program Lines Description This routine defines the new coordinate system Prompts for and stores M the new origin s x coordinate Prompts for and stores N the new origin s y coordinate Prompts for and stores T the angle θ Loops for review of inputs Checksum and length 2ED3 007 5 This routine converts from the old system to the new system ...

Страница 260: ... º Calculates X M cos T Y N sin T and Y N cos T X M sin T Stores x coordinate in variable U º65 Swaps positions of the coordinates Stores y coordinate in variable V º65 Swaps positions of coordinates back Halts program to display U Halts program to display V Goes back for another calculation Checksum and length 3A46 028 5 This routine converts from the new system to the old system Prompts for and ...

Страница 261: ...start the prompt sequence which defines the coordinate transformation 3 Key in the x coordinate of the origin of the new system M and press f 4 Key in the y coordinate of the origin of the new system N and press f 5 Key in the rotation angle T and press f 6 To translate from the old system to the new system continue with step 7 To translate from the new system to the old system skip to step 12 7 P...

Страница 262: ...n of the new system N The y coordinate of the origin of the new system T The rotation angle θ between the old and new systems X The x coordinate f a point in the old system Y The y coordinate of a point in the old system U The x coordinate of a point in the new system V The y coordinate of a point in the new system Remark For translation only key in zero for T For rotation only key in zero for M a...

Страница 263: ...y x P3 6 8 P1 _9 7 P2 _5 _4 P 4 2 7 _3 6 7 _4 T 27 M N o M N T Keys Display Description z Sets Degrees mode since T is given in degrees W D value Starts the routine that defines the transformation 7 f value Store 7 in M 4 _ f value Store 4 in N 27 f Stores 27 in T W N value Starts the old to new routine ...

Страница 264: ...ates U f Calculates V f Resumes the old to new routine for next problem 5 _ f Stores 5 in X 4 _ f Stores 4 in Y f Calculates V f Resumes the old to new routine for next problem 6 f Stores 6 in X 8 f Stores 8 in Y and calculates U f Calculates V W O Starts the new to old routine 2 7 f Stores 2 7 in U 3 6 _ f Stores 3 6 in V and calculates X f Calculates Y ...

Страница 265: ...exponential curve and the power curve The program accepts two or more x y data pairs and then calculates the correlation coefficient r and the two regression coefficients m and b The program includes a routine to calculate the estimates x and y For definitions of these values see Linear Regression in chapter 11 Samples of the curves and the relevant equations are shown below The internal regressio...

Страница 266: ...To fit logarithmic curves values of x must be positive To fit exponential curves values of y must be positive To fit power curves both x and y must be positive A 1 2 error will occur if a negative number is entered for these cases Data values of large magnitude but relatively small differences can incur problems of precision as can data values of greatly different magnitudes Refer to Limitations i...

Страница 267: ...r indirect addressing Sets flag 0 the indicator for ln X Clears flag 1 the indicator ln Y Branches to common entry point Z Checksum and length 7462 007 5 This routine sets the status for the exponential model Enters index value for later storage in i for indirect addressing Clears flag 0 the indicator for ln X Sets flag 1 the indicator for ln Y Branches to common entry point Z Checksum and length ...

Страница 268: ...ores X input If flag 0 is set takes the natural log of the X input Stores that value for the correction routine Prompts for and stores Y If flag 1 is set takes the natural log of the Y input Accumulates B and R as x y data pair in statistics registers Loops for another X Y pair Checksum and length AAD5 022 5 Defines the beginning of the undo routine Recalls the most recent data pair Deletes this p...

Страница 269: ...loop Displays prompts for and if changed stores x value in X 1L2 Calls subroutine to compute y Stores y value in Y Displays prompts for and if changed stores y value in Y L Adjusts index value to address the appropriate subroutine 1L2 Calls subroutine to compute x Stores x in X for next loop Loops for another estimate Checksum and length BA07 015 This subroutine calculates y for the straight line ...

Страница 270: ...broutine calculates y for the logarithmic model º Calculates y M In X B Returns to the calling routine Checksum and length 7AB7 009 0 This subroutine calculates x for the logarithmic model L Restores index value to its original value ª H Calculates x e Y B M Returns to the calling routine Checksum and length B00D 010 5 This subroutine calculates y for the exponential model º H º Calculates y BeMX ...

Страница 271: ...utine Checksum and length 7D3B 010 5 This subroutine calculates y for the power model º Calculates Y B XM Returns to the calling routine Checksum and length 30CD 009 0 This subroutine calculates x for the power model L Restores index value to its original value ª º Calculates x Y B 1 M Returns to the calling routine Checksums and length 7139 012 0 Flags Used Flag 0 is set if a natural log is requi...

Страница 272: ...e value prompt still visible press f again displaying the value prompt and press W U to undo remove the last data pair If you discover that you made an error after step 4 press W U In either case continue at step 3 6 After all data are keyed in press W R to see the correlation coefficient R 7 Press f to see the regression coefficient B 8 Press f to see the regression coefficient M 9 Press f to see...

Страница 273: ...ct x y projection equation Statistics registers Statistical accumulation and computation Example 1 Fit a straight line to the data below Make an intentional error when keying in the third data pair and correct it with the undo routine Also estimate y for an x value of 37 Estimate x for a y value of 101 X 40 5 38 6 37 9 36 2 35 1 34 6 Y 104 5 102 1 00 97 5 95 5 94 Keys Display Description W S Start...

Страница 274: ...data pair 94 f Enters y value of data pair W R Calculates the correlation coefficient f Calculates regression coefficient B f Calculates regression coefficient M f Prompts for hypothetical x value 37 f Stores 37 in X and calculates y 101 f Stores 101 in Y and calculates x Example 2 Repeat example 1 using the same data for logarithmic exponential and power curve fits The table below gives you the s...

Страница 275: ...tribution is frequently used to model the behavior of random variation about a mean This model assumes that the sample distribution is symmetric about the mean M with a standard deviation S and approximates the shape of the bell shaped curve shown below Given a value x this program calculates the probability that a random selection from the sample data will have a higher value This is known as the...

Страница 276: ...res default value for mean Prompts for and stores mean M Stores default value for standard deviation Prompts for and stores standard deviation S Stops displaying value of standard deviation Checksum and length E5FA 012 0 This routine calculates Q X given X Prompts for and stores X Calculates upper tail area Stores value in Q so VIEW function can display it Displays Q X Loops to calculate another Q...

Страница 277: ...cant Continues if correction is not significant Displays the calculated value of X Loops to calculate another X Checksum and length C2AD 033 5 This subroutine calculates the upper tail area Q x Recalls the lower limit of integration Recalls the upper limit of integration Selects the function defined by LBL F for integration G Integrates the normal function using the dummy variable D π º º Calculat...

Страница 278: ... Flags Used None Memory Required 155 5 bytes 107 5 for program 48 for variables Remarks The accuracy of this program is dependent on the display setting For inputs in the rare between 3 standard deviations a display of four or more significant figures is adequate for most application At full precision the input limit becomes 5 standard deviations Computation time is significantly less with a lower...

Страница 279: ... instructions 6 To calculate Q X given X W D 7 After the prompt key in the value of X and press f The result Q X is displayed 8 To calculate Q X for a new X with the same mean and standard deviation press f and go to step 7 9 To calculate X given Q X press W I 10 After the prompt key in the value of Q X and press f The result X is displayed 11 To calculate X for a new Q X with the same mean and st...

Страница 280: ...se the default value of zero for M and 1 for S Keys Display Description W S Starts the initialization routine f Accepts the default value of zero for M f Accepts the default value of 1 for S W D value Starts the distribution program and prompts for X 3 f Enters 3 for X and starts computation of Q X Displays the ratio of the population smarter than everyone within three standard deviations of the m...

Страница 281: ...at is the score that only 10 percent of the students would be expected to have surpassed What would he the score that only 20 percent of the students would have failed to achieve Keys Display Description W S Starts the initialization routine 55 f Stores 55 for the mean 15 3 f Stores 15 3 for the standard deviation W D value Starts the distribution program and prompts for X 90 f Enters 90 for X and...

Страница 282: ... 2 2 i i i i i xg f f f x x S This program allows you to input data correct entries and calculate the standard deviation and weighted mean of the grouped data Program Lines Description Start grouped standard deviation program Clears statistics registers 28 through 33 Clears the count N Checksum and length 104F 006 0 Input statistical data points Stores data point in X Stores data point frequency i...

Страница 283: ...1 º65 Gets 1 or 1 Increments or decrements N Displays current number of data pairs Goes to label I for next data input Checksum and length 214E 030 0 Calculates statistics for grouped data Uº Grouped standard deviation Display grouped standard deviation º Weighted mean Displays weighted mean Goes back for more points Checksum and length 4A4A 012 0 Undo data entry error Enters decrement for N Recal...

Страница 284: ...6 Repeat steps 3 through 5 for each data point If you discover that you have made a data entry error xi or fi after you have pressed f in step 4 press W U and then press f again Then go back to step 3 to enter the correct data 7 When the last data pair has been input press W G to calculate and display the grouped standard deviation 8 Press f to display the weighted mean of the grouped data 9 To ad...

Страница 285: ...xi 5 8 13 15 22 37 fi 17 26 37 43 73 115 Keys Display Description W S value Prompts for the first xi 5 f value Stores 5 in X prompts for first fi 17 f Stores 17 in F displays the counter f Prompts for the second xi 8 f Prompts for second fi 26 f Displays the counter f Prompts for the third xi 14 f Prompts for the third fi 37 f Displays the counter You erred by entering 14 instead of 13 for x3 Undo...

Страница 286: ...rth xi 15 f Prompts for the fourth fi 43 f Displays the counter f Prompts for the fifth x1 22 f Prompts for the fifth fi 73 f Displays the counter f Prompts for the sixth xi 37 f Prompts for the sixth fi 115 f Displays the counter W G Calculates and displays the grouped standard deviation sx of the six data points f Calculates and displays weighted mean x Clears VIEW ...

Страница 287: ...e for the fifth value This equation is useful in a wide variety of financial applications such as consumer and home loans and savings accounts The TVM equation is 0 100 1 100 100 1 1 B I F I I P N N Balance B Future Value F Payments P N_1 N 1 2 3 The signs of the cash values balance B payment P and future balance F correspond to the direction of the cash flow Money that you receive has a positive ...

Страница 288: ...sed signs Equation Entry Key in this equation º º1 1 ª 2 2ª º1 ª 2 Keys Display Description G or current equation Selects Equation mode K P y 100 º _ Starts entering equation y 1 º º1 y 1 º º1 1 K I p 100 1 ª _ 0 1 ª 2 K N ª 2 2 p K I K F y 2 2ª º 1 K I 2ª º1 p 100 º1 ª 2 0 K N ª 2 K B ª 2 º º1 1 Terminates the equation hold Checksum and length Memory Required 94 bytes 54 bytes for the equation 40...

Страница 289: ...uation 3 Do one of the following five operations a Press N to calculate the number of compounding periods b Press I to calculate periodic interest For monthly payments the result returned for I is the monthly interest rate i press 12 y to see the annual interest rate c Press B to calculate initial balance of a loan or savings account d Press P to calculate periodic payment e Press F to calculate f...

Страница 290: ...odic payment F The future value of a savings account or balance of a loan Example Part 1 You are financing the purchase of a car with a 3 year 36 montld loan at 10 5 annual interest compounded monthly The purchase price of the car is 7 250 Your down payment is 1 500 B 7 250 _ 1 500 I 10 5 per year N 36 months F 0 P Keys Display Description z 2 Selects FIX 2 display format G z as needed Rº º1 1 Dis...

Страница 291: ...hile money paid out is negative Part 2 What interest rate would reduce the monthly payment by 10 Keys Display Description G Rº º1 1 Displays the leftmost hart of the TVM equation I R Selects I prompts for P z I R Rounds the payment to two decimal places 10 R Calculates new payment f Stores 176 89 in P prompts for N f Retains 36 in N prompts for F f 8 Retains 0 in F prompts for B f Retains 5750 in ...

Страница 292: ...e Again the sign is negative indicating that you must pay out this money z 4 Sets FIX 4 display format Prime Number Generator This program accepts any positive integer greater than 3 If the number is a prime number not evenly divisible by integers other than itself and 1 then the program returns the input value If the input is not a prime number then the program returns the first prime number larg...

Страница 293: ...s and Equations 17 7 File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm LBL Y VIEW Prime LBL Z P 2 x LBL P x P 3 D LBL X FP x P D x 0 yes no D D 2 Start no yes D P Note x is the value in the X register ...

Страница 294: ...ne adds 2 to P Checksum and length 0C68 004 5 This routine stores the input value for P ª º Tests for even input Increments P if input an even number Stores 3 in test divisor D Checksum and length 40BA 016 5 This routine tests P to see if it is prime ª Finds the fractional part of P D º Tests for a remainder of zero not prime If the number is not prime tries next possibility º Tests to see whether...

Страница 295: ... Memory Required 61 bytes 45 for program 16 for variables Program Instructions 1 Key in the program routines press when done 2 Key in a positive integer greater than 3 3 Press W P to run program Prime number P will b e displayed 4 To see the next prime number press f Variables Used P Prime value and potential prime values D Divisor used to test the current value of P Remarks No test is made to ens...

Страница 296: ...7 10 Miscellaneous Programs and Equations File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm 789 W P Calculates next prime number after 789 f Calculates next prime number after 797 ...

Страница 297: ...File name 32sii Manual E 0424 Printed Date 2003 4 24 Size 17 7 x 25 2 cm Part 3 Appendixes and Reference ...

Страница 298: ......

Страница 299: ...ess or phone number listed on the inside back cover Answers to Common Questions Q How can I determine if the calculator is operating properly A Refer to page A 5 which describes the diagnostic self test Q My numbers contain commas instead of periods as decimal points How do I restore the periods A Use the z function page 1 14 Q How do l change the number of decimal places in the display A Use the ...

Страница 300: ...ator Q Why do I get incorrect answers when I use the trigonometric functions A You must make sure the calculator is using the correct angular mode z or Q What does the symbol in the display mean A This is an annuncidor and it indicates something about the status of the calculator See Annunciators in chapter 1 Q Numbers show up as fractions How do I get decimal numbers A Press z Environmental Limit...

Страница 301: ...357 SP357 V357 and SR44W 1 Have three fresh button cell batteries at hand Avoid touching the battery terminals handle batteries only by their edges 2 Make sure the calculator is OFF Do not press ON again until the entire battery changing procedure is completed If the calculator is ON when the batteries are removed the contents of Continuous Memory will be erased 3 Remove the battery compartment do...

Страница 302: ...ed and the message is displayed when you release all three keys 3 Remove the batteries see Changing the Batteries and lightly press a coin against both battery contacts in the calculator Replace the batteries and turn on the calculator It should display 4 Install new batteries see Changing the Batteries If these steps fail to restore calculator operation it requires service If the calculator respo...

Страница 303: ...isplays followed by two digit numbers The calculator is counting the keys using hexadecimal base If you press a key out of order or if a key isn t functioning properly the next keystroke displays a fail message see step 4 4 The self test produces one of these two results The calculator displays if it passed the self test Go to step 5 The calculator displays followed by a one digit number if it fai...

Страница 304: ...s that vary from state to state province to province or country to country What Is Not Covered Batteries and damage caused by the batteries are not covered by the Hewlett Packard warranty Check with the battery manufacturer about battery and battery leakage warranties This warranty does not apply if the product has been damaged by accident or misuse or as the result of service or modification by o...

Страница 305: ... newer model whether it is under warranty or not There is a charge for service after the warranty period Calculators normally are serviced and reshipped within 5 working days In the United States Send the calculator to the Calculator Service Center listed on the inside of the back cover In Europe Contact your HP sales office or dealer or HP s European headquarters for the location of the nearest s...

Страница 306: ...ator requires service ship it to the nearest authorized service center or collection point Be sure to Include your return address and description of the problem Include proof of purchase date if the warranty has not expired Include a purchase order check or credit card number plus expiration date Visa or MasterCard to cover the standard repair charge In the United States and some other countries t...

Страница 307: ... be determined by turning the calculator off and on or by removing the batteries try Reorienting the receiving antenna Relocating the calculator with respect to the receiver For more information consult your dealer an experienced radio or television technician or the following booklet prepared by the Federal Corrnunications Commission How to Identify and Resolve Radio TV Interference Problems This...

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Страница 309: ...es equations or program lines SOLVE FN and statistical calculations also require user memory The FN operation is particularly expensive to run All of your stored data is preserved until you explicitly clear it The message means that there is currently not enough memory available for the operation you just attempted You need to clear some or all of user memory For instance you can Clear the content...

Страница 310: ... memory is available press z X The display shows the number of bytes available To see the memory requirements of specific equations in the equation list 1 Press G to activate Equation mode or the left end of the current equation will be displayed 2 If necessary scroll through the equation list press z or z until you see the desired equation 3 Press to see the checksum hexadecimal and length in byt...

Страница 311: ...splay Stored data usually remain intact To reset the calculator hold down the key and press If you are unable to reset the calculator try installing fresh batteries If the calculator cannot be reset or if it still fails to operate properly you should attempt to clear memory using the special procedure described in the next section The calculator can reset itself if it is dropped or if power is int...

Страница 312: ...leared Fraction display mode Unchanged Off Random number seed Unchanged Zero Equation pointer EQN LIST TOP EQN LIST TOP Equation list Cleared Cleared FN label Null Null Program pointer PRGM TOP PRGM TOP Program memory Cleared Cleared Stack lift Enabled Enabled Stack registers Cleared to zero Cleared to zero Variables Cleared to zero Cleared to zero Memory may inadvertently be cleared if the calcul...

Страница 313: ...act like CLx they also disable stack lift The INPUT function disables stack lift as it halts a program for prompting so any number you then enter writes over the X register but it enables stack lift when the program resumes Neutral Operations The following operations do not affect the status of stack lift DEG RAD GRAD FIX SCI ENG ALL DEC HEX OCT BIN CLVARS PSE SHOW RADIX RADIX CLΣ f and STOP z and...

Страница 314: ...SIN ACOS ATAN SINH COSH TANH ASINH ACOSH ATANH IP FP RND ABS CHG Σ Σ RCL y x θ r θ r y x HR HMS DEG RAD Cn r Pn r x CMPLX CMPLX CMPLX ex LN yx 1 x CMPLX SIN COS TAN kg lb l gal C F cm in Notice that c does riot affect the LAST X register The recall arithmetic sequence x K variable stores a different value in the LAST X register than the sequence x K variable does The former stores x in LAST X the ...

Страница 315: ... successive estimates of the function f x have opposite signs then SOLVE presumes that the function f x crosses the x axis in at least one place between the two estimates This interval is systematically narrowed until a root is found For SOLVE to find a root the root has to exist within the range of numbers of the calculator and the function must be mathematically defined where the iterative searc...

Страница 316: ...x figure d below f x x a f x b x f x x c f x x d Function Whose Roots Can Be Found In most situations the calculated root is an accurate estimate of the theoretical infinitely precise root of the equation An ideal solution is one for which f x 0 However a very small non zero value for f x is often acceptable because it might result from approximating numbers with limited 12 digit precision ...

Страница 317: ...iffer by 1 in the 12th digit and the function s value is positive for one estimate and negative for the other Or they are 0 10 499 or 0 10 499 In most cases f x will be relatively close to zero f x x a f x x b Cases Where a Root Is Found To obtain additional information about the result press 9 see the previous estimate of the root x which was left in the Y register Press 9 again to see the value ...

Страница 318: ... Now salve the equation to find the root Keys Display Description 0 H X 10 _ Initial guesses for the root G º º Selects Equation mode displays the left end of the equation X Solves for X displays the result 9 Final two estimates are the same to four decimal places 9 f x is very small so the approximation is a good root Example An Equation with Two Roots Find the two roots of the parabolic equation...

Страница 319: ...guesses 0 an 10 9 Final two estimates are they same 9 f x 0 0 H X 10 _ _ Your initial guesses for the negative root G Redisplays the equation X Calculates negative root using guesses 0 and 10 9 9 f x 0 Certain cases require special consideration If the function s graph has a discontinuity that crosses the x axis then the SOLVE operation returns a value adjacent to the discontinuity see figure a be...

Страница 320: ...rge If the pole occurs at a value of x that is exactly represented with 12 digits then that value would cause the calculation to halt with an error message f x x a f x x b Special Case A Discontinuity and a Pole Example Discontinuous Function Find the root of the equation IP x 1 5 Enter the equation Keys Display Description z G Selects Equation mode z PARTS K X 1 5 1 2 Enter the equation Checksum ...

Страница 321: ...previous estimate is slightly bigger 9 f x is relatively large Note the difference between the last two estimates as well as the relatively large value for f x The problem is that there is no value of x for which f x equals zero However at x 1 99999999999 there is a neighboring value of x that yields ant opposite sign for f x Example A Pole Find the root of the equation 0 1 6 2 x x As x approaches...

Страница 322: ...elded opposite signs for f x and the interval between successive estimates was narrowed until two neighbors were found Unfortunately these neighbors made f x approach a pole instead of the x axis The function does have roots at 2 and 3 which can be found by entering better guesses When SOLVE Cannot Find Root Sometimes SOLVE fails to find a root The following conditions cause the message The search...

Страница 323: ...of the function see figure c below The ending value of f x is the value of the function in this region f x x a f x x b f x x c Case Where No Root Is Found The SOLVE operation returns a math error if an estimate produces an operation that is not allowed for example division by zero a square root of a negative number or a logarithm of zero Keep in mind that SOLVE can generate estimates over a wide r...

Страница 324: ...ription G Selects Equation mode K X 0 2 6 y K X 13 º Enters the equation Checksum and length Cancels Equation mode Now solve to find the root Keys Display Description 0 H X 10 _ Your initial guesses for the root G º Selects Equation mode displays the equation X Search fails with guesses 0 and 10 Displays the final estimate of x 9 Previous estimate was not the same 9 Final value for f x is relative...

Страница 325: ...de G 1 2 Your positive guesses for the root X Selects Equation mode displays the equation 9 Solves for x using guesses 0 005 and 5 9 Previous estimate is the same Watch what happens when you use negative values for guesses Keys Display Description 1 _ H X Your negative guesses for the root 2 _ G 1 2 Selects Equation mode displays the equation X No root found for f x 8 8 Displays last estimate of x...

Страница 326: ...play Description G Selects Equation mode K X p K X 3 5 1 ª1 Enters the equation Checksum and length Cancels Equation mode First attempt to find a positive root Keys Display Description 0 H X 10 _ Your positive guesses for the root G 1 ª1 Selects Equation mode displays the left end of the equation X Calculates the root using guesses 0 and 10 Now attempt to find a negative root by entering guesses 0...

Страница 327: ...s the left end of the equation X 1 2 Math error Clears error message cancels Equation mode X Displays the final estimate of x Example A Local Flat Region Find the root of the function f x x 2 if x 1 f x 1 for 1 x 1 a local flat region f x x 2 if x 1 Enter the function as the program º6 º5 Checksum and length 23C2 019 5 You can subsequently delete line J03 to save memory ...

Страница 328: ...guesses then SOLVE can find the roots which are outside the flat region at x 2 and x 2 Round Off Error The limited 12 digit precision of the calculator can cause errors due to rounding off which adversely affect the iterative solutions of SOLVE and integration For example 0 10 10 1 x 30 2 15 has no roots because f x is always greater than zero However given initial guesses of 1 and 2 SOLVE returns...

Страница 329: ...st possible 12 digit approximation of the root when the routine quits Underflow Underflow occurs when the magnitude of a number is smaller than the calculator can represent so it substitutes zero This can affect SOLVE results For example consider the equation 2 1 x whose root is infinite in value Because of underflow SOLVE returns a very large value as a root The calculator cannot represent infini...

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Страница 331: ...ion imposed by the inaccuracy in the calculated function f x always provide an exact answer Evaluating the function at an infinite number of sample points would take forever However this is not necessary since the maximum accuracy of the calculated integral is limited by the accuracy of the calculated function values Using only a finite number of sample points the algorithm can calculate an integr...

Страница 332: ...s not vary rapidly Although we can t know the error in the final approximation the error is extremely unlikely to exceed the displayed uncertainty of the approximation In other words the uncertainty estimate in the Y register is an almost certain upper bound on the difference between the approximation and the actual integral Conditions That Could Cause Incorrect Results Although the integration al...

Страница 333: ...ions However the actual integral of the function shown with a dashed line is quite different from those of the others so the current approximation will be rather inaccurate if f x is this function The algorithm cores to know the general behavior of the function by sampling the function at more and more points If a fluctuation of the function in one region is not unlike the behavior over the rest o...

Страница 334: ...th Cancels Equation mode Set the display format to SCI 3 specify the lower and upper limits of integration as zero and 100499 than start the integration Keys Display Description z 3 0 499 _ Specifies accuracy level and limits of integration G º º 1 2 Selects Equation mode displays the equation X Approximation of the integral The answer returned by the calculator is clearly incorrect since the actu...

Страница 335: ...n Time Fortunately functions exhibiting such aberrations a fluctuation that is uncharacteristic of the behavior of the function elsewhere are unusual enough that you are unlikely to have to integrate one unknowingly A function that could lead to incorrect results can be identified in simple terms by how rapidly it and its low order derivatives vary across the interval of integration Basically the ...

Страница 336: ...y are confined to only a small fraction of the interval These two situations are shown in the following two illustrations Considering the variations or fluctuation as a type of oscillation in the function the criterion of interest is the ratio of the period of the oscillations to the width of the interval of integration the larger this ratio the more quickly the calculation will finish and the mor...

Страница 337: ... of this function will be accurate f x a b x Calculated integral of this function may be accurate a b In many cases you will be familiar enough with the function you want to integrate that you will know whether the function has any quick wiggles relative to the interval of integration If you re not familiar with the function ...

Страница 338: ...preceding example the algorithm gave an incorrect answer because it never detected the spike in the function This happened because the variation in the function was too quick relative to the width of the interval of integration If the width of the interval were smaller you would get the correct answer but it would take a very long time if the interval were still too wide Consider an integral where...

Страница 339: ...gorithm samples the function with higher densities of sample points until the disparity between successive approximations becomes sufficiently small For a narrow interval in an area where the function is interesting it takes less time to reach this critical density To achieve the same density of sample points the total number of sample points required over the larger interval is much greater than ...

Страница 340: ...s where the function is not interesting Fortunately if you must calculate such an integral you can modify the problem so that the calculation time is considerably reduced Two such techniques are subdividing the interval of integration and transformation of variables These methods enable you to change the function or the limits of integration so that the integrand is better behaved over the interva...

Страница 341: ...grate a program G variable while another integration calculation was running 1 2 A running program attempted to solve a program while an integration calculation was running The catalog of variables z X indicates no values stored The calculator is executing a function that might take a while Allows you to verily clearing the equation you are editing Occurs only in Equation entry mode Allows you to ...

Страница 342: ...equation evaluation SOLVE or FN º7 Attempted a factorial or gamma operation with x as a negative integer º Exponentiation error Attempted to raise 0 to the 0th power or to a negative power Attempted to raise a negative number to a non integer power Attempted to raise complex number 0 i 0 to a number with a negative real part 1L2 Attempted an operation with an indirect address but the number in the...

Страница 343: ...or the calculator to handle The calculator returns 9 99999999999E499 in the current display format See Range of Numbers and Overflow on page 1 12 This condition sets flag 6 If flag 5 is set overflow has the added effect of halting a running program and leaving the message in the display until you press a key Indicates the top of program memory The memory scheme is circular so is also the line afte...

Страница 344: ...empted to calculate x y r m or b with all x values equal The magnitude of the number is too large to be converted to HEX OCT or BIN base the number must be in the range 34 359 738 368 n 34 359 738 367 A running program attempted an eighth nested label Up to seven subroutines can be nested Since SOLVE and FN each uses a level they can also generate this error The condition checked by a test instruc...

Страница 345: ... names preceded by arrows for example DEG are alphabetized as if the arrow were not there The last column marked refers to notes at the end of the table Name Keys and Description Page _ Changes the sign of a number 1 10 1 Addition Returns y x 1 13 1 Subtraction Returns y x 1 13 1 y Multiplication Returns y x 1 13 1 p Division Returns y x 1 13 1 0 Power Indicates an exponent 6 17 2 a Deletes the la...

Страница 346: ...4 2 1 P Percent Returns y x 100 4 5 1 CHG S Percent change Returns x y 100 y 4 5 1 π M Returns the approximation 3 14159265359 12 digits 4 3 1 Σ 6 Accumulates y x into statistics registers 11 2 Σ z 4 Removes y z from statistics registers 11 2 Σx 5 º Returns the sum of x values 11 11 1 Σx2 5 º Returns the sum of squares of x values 11 11 1 Σxy 5 º Returns the sum of products of x and y values 11 11...

Страница 347: ...ster and upper limit of the variable if integration in the X register 8 2 14 7 Open parenthesis Starts a quantity associated with a function in an equation 6 7 2 Close parenthesis Ends a quantity associated with a function in an equation 6 7 2 A through Z K variable or H variable Value of named variable 6 5 2 ABS PARTS Absolute value Returns x 4 14 1 ACOS z O Arc cosine Returns cos 1x 4 4 1 ACOSH ...

Страница 348: ...urns on calculator clears x clears messages and prompts cancels menus cancels catalogs cancels equation entry cancels program entry halts execution of an equation halts a running program 1 1 1 3 1 7 1 20 6 3 12 6 12 18 c z Denominator Sets denominator limit for displayed fractions to x If x 1 displays current c value 5 5 C z Converts F to C 4 11 1 CF n x n Clears flag n n 0 through 11 13 12 z b Di...

Страница 349: ...isplays the CMPLX_ prefix for complex functions 9 3 CMPLX z F _ Complex change sign Returns zx i zy 9 3 CMPLX z F Complex addition Returns z1x i z1y z2x i z2y 9 3 CMPLX z F Complex subtraction Returns z1x i z1y z2x i z2y 9 3 CMPLX z F y Complex multiplication Returns z1x i z1y z2x i z2y 9 3 CMPLX z F p Complex division Returns z1x i z1y z2x i z2y 9 3 CMPLX1 x z F 3 Complex reciprocal Returns 1 zx ...

Страница 350: ...z 7 Q Hyperbolic cosine Returns cosh x 4 5 1 DEC z w Selects Decimal mode 10 1 DEG z Selects Degrees angular mode 4 3 DEG z u Radians to degrees Returns 360 2π x 4 10 1 z Displays menu to set the display format 1 15 DSE variable z m variable Decrement Skip if Equal or less For control number ccccccc fffii stored in a variable subtracts ii increment value from ccccccc counter value and if the resul...

Страница 351: ...toggles Equation entry mode 6 3 12 6 ex Natural exponential Returns e raised to the x power 4 1 1 EXP Natural exponential Returns e raised to the specified power 6 17 2 F Converts C to F 4 11 1 z Turn on and off Fraction display mode 5 1 FIX n z n Selects Fixed display with n decimal places 0 n 11 1 15 x Displays the menu to set clear and test flags 13 12 FN label V label Selects labeled program a...

Страница 352: ...bolic functions 4 5 HMS z t Hours to hours minutes seconds Converts x from a decimal fraction to hours minutes seconds format 4 9 1 HR z s Hours minutes seconds to hours Converts x from hours minutes seconds format to a decimal fraction 4 9 1 i K i or H i Value of variable i 6 5 2 i K H Indirect Value of variable whose letter corresponds to the numeric value stored in variable i 6 5 13 21 2 IN Con...

Страница 353: ...3 17 KG z Converts pounds to kilograms 4 11 1 L z Converts gallons to liters 4 11 1 LASTx z Returns number stored in the LAST X register 2 8 LB Converts kilograms to pounds 4 11 1 LBL label z label Labels a program with a single letter for reference by the XEQ GTO or FN operations Used only in programs 12 3 LN Natural logarithm Returns log e x 4 1 1 LOG z Common logarithm Returns log10 x 4 1 1 Dis...

Страница 354: ...n r PROB Q8T Permutations of n items taken r at a time Returns n n r 4 11 1 z d Activates or cancels toggles Program entry mode 12 5 PROB Displays the menu for probability functions 4 11 PSE e Pause Halts program execution briefly to display x variable or equation then resumes Used only in programs 12 17 12 18 r T Returns the correlation coefficient between the x and y values 2 2 y y x x y y x x i...

Страница 355: ...variable Returns x variable 3 5 RCL variable K p Round Returns x variable 3 5 RND z I Round Rounds x to n decimal places in FIX n display mode to n 1 significant digits in SCI n or ENG n display mode or to decimal number closest to displayed fraction in Fraction display mode 4 14 5 8 1 RTN Return Marks the end of a program the program pointer returns to the top or to the calling routine 12 3 13 2 ...

Страница 356: ...ne displays hex checksum and decimal byte length for equations and programs 6 20 12 22 SIN N Sine Returns sin x 4 4 1 SINH z 7 N Hyperbolic sine Returns sinh x 4 5 1 SOLVE variable variable Solves the displayed equation or the program selected by FN using initial estimates in variable and x 7 1 14 1 o f Inserts a blank space character during equation entry 6 6 2 SQ z Square of argument 6 17 2 SQRT...

Страница 357: ...tion of x values 1 2 n x xi 11 6 1 sy 2 U Returns sample standard deviation of y values 1 2 n y yi 11 6 1 TAN T Tangent Returns tan x 4 4 1 TANH z 7 T Hyperbolic tangent Returns tanh x 4 5 1 VIEW variable variable Displays the labeled contents of variable without recalling the value to the stack 3 2 12 14 W Evaluates the displayed equation 6 14 XEQ label W label Executes the program identified by ...

Страница 358: ...le 3 6 x y Z x exchange y Moves x to the Y register and y to the X register 2 4 z l Displays the x y comparison tests menu 13 8 x y z l If x y executes next program line if x y skips the next program line 13 8 x y z l If x y executes next program line if x y skips next program line 13 8 x y z l If x y executes next program line if x y skips next program line 13 8 x y z l If x y executes next progr...

Страница 359: ...x 0 executes next program line if x 0 skips the next program line 13 8 x 0 z n If x 0 executes next program line if x 0 skips the next program line 13 8 x 0 z n If x 0 executes next program line if x 0 skips next program lire 13 8 y z Returns the mean of y values Σyi n 11 4 1 y z ˆ Given an x value in the X register returns the y estimate based on the regression line y m x b 11 11 1 y x θ r z q Re...

Страница 360: ......

Страница 361: ...te value real number 4 15 addressing indirect 13 19 13 20 13 21 ALL format See display format in equations 6 6 in programs 12 6 Setting 1 17 alpha characters 1 2 angles between vectors 15 1 converting format 4 11 converting units 4 11 implied units 4 3 A 2 angular mode 4 3 A 2 B 5 annunciators alpha 1 2 battery 1 1 A 2 descriptions 1 8 flags 13 11 list of 1 9 low power 1 1 A 2 shift keys 1 2 answe...

Страница 362: ...best fit regression 11 8 16 1 BIN annunciator 10 1 binary numbers See numbers arithmetic 10 3 converting to 10 1 range of 10 6 scrolling 10 7 typing 10 1 viewing all digits 3 4 10 7 borrower finance 17 1 branching 13 2 13 15 14 6 C adjusting contrast 1 1 canceling prompts 1 3 6 16 12 14 canceling VIEW 3 4 clearing messages 1 3 E 1 clearing X register 2 2 2 8 interrupting programs 12 19 leaving cat...

Страница 363: ...mmas in numbers 1 16 A 1 comparison tests 13 7 complex numbers coordinate systems 9 6 entering 9 1 on stack 9 2 operations 9 1 9 3 polynomial roots 15 22 viewing 9 2 conditional tests 13 6 13 7 13 8 13 11 13 16 14 6 constant filling stack 2 7 Continuous Memory 1 1 contrast adjustment 1 1 conversion functions 4 8 conversions angle format 4 11 angle units 4 11 coordinates 4 8 9 6 15 1 length units 4...

Страница 364: ... 17 A 1 ENG format 1 17 See also display format clearing stack 2 6 copying viewed variable 12 15 duplicating numbers 2 6 ending equations 6 5 6 9 6 10 12 6 evaluating equations 6 12 6 13 separating numbers 1 13 1 15 2 6 stack operation 2 6 EQN annunciator in equation list 6 5 6 8 in Program mode 12 6 EQN LIST TOP 6 8 E 2 equality equations 6 11 6 12 7 1 equation entry cursor backspacing 1 3 6 9 12...

Страница 365: ... polynomial 15 22 precedence of operators 6 16 prompt for values 6 13 6 15 prompting in programs 13 10 14 2 14 8 roots 7 1 scrolling 6 8 12 7 12 16 simultaneous 15 13 solving 7 2 C 1 stack usage 6 13 storing variable value 6 13 syntax 6 16 6 20 12 15 TVM equation 17 1 types of 6 11 uses 6 1 variables in 6 5 7 1 with i 13 24 error messages E 1 errors clearing 1 3 correcting 2 9 E 1 estimation stati...

Страница 366: ...ors 1 19 5 5 5 6 13 9 13 3 displaying 1 20 5 1 5 2 5 5 A 2 flags 5 6 13 9 formats 5 6 not statistics registers 5 2 reducing 5 3 5 6 rounding 5 9 round off 5 4 5 9 setting format 5 6 13 9 13 13 showing integer digits 3 3 5 5 typing 1 19 5 1 functions complex number 9 3 in equations 6 6 6 17 F 1 in programs 12 7 list of F 1 memory usage 12 22 B 2 names in display 4 15 12 7 nonprogrammable 12 24 one ...

Страница 367: ...on accuracy 8 2 8 6 8 7 D 2 base mode 12 25 14 10 difficult functions D 2 D 7 display format 8 2 8 6 8 8 evaluating programs 14 7 how it works D 1 in programs 14 9 interrupting B 3 limits of 8 2 14 7 D 7 memory usage 8 2 12 22 B 2 B 3 purpose 8 1 restrictions 14 10 results on stack 8 2 8 7 resuming 14 7 stopping 8 2 14 7 subintervals D 7 D 9 time required 8 6 D 7 transforming variables D 9 uncerta...

Страница 368: ...function C 9 mean menu 11 4 means statistics calculating 11 4 normal distribution 16 12 X program catalog 1 21 12 22 reviews memory 1 21 variable catalog 1 21 3 4 memory amount available 1 21 B 2 clearing 1 4 1 22 A 1 A 4 B 1 11 4 clearing equations 6 10 clearing programs 1 22 12 6 12 23 clearing statistics registers 11 2 11 13 clearing variables 1 22 3 5 contents 1 21 deallocating B 3 equations B...

Страница 369: ...in 1 11 1 12 A 1 exchanging 2 4 finding parts of 4 15 fractions in 1 19 5 1 in equations 6 0i in programs 12 6 internal representation 1 16 10 5 large and small 1 11 1 13 limitations 1 11 mantissa 1 12 memory usage 12 22 B 2 negative 1 11 9 3 10 5 order in calculations 1 15 periods and commas in 1 16 A 1 precision 1 16 C 16 prime 17 7 range of 1 13 10 6 real 4 1 8 1 recalling 3 2 reusing 2 6 2 11 ...

Страница 370: ...4 13 program catalog 1 21 12 22 Program entry mode 1 3 12 6 program labels branching to 13 2 13 4 13 15 checksums 12 23 clearing 12 6 duplicate 12 6 entering 12 3 12 6 executing 12 10 indirect addressing 13 19 13 20 13 21 moving to 12 10 12 21 purpose 12 3 typing name 1 2 viewing 12 22 program lines See programs program names See program labels program pointer 12 6 12 10 12 11 12 19 12 21 B 5 prog...

Страница 371: ...pting for data 12 12 purpose 12 1 resuming 1 2 15 return at end 12 4 routines 13 1 RPN operations 12 4 running 12 10 12 22 showing long number 12 6 stepping through 12 10 stopping 12 14 12 16 12 19 techniques 13 1 testing 12 10 using integration 14 9 using SOLVE 14 5 variables in 12 12 1 4 1 14 7 prompts affect stack 6 16 12 13 clearing 1 3 6 16 12 14 equations 6 15 INPUT 12 12 12 14 14 2 14 8 pro...

Страница 372: ... SOLVE C 16 statistics 11 11 trig functions 4 4 routines calling 13 2 nesting 13 3 14 10 parts of programs 13 1 RPN compared to equations 6 18 12 4 in programs 12 4 origins 2 1 f ending prompts 6 13 6 15 7 2 12 14 interrupting programs 12 19 resuming programs 12 15 12 16 12 19 running programs 12 22 stopping integration 8 2 14 7 stopping SOLVE 7 7 14 1 running programs 12 10 12 22 S sample standar...

Страница 373: ... 14 2 results on stack 7 2 7 6 C 3 resuming 14 1 round off C 16 stopping 7 2 7 7 underflow C 16 using 7 2 o 6 6 6 18 square function 1 14 4 2 square root function 1 14 stack See stack lift affected by prompts 6 16 12 13 complex numbers 9 2 effect of 2 6 equation usage 6 13 exchanging with variables 3 8 exchanging X and Y 2 4 filling with constant 2 7 long calculations 2 13 operation 2 1 2 5 9 2 pr...

Страница 374: ...age 12 22 B 2 no fractions 5 2 viewing 11 12 STO 3 2 12 12 STO arithmetic 3 5 STOP 12 19 storage arithmetic 3 5 subroutines See routines sums of statistical variables 11 12 syntax equations 6 16 6 20 12 15 T tangent trig 4 4 9 3 A 2 temperatures converting units 4 12 limits for calculator A 2 testing the calculator A 4 A 5 test menus 13 7 time formats 4 11 time value of money 17 1 transforming coo...

Страница 375: ...ing name 1 2 viewing 3 3 12 14 12 18 vectors application program 15 1 coordinate conversions 4 10 9 7 15 1 operations 15 1 VIEW displaying program data 12 14 12 18 14 5 displaying variables 3 3 10 8 no stack effect 12 15 stopping programs 12 14 volume conversions 4 12 w warranty A 6 weight conversions 4 12 weighted means 11 4 windows binary numbers 10 7 X W evaluating equations 6 12 6 14 running p...

Страница 376: ... Date 2003 4 24 Size 17 7 x 25 2 cm Batteries are delivered with this product when empty do not throw them away but correct as small chemical waste Bij dit produkt zijn batterijen Wanneer deze leeg zijn moet u ze niet weggooien maar inleveren aIs KCA ...

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