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More about Integration

E–5

File name 33s-English-Manual-040130-Publication(Edition 2).doc Page : 388
Printed Date : 2004/1/30 Size : 13.7 x 21.2 cm

f (x)

x

The graph is a spike very close to the origin. Because no sample point happened
to discover the spike, the algorithm assumed that

f(x)

was identically equal to zero

throughout the interval of integration. Even if you increased the number of sample
points by calculating the integral in SCI 11 or ALL format, none of the additional
sample points would discover the spike when this particular function is integrated
over this particular interval. (For better approaches to problems such as this, see
the next topic, "Conditions That Prolong Calculation 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 more
rapid the variation in the function or its derivatives, and the lower the order of such
rapidly varying derivatives, the less quickly will the calculation finish, and the less
reliable will be the resulting approximation.

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Summary of Contents for 33S

Page 1: ... HP 33s scientific calculator user s manual H HP Part number F2216A 90020 Printed in China Edition 2 ...

Page 2: ...hing performance or use of this manual or the examples contained herein Copyright 2003 Hewlett Packard Development Company L P 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 ada...

Page 3: ...lpha Keys 1 3 Cursor Keys 1 3 Silver Paint Keys 1 4 Backspacing and Clearing 1 4 Using Menus 1 7 Exiting Menus 1 9 RPN and ALG Keys 1 10 The Display and Annunciators 1 11 Keying in Numbers 1 14 Making Numbers Negative 1 14 Exponents of Ten 1 14 Understanding Digit Entry 1 15 Range of Numbers and OVERFLOW 1 16 Doing Arithmetic 1 16 One Number Functions 1 17 Two Number Functions 1 17 Controlling the...

Page 4: ...matic Memory Stack What the Stack Is 2 1 The X and Y Registers are 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 6 The LAST X Register 2 7 Correcting Mistakes with LAST X 2 8 Reusing Numbers with LAST X 2 9 Chain Calculations in RPN mode 2 11 Work ...

Page 5: ...g x with Any Variable 3 6 The Variable i 3 7 4 Real Number Functions Exponential and Logarithmic Functions 4 1 Quotient and Remainder of Division 4 2 Power Functions 4 2 Trigonometry 4 3 Entering π 4 3 Setting the Angular Mode 4 4 Trigonometric Functions 4 4 Hyperbolic Functions 4 6 Percentage Functions 4 6 Physics Constants 4 8 Conversion Functions 4 9 Coordinate Conversions 4 10 Time Conversions...

Page 6: ...ing the Maximum Denominator 5 5 Choosing a Fraction Format 5 5 Examples of Fraction Displays 5 6 Rounding Fractions 5 7 Fractions in Equations 5 8 Fractions in Programs 5 9 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 Variables in Equations 6 4 Numbers in Equations 6 5 Functions in Equations 6 5 P...

Page 7: ...rors 6 18 Verifying Equations 6 18 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 Integrating Equations FN 8 2 Accuracy of Integration 8 5 Specifying Accuracy 8 6 Interpreting Accuracy 8 6 For More Information 8 ...

Page 8: ...tering One Variable Data 11 2 Entering Two Variable Data 11 2 Correcting Errors in Data Entry 11 2 Statistical Calculations 11 4 Mean 11 4 Sample Standard Deviation 11 6 Population Standard Deviation 11 6 Linear Regression 11 7 Limitations on Precision of Data 11 9 Summation Values and the Statistics Registers 11 10 Summation Statistics 11 10 The Statistics Registers in Calculator Memory 11 11 Acc...

Page 9: ...INPUT for Entering Data 12 11 Using VIEW for Displaying Data 12 13 Using Equations to Display Messages 12 14 Displaying Information without Stopping 12 16 Stopping or Interrupting a Program 12 17 Programming a Stop or Pause STOP PSE 12 17 Interrupting a Running Program 12 17 Error Stops 12 17 Editing a Program 12 18 Program Memory 12 19 Viewing Program Memory 12 19 Memory Usage 12 20 The Catalog o...

Page 10: ...m the Keyboard 13 5 Conditional Instructions 13 6 Tests of Comparison x y x 0 13 7 Flags 13 8 Loops 13 16 Conditional Loops GTO 13 17 Loops with Counters DSE ISG 13 18 Indirectly Addressing Variables and Labels 13 20 The Variable i 13 20 The Indirect Address i 13 21 Program Control with i 13 22 Equations with i 13 24 14 Solving and Integrating Programs Solving a Program 14 1 Using SOLVE in a Progr...

Page 11: ...uped Standard Deviation 16 17 17 Miscellaneous Programs and Equations Time Value of Money 17 1 Prime Number Generator 17 6 Part 3 Appendixes and Reference A Support Batteries and Service Calculator Support A 1 Answers to Common Questions A 1 Environmental Limits A 2 Changing the Batteries A 2 Testing Calculator Operation A 4 The Self Test A 5 Warranty A 6 Service A 7 Regulatory Information A 9 B U...

Page 12: ...s C 2 Percentage Calculations C 3 Permutations and Combinations C 4 Quotient and Remainder Of Division C 4 Parentheses Calculations C 5 Chain Calculations C 5 Reviewing the Stack C 6 Coordinate Conversions C 7 Integrating an Equation C 8 Operations with Complex Numbers C 9 Arithmetic in Bases 2 8 and 16 C 11 Entering Statistical Two Variable Data C 12 D More about Solving How SOLVE Finds a Root D ...

Page 13: ...s 11 Underflow D 14 E More about Integration How the Integral Is Evaluated E 1 Conditions That Could Cause Incorrect Results E 2 Conditions That Prolong Calculation Time E 7 F Messages G Operation Index Index ...

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Page 15: ...Part 1 Basic Operation ...

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Page 17: ...f press º Ä That is press and release the º shift key then press Å which has OFF printed in purple above it Since the calculator has Continuous Memory turning it off does not affect any information you ve stored To conserve energy the calculator turns itself off after 10 minutes of no use If you see the low power indicator ã in the display replace the batteries as soon as possible See appendix A f...

Page 18: ...ts face a left shifted function Green and a right shifted function Purple The shifted function names are printed in green and purple above each key Press the appropriate shift key or º before pressing the key for the desired function For example to turn the calculator off press and release the º shift key then press Å ...

Page 19: ...etic key G 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 Z annunciator appears in the display indicating that the alpha keys are active Variables are covered in chapter 3 labels are covered in chapter 12 Cursor Keys Note that the cursor key itself is not actually marked with arrows To make the explanat...

Page 20: ...ssure points marked in blue position in the illustration below To use those keys make sure to press down the corresponding position for the desired function Backspacing and Clearing One of the first things you need to know is how to clear how to correct numbers clear the display or start over ...

Page 21: ...cter immediately to the left of the equation entry cursor If a number entry in your equation is complete erases the entire number If the number is not complete erases the character immediately to the left of _ the number entry cursor _ changes back to when number entry is complete also clears error messages and deletes the current program line during program entry Å Clear or Cancel Clears the disp...

Page 22: ... verify your decision before erasing everything in memory During program entry is replaced by If you select a new menu is displayed so you can verify your 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...

Page 23: ...tting and linear estimation 11 x y Arithmetic mean of statistical x and y values weighted mean of statistical x values 11 s σ σ σ Sample standard deviation population standard deviation 11 CONST Functions to use 40 physics constants refer to Physics constants on page 4 8 4 SUMS Statistical data summations 11 BASE Base conversions decimal hexadecimal octal and binary 11 Programming Instructions FLA...

Page 24: ...r different portions of memory refer to in the table on page 1 6 1 3 6 12 To use a menu function 1 Press a menu key shifted to produce a menu in the display a series of choices 2 Press Õ Ö Ø to move the underline to the item you want to select 3 Press Ï while the item is underlined With numbered menu items you can either press Ï while the item is underlined or just enter the number of the item The...

Page 25: ...ted on its keyboard Exiting Menus Whenever you execute a menu function the menu automatically disappears as in the above example If you want to leave a menu without executing a function you have three options Pressing backs out of the 2 level CLEAR or MEM menu one level at a time Refer to in the table on page 1 6 Pressing or Å cancels any other menu Keys Display 123 5678 _ Þ or Å Pressing another ...

Page 26: ...mode When the calculator is in ALG mode the ALG annunciator is on Example Suppose you want to calculate 1 2 3 In RPN mode you enter the first number press the Ï key enter the second number and finally press the arithmetic operator key Ù In ALG mode you enter the first number press Ù enter the second number and finally press the Ï key RPN mode ALG mode 1 Ï 2 Ù 1 Ù 2 Ï In ALG mode the results and th...

Page 27: ... are more than 255 characters the characters from the 256th onward are replaced with an ellipsis During inputting the second line displays an entry after calculating it displays the result of a calculation Every calculation is displayed in up to 14 digits including an sign exponent and exponent value up to three digits The symbols on the display shown in the above figure are called annunciators Ea...

Page 28: ...s on the exact value of the fraction is being displayed 5 ß Left shift is active 1 à Right shift is active 1 RPN Reverse Polish Notation mode is active 1 2 ALG Algebraic mode is active 1 C PRGM Program entry is active 12 EQN Equation entry mode is active or the calculator is evaluating an expression or executing an equation 6 0 1 2 3 4 Indicates which flags are set flags 5 through 11 have no annun...

Page 29: ...ating that there are more characters to the left and to the right Press either of the indicated cursor keys Ö or Õ to see the leading or trailing characters When an entry or equation has more than one display you can press º or followed by Ö to skip from the current display to the first one To skip to the last display press º or followed by Õ In the CONST and SUMS menus you can press Ö and Õ to ac...

Page 30: ... that was entered previously just press z If the number has an exponent z affects only the mantissa the non exponent part of the number Exponents of Ten Exponents in the Display Numbers with exponents of ten such as 4 2 10 5 are displayed with an preceding the exponent such as A number whose magnitude is too large or too small for the display format will automatically be displayed in exponential f...

Page 31: ...ible exponent is 499 If the exponent is negative press z after you key in the or after you key in the value of the exponent 34 z _ For a power of ten without a multiplier such as 1034 just press 34 The calculator displays Other Exponent Functions To calculate an exponent of ten the base 10 antilogarithm use To calculate the result of any number raised to a power exponentiation use see chapter 4 Un...

Page 32: ...try is terminated no cursor acts like Å and clears the entire number Try it Range of Numbers and OVERFLOW The smallest 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 pr...

Page 33: ...f 148 84 Square of 12 2 z 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 In RPN mode to use a two number function such as Ù Ã b º x m or º p 1 Key in the first number 2 Press Ï to separate the first number from the second 3 Key in the second number Do not pre...

Page 34: ...ng them by pressing w 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 Ý to display the MODES menu...

Page 35: ...1 places press Ë 0 or Ë 1 For example in the number the 7 0 8 and 9 are the decimal digits you see when the calculator is set to FIX 4 display mode Any number that 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 digit before the or radix mark with...

Page 36: ...ple key in the number and pressing _ will convert the displayed value to which the mantissa n satisfies 1 n 1000 and the exponent is a multiple of 3 When you press _ again the displayed value is converted to by shifting the decimal point three places to the right and converting the exponent to the next lower multiple of 3 Key in the number and pressing º will convert the displayed value to which t...

Page 37: ...mat two decimal places and an exponent Þ 2 Engineering format Þ All significant digits trailing zeros dropped Þ 4 Four decimal places no exponent Reciprocal of 58 5 º Î hold Shows full precision until you release Î Fractions The HP 33s 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 a...

Page 38: ...iption 12 _ Enters the integer part of the number Ë _ The Ë key is interpreted in the normal manner 3 _ Enters the numerator of the fraction the number is still displayed in decimal form Ë _ The calculator interprets the second Ë as a fraction and separates the numerator from denominator 8 _ Appends the denominator of the fraction Ï Terminates digit entry displays the number in the current display...

Page 39: ...dds the numbers in the X and Y registers displays the result as a fraction É 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 â symbol comes on to call your attention to the message To clear a message press Å or To clear a message and pe...

Page 40: ...ys 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 Ø or 3 To delete a variable or a program press while viewing it in its catalog 4 To exit the catalog press Å Clearing All of Memory Clearing all of memory erases all numbers equations and programs you ve stored It does not affect mode and format settings To cle...

Page 41: ... 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 Łukasiewicz s notation places them before the numbers or variables For opti...

Page 42: ...age or a 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 raises ten to the power of the number in the X register Clearing the X Register Pressing always clears the X register to zero it is also used to program this instruction The Å key in contrast is context sensiti...

Page 43: ...2 1 4 3 2 Y 3 2 1 4 3 X 4 3 2 1 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 contents of the registers are rolled the registers themselves maintain their positions and only the X and Y register s contents are displayed R Roll Up The º roll up key has a similar function to except that it rolls the stack c...

Page 44: ...13 Ï 8 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 register will be lost whenever a fifth number is entered Arithmetic How the Stack Does It The contents of the stack move up and down automatically as new numbers enter the X register lifting the stack and as operators combine two numbers in the X and Y registe...

Page 45: ...arates two numbers keyed in one after the other In terms of the stack how does it do this Suppose the stack is again filled with 1 2 3 and 4 Now enter and add two new numbers 1 lost 2 lost T 1 2 3 3 3 Z 2 3 4 4 3 Y 3 4 5 5 4 X 4 5 5 6 11 1 2 3 4 1 Lifts the stack 2 Lifts the stack and replicates the X register 3 Does not lift the stack 4 Drops the stack and replicates the T register Ï replicates t...

Page 46: ...pulation of 100 be at the end of 3 days Replicates T register T 1 5 1 5 1 5 1 5 1 5 Z 1 5 1 5 1 5 1 5 1 5 Y 1 5 1 5 1 5 1 5 1 5 1 5 X 1 5 100 100 150 225 337 5 1 2 3 4 5 1 Fills the stack with the growth rate 2 Keys in the initial population 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 X reg...

Page 47: ...tended to enter 1 and 3 but mistakenly entered 1 and 2 this is what you should do to 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 Lifts 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 w...

Page 48: ...u don t have to start over To find the correct result press Í Mistakes with Two number Functions If you make a mistake with a two number operation Ù Ã b º x m or º p you can correct it by using Í and the inverse of the two number function 1 Press Í to recover the second number x just before the operation 2 Execute the inverse operation This returns the number that was originally first The second n...

Page 49: ...function Í Ù Í 15 Ï 19 Wrong first number 16 Í 16 Ï 18 Wrong second number Í 19 Reusing Numbers with LAST X You can use Í 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 Í Example Calculate 3947 52 3947 52...

Page 50: ...ber 52 3947 Ù Intermediate result Í Brings back display from before Ù 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 these stars into meters To Rigel Centaurus 4 3 yr 9 5 1015 m yr To Sirius 8 7 yr 9 5 1015 m yr Keys Displa...

Page 51: ...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 problem in the same way on the HP 33s starting inside the parentheses Keys Display Description 12 Ï 3 Ù Calculates the intermediate result first You don t need to press Ï to save this intermediate result before proceedi...

Page 52: ...ion 7 Ï 3 Calculates 7 3 14 Ù 2 Ã Calculates denominator 4 w Puts 4 before 33 in preparation for division Calculates 4 33 the answer Problems that have multiple parentheses can be solved in the same manner using the automatic storage of intermediate results For example to solve 3 4 5 6 on paper you would first calculate the quantity 3 4 Then you would calculate 5 6 Finally you would multiply the t...

Page 53: ...17 Ï 12 Ã 4 Order of Calculation We recommend solving chain calculations by working from the innermost parentheses outward However you can also choose to work problems in a left to right order For example you have already calculated 4 14 7 3 2 by starting with the innermost parentheses 7 3 and working outward just as you would with pencil and paper The keystrokes were 7 Ï 3 14 Ù 2 Ã 4 w If you wor...

Page 54: ...egisters in the stack Note When using the left to right method be sure that no more than four intermediate numbers or results will be needed at one time the stack can hold no more than four numbers The above example when solved left to right needed all registers in the stack at one point Keys Display Description 4 Ï 14 Ï Saves 4 and 14 as intermediate numbers in the stack 7 Ï 3 _ At this point the...

Page 55: ...te 232 13 9 1 7 412 1429 A Solution 23 13 Ï 9 Ã 7 Ù Calculate 5961 0 7 0 5 12 8 0 4 5 3 Solution 5 4 Ï 8 7 Ï 3 12 5 w Ã or 5 4 Ï 8 12 5 Ï 7 Ï 3 Ã Calculate 5728 4 01 2 71 1 75 2 15 3 3 4 32 0 46 7 33 8 2 5 4 33 8 A Solution 4 Ï 5 2 Ã 8 33 Í 7 46 Ã 0 32 3 15 Ï 2 75 Ã 4 3 1 71 Ï 2 01 Ã ...

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Page 57: ...re numbers equations and program lines Numbers are stored in locations called variables each named with a letter from A through Z You can choose the letter to remind you of what is stored there such as B for bank balance and C for the speed of light 1 Cursor prompts for variable 2 Indicates letter keys are active 3 Letter keys ...

Page 58: ...les with the e store and h recall functions To store a copy of a displayed number X register to a variable Press e letter key To recall a copy of a number from a variable to the display Press h letter key Example Storing Numbers Store Avogadro s number approximately 6 0221 1023 in A Keys Display Description 6 0221 23 _ Avogadro s number e _ Prompts for variable A hold key Displays function as long...

Page 59: ...s of available memory Pressing the menu key displays the catalog of variables Pressing the menu key displays the catalog of programs To review the values at any or all non zero variables 1 Press u VAR 2 Press Ø or to move the list and display the desired variable Note the annunciators indicating that the Ø and keys are active If Fraction display mode is active does not indicate accuracy To see all...

Page 60: ...ariables Storage arithmetic and recall arithmetic allow you to 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 e Ù e Ã e or e to do arithmetic in the variable itself and to store the result there It uses the value i...

Page 61: ...w 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 h A Now x 0 25 while 12 is still in A Recall arithmetic saves memory in programs using h Ù A one instruction uses half as much memory as h A Ù two instructions A 12 A 12 T t T t Z z Z z Y y Y y X 3 X 0 25 Result 3 12 that is x 12 Example Suppose the variables D E and F...

Page 62: ...ables 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 h D Calculates 3 D h E 3 D E h Ù F 3 D E F Exchanging x with Any Variable The º v key allows you to exchange the contents of x the displayed X register with the contents of any variable Executing this function does not affect the Y Z or T registers Ex...

Page 63: ...ble that you can access directly the variable i The Ë 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 called indirect addressing that is covered under Indirectly Addressing Variabl...

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Page 65: ...d Trigonometric functions Hyperbolic functions Percentage functions Physics constants Conversion functions 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 ...

Page 66: ...e first number from the second 3 Key in the second number Do not press Ï 4 Press the function key Example To display the quotient and remainder produced by 58 9 Keys Display Description 58 Ï 9 b Displays the quotient 58 Ï 9 º Displays the remainder Power Functions To calculate the square of a number x key in x and press To calculate the square root of a number x key in x and press To calculate the...

Page 67: ...5 z In RPN mode to calculate a root x of a number y the xth root of y key in y Ï x then press For y 0 x must be an integer To Calculate Press Result 4 625 625 Ï 4 4 1 37893 37893 Ï 1 4 z Trigonometry Entering π Press º j to place the first 12 digits of π into the X register The number displayed depends on the display format Because π is a function it doesn t need to be separated from another numbe...

Page 68: ...iption Annunciator Sets Degrees mode DEG Uses decimal degrees not degrees minutes and seconds none Sets Radians mode RAD RAD Sets Grads mode GRAD GRAD Trigonometric Functions With x in the display To Calculate Press Sine of x k Cosine of x n Tangent of x q Arc sine of x i Arc cosine of x l Arc tangent of x o Note Calculations with the irrational number π cannot be expressed exactly by the 12 digit...

Page 69: ... Degrees mode no annunciator 128 57 n Calculates cos 128 57 which is the same as cos 5 7 π Programming Note Equations using inverse trigonometric functions to determine an angle θ often look something like this θ arctan y x If x 0 then y x is undefined resulting in the error For a program then it would be more reliable to determine θ by a rectangular to polar conversion which converts x y to r θ S...

Page 70: ... they preserve the value of the base number in the Y register when they return the result of the percentage calculation in the X register You can then carry out subsequent calculations using both the base number and the result without reentering the base number To Calculate Press x of y y Ï x m Percentage change from y to x y 0 y Ï x º p Example Find the sales tax at 6 and the total cost of a 15 7...

Page 71: ...ge change from last year s price to this year s Keys Display Description 16 12 Ï 15 76 º p This year s price dropped about 2 2 from last year s price Þ 4 Restores FIX 4 format Note The order of the two numbers is important for the CHG function The order affects whether the percentage change is considered positive or negative ...

Page 72: ...8 10 27 kg Neutron mass 1 67492716 10 27 kg Muon mass 1 88353109 10 28 kg Boltzmann constant 1 3806503 10 23 J K 1 Planck constant 6 62606876 10 34 J s Planck constant over 2 pi 1 054571596 10 34 J s Magnetic flux quantum 2 067833636 10 15 Wb Bohr radius 5 291772083 10 11 m ε Electric constant 8 854187817 10 12 F m 1 Molar gas constant 8 314472 J mol 1 k 1 Faraday constant 96485 3415 C mol 1 Atomi...

Page 73: ...014387752 m K Conductance quantum 7 748091696 10 5 S Reference Peter J Mohr and Barry N Taylor CODATA Recommended Values of the Fundamental Physical Constants 1998 Journal of Physical and Chemical Reference Data Vol 28 No 6 1999 and Reviews of Modern Physics Vol 72 No 2 2000 To insert a constant 1 Position your cursor where you want the constant inserted 2 Press º Ü to display the physics constant...

Page 74: ...and 180 between π and π radians or between 200 and 200 grads To convert between rectangular and polar coordinates 1 Enter the coordinates in rectangular or polar form that you want to convert In RPN mode the order is y Ï x or θ Ï r 2 Execute the conversion you want press rectangular to polar or º polar to rectangular The converted coordinates occupy the X and Y registers 3 The resulting display th...

Page 75: ...lculates hypotenuse r w Displays θ Example Conversion with Vectors Engineer P C Bord has determined that in the RC circuit shown the total impedance is 77 8 ohms and voltage lags current by 36 5º What are the values of resistance R and capacitive reactance XC in the circuit Use a vector diagram as shown with impedance equal to the polar magnitude r and voltage lag equal to the angle θ in degrees W...

Page 76: ...ematics Programs Time Conversions Values for time in hours H or angles in degrees D can be converted between a decimal fraction form H h or D d and a minutes seconds form H MMSSss or D MMSSss using the or º keys To convert between decimal fractions and minutes seconds 1 Key in the time or angle in decimal form or minutes seconds form that you want to convert 2 Press º or The result is displayed Ex...

Page 77: ... radians To convert an angle between degrees and radians 1 Key in the angle in decimal degrees or radians that you want to convert 2 Press º µ or The result is displayed Unit Conversions The HP 33s has eight unit conversion functions on the keyboard kg lb ºC ºF cm in l gal To Convert To Press Displayed Results 1 lb kg 1 kilograms 1 kg lb 1 º pounds 32 ºF ºC 32 C 100 ºC ºF 100 º F 1 in cm 1 centime...

Page 78: ...n a set and different orders of the same r items are not counted separately Permutations To calculate the number of possible arrangements of n items taken r at a time enter n first then r nonnegative integers only No item occurs more than once in an arrangement and different orders of the same r items are counted separately Seed To store the number in x as a new seed for the random number generato...

Page 79: ...ty committee How many different combinations of people are possible Keys Display Description 24 Ï 6 _ Twenty four people grouped six at a time x Total 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 combinati...

Page 80: ...he sign of x press º a If the x value is negative 1 0000 is displayed if zero 0 0000 is displayed if positive 1 0000 is displayed Greatest integer To obtain the greatest integer equal to or less than given number press º g Example To calculate Press Display The integer part of 2 47 2 47 º The fractional part of 2 47 2 47 º The absolute value of 7 7 z The sign value of 9 9 º a The greatest integer ...

Page 81: ...a function appears in the display when you press and hold the key to execute it The name remains displayed for as long as you hold the key down For instance while pressing k the display shows SIN is the name of the function as it will appear in program lines and usually in equations also ...

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Page 83: ...ame 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 fraction where the numerator is larger than the denominator However the calculator displays â if you disregard these two restr...

Page 84: ...w the direction of any inaccuracy of the fraction compared to its 12 digit decimal value Most statistics registers are exceptions they re always shown as decimal numbers Display Rules The fraction you see may differ from the one you enter In its default condition the calculator displays a fractional number according to the following rules To change the rules see Changing the Fraction Display later...

Page 85: ...it the fractional part of the internal 12 digit value exactly matches the value of the displayed fraction If is lit the fractional part of the internal 12 digit value is slightly less than the displayed fraction the exact numerator is no more than 0 5 below the displayed numerator If is lit the fractional part of the internal 12 digit value is slightly greater than the displayed fraction the exact...

Page 86: ...rnal value has an integer part its fractional part contains less than 12 digits and it can t exactly match a fraction that uses all 12 digits Longer Fractions If the displayed fraction is too long to fit in the display it s shown with at the beginning The fraction part always fits the means the integer part isn t shown completely To see the integer part and the decimal fraction press and hold º Î ...

Page 87: ...he c function uses the absolute value of the integer part of the number in the X register It doesn t change the value in the LAST X register Choosing a Fraction Format The calculator has three fraction formats Regardless of the format the displayed fractions are always the closest fractions within the rules for that format Most precise fractions Fractions have any denominator up to the c value and...

Page 88: ...Press º to get the flag menu 2 To set a flag press 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 Å or 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 ...

Page 89: ...rs flag 9 for factors of denominator format 8 º Ê Sets up fraction format for 1 8 increments 48 Ë 1 Ë 4 Ï Enters the starting value 2 Ë 5 Ë 8 Ã Subtracts the change 85 m Finds the 85 percent value to the nearest 1 8 Rounding Fractions If Fraction display mode is active the RND function converts the number in the X register to the closest decimal representation of the fraction The rounding is done ...

Page 90: ...ious example 56 Ë 3 Ë 4 e D Stores the distance in D 6 The sections are a bit wider than 9 7 16 inches f Rounds the width to this value 6 Width of six sections h D Ã The cumulative round off error º 8 Clears flag 8 É Turns off Fraction display mode Fractions in Equations When you re typing an equation you can t type a number as a fraction When an equation is displayed all numeric values are shown ...

Page 91: ...g 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 by setting and clearing flags 7 8 and 9 Setting flag 7 turns on Fraction display mode É isn t programmable See Flags in chapter 13 See chapters...

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Page 93: ...straight section of pipe The equation is V 25 π d2 l where 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 Ï º j 2 5 16 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 33s to remember the relationship between diameter length and volume so you can...

Page 94: ...he 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 entered the equation properly See Verifying Equations at the end of this chapter for more information Evaluate the equation to calculate V Keys Display Description Ï value Prompts for variables on the right hand side of the equation Prompts for D f...

Page 95: ...ations later in this chapter t Evaluates the displayed equation Calculates its value replacing with if an is present Û Solves the displayed equation for the unknown variable you specify See chapter 7 º Integrates the displayed equation with respect to the variable you specify See chapter 8 Begins editing the displayed equation subsequent presses delete the rightmost function or variable Deletes th...

Page 96: ...rs per equation 4 Press Ï to terminate the equation and see it in the display The equation is automatically saved in the equation list right after the entry that was displayed when you started typing If you press Å 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 va...

Page 97: ... complete list is given under Equation Functions later in this chapter Appendix G Operation Index also gives this information When you enter an equation you enter functions in about the same way you put them in ordinary algebraic equations In an equation certain functions are normally shown between their arguments such as and For such infix operators enter them in an equation in the same order Oth...

Page 98: ...º Starts a new equation with variable R 2 _ Enters a number changing the cursor to _ h C Enters infix operators n Enters a prefix function with a left parenthesis h T Ã h A º Ù 25 _ Enters the argument and right parenthesis Ï Terminates the equation and displays it º Î Shows its checksum and length Å Leaves Equation mode Displaying and Selecting Equations The equation list contains the equations y...

Page 99: ...ess Õ to scroll the equation one character at a time showing characters to the right Press Ö to show characters to the left and turn off if there are no more characters to the left or right To select an equation Display the equation in the equation list as described above The displayed equation is the one that s used for all equation operations Example Viewing an Equation View the last equation yo...

Page 100: ...bove 2 Press once only to start editing the equation The equation entry cursor appears at the end of the equation Nothing is deleted from the equation 3 Use to edit the equation as described above 4 Press Ï or Å to save the edited equation in the equation list replacing the previous version To clear an equation you re typing Press then press The display goes back to the previous entry in the equat...

Page 101: ... left side contains just a single variable For example A 0 5 b h is an assignment Expressions The equation does not contain an For example x3 1 is an expression When you re calculating with an equation you might use any type of equation although the type can affect how it s evaluated When you re solving a problem for an unknown variable you ll probably use an equality or assignment When you re int...

Page 102: ...s that value into the variable on the left side it stores the value in the variable The following table shows the two ways to evaluate equations Type of Equation Result for Ï Result for t Equality g x f x Example x2 y2 r2 g x f x x2 y2 r2 Assignment y f x Example A 0 5 b x h f x 0 5 b h y f x A 0 5 b h Expression f x Example x3 1 f x x3 1 Also stores the result in the left hand variable A for exam...

Page 103: ...ariable then the variable is VIEWed in the display Essentially Ï finds the value of the left hand variable If the equation is an equality or expression the entire equation is evaluated just as it is for t The result 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...

Page 104: ...play Description º d π Displays the desired equation t Starts evaluating the equation to find its value Prompts for all variables Keeps the same V prompts for D 35 5 Stores new D Prompts for L Keeps the same L calculates the value of the equation the imbalance between the left and right sides 6 Changes cubic millimeters to liters The value of the equation is the old volume from V minus the new vol...

Page 105: ... during digit entry it clears the number to zero Press Å again to cancel the prompt To display digits hidden by the prompt press º Î 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 stack lift is enabled so the value is retained on the stack The Syntax of Equations Equations follo...

Page 106: ...6 Equality So for example all operations inside parentheses are performed before operations outside the parentheses Examples Equations Meaning a b3 c a b 3 c a b c 12 a b c 12 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 with the operator inserted between P and the left parenthesis ...

Page 107: ...r convenience 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 RND XROOT IDIV RMDR Cn r and Pn r Separate the two arguments with a colon In an equation the XROOT function takes its arguments in the opposite order from RPN usage For example 8 Ï 3 to is equivalent to All other two argument ...

Page 108: ...n function x2 SQ x SQRT ex EXP 10x ALOG 1 x INV X y XROOT yx INT IDIV Rmdr RMDR x3 CB 3 x CBRT 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 33s equations ...

Page 109: ... fractional form Notice that the SIN function is nested inside the INV function INV is typed by 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 specify this equation as π π Notice how the operators and functions combine to give the desired equation You can enter the equation into the equation list using...

Page 110: ... about the equation the equation s checksum and its length Hold the Î key to keep the values in the display The checksum is a four digit hexadecimal value that uniquely identifies this equation No other equation will have this value If you enter the equation incorrectly it will not have this checksum The length is the number of bytes of calculator memory used by the equation The checksum and lengt...

Page 111: ...d 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 the value of the equation being zero Solving an Equation To solve an equation for an unk...

Page 112: ... calculator displays See Verifying the Result later in this chapter and Interpreting Results and When SOLVE Cannot Find a Root in appendix D For certain equations it helps to provide one or two initial guesses for the unknown variable before solving the equation This can speed up the calculation direct the answer toward a realistic solution and find more than one solution if appropriate See Choosi...

Page 113: ... equation is already in the display you can start solving for D Keys Display Description Û _ Prompts for unknown variable D value Selects D prompts for V 0 value Stores 0 in V prompts for T 5 value Stores 5 in T prompts for G 9 8 Stores 9 8 in G solves for D Try another calculation using the same equation how long does it take an object to fall 500 meters from rest Keys Display Description º d Dis...

Page 114: ... Keys Display Description º d h P Selects Equation mode and starts the equation h V º h N h R h T Ï Terminates and displays the equation º Î 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 turned on and the desired equation is already in the display you can start solv...

Page 115: ...or T 18 Ï 273 1 Ù Calculates T Kelvins Stores 291 1 in T solves for N 28 Calculates mass in grams N 28 h V Calculates density in grams per liter Understanding and Controlling SOLVE SOLVE first attempts to solve the equation directly for the unknown variable If the attempt fails SOLVE changes to an iterative repetitive procedure The procedure starts by evaluating the equation using two initial gues...

Page 116: ...ress 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 The Z register press again contains this value of the equation at the root For an exact root this should be zero If it i...

Page 117: ...e 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 guesses can reduce the time to find a solution If there is more than one mathematical solution guesses can direct the SOLVE procedure to the desired answer or range of answers For example the equation of linear motion d v0 t 1...

Page 118: ...sing 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 the box that is the amount to be folded up along each of the four sides that gives the specified volume A taller box is preferred to a shorter one 40 80 40_2H H H 80_2H H H If H is the height then the length of the box is 80 2H and the ...

Page 119: ...eight are reasonable However heights greater than 20 cm are not physically possible because the metal sheet is only 40 cm wide Initial estimates of 10 and 20 cm are therefore appropriate Keys Display Description Å Leaves Equation mode 10 e H 20 _ Stores lower and upper limit guesses º d Displays current equation Û H value Solves for H prompts for V 7500 Stores 7500 in V solves for H Now check the ...

Page 120: ...m 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 understand the behavior of the equation Evaluate your equation for several values of the unknown For each point on the graph display the equation and press t at the prompt for x enter the x coordinate and then obtain the corresponding value of the equat...

Page 121: ...uctions for solving for unknowns or roots over a wide range of applications Appendix D 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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Page 123: ...gral 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 FN integrates the current equation with respect to a specified variable d_ The function may have m...

Page 124: ...n by pressing Å or However no information about the integration is available until the calculation finishes normally The display format setting affects the level of accuracy assumed for your function and used for the result The integration is more precise but takes much longer in the and higher and settings The uncertainty of the result ends up in the Y register pushing the limits of integration u...

Page 125: ... º º Ï Terminates the expression and displays its left end º Î Checksum and length Å Leaves Equation mode Now integrate this function with respect to t from zero to π x 2 Keys Display Description Ý Selects Radians mode 0 Ï º j Enters the limits of integration lower limit first º d Displays the function º _ Prompts for the variable of integration T value Prompts for value of X 2 x 2 Starts integrat...

Page 126: ...l result for J0 3 Example Sine Integral Certain problems in communications theory for example pulse transmission through idealized networks require calculating an integral sometimes called the sine integral of the form dx x x t S t i sin 0 Find Si 2 Enter the expression that defines the integrand s function x x sin If the calculator attempted to evaluate this function at x 0 the lower limit of int...

Page 127: ... º X Calculates the result for Si 2 Accuracy of Integration Since the calculator cannot compute the value of an integral exactly it approximates it The accuracy of this approximation depends on the accuracy of the integrand s function itself as calculated by your equation This is affected by round off error in the calculator and the accuracy of the empirical constants Integrals of functions with c...

Page 128: ... This same level of accuracy and precision will be reflected in the result of integration If Fraction display mode is on flag 7 set the accuracy is specified by the previous display format Interpreting Accuracy After calculating the integral the calculator places the estimated uncertainty of that integral s result in the Y register Press w to view the value of the uncertainty For example if the in...

Page 129: ...number of digits shown in the display In general the uncertainty of an integration calculation decreases by a factor of ten for each additional digit specified in the display format Example Changing the Accuracy For the integral of Si 2 just calculated specify that the result be accurate to four decimal places instead of only two Keys Display Description Þ 4 Specifies accuracy to four decimal plac...

Page 130: ...is calculated conservatively the calculator s approximation in most cases is more accurate than its uncertainty indicates For More Information This chapter gives you instructions for using integration in the HP 33s over a wide range of applications Appendix E contains more detailed information about how the algorithm for integration works conditions that could cause incorrect results and condition...

Page 131: ...the real part Complex numbers in the HP 33s 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 c before the operator For example to do 2 i 4 3 i 5 press 4 Ï 2 Ï 5 Ï 3 c Ù The result is 5 i 9 The first line is the imaginary and the second is the real part The Comple...

Page 132: ...enter the imaginary part the y part of a number first The real portion of the result zx is displayed on the second line the imaginary portion zy is displayed on the first line For two number operations the first complex number z1 is replicated in the stack s Z and T registers Complex Operations Use the complex operations as you do real operations but precede the operator with c To do an operation ...

Page 133: ...lex numbers 1 Enter the first complex number z1 composed of x1 i y1 by keying in y1 Ï x1 Ï For 2 1 z z key in the base part z1 first 2 Enter the second complex number z2 by keying in y2 Ï x2 For 2 1 z z key in the exponent z2 second 3 Select the arithmetic operation Arithmetic With Two Complex Numbers z1 and z2 To Calculate Press Addition z1 z2 c Ù Subtraction z1 z2 c Ã Multiplication z1 z2 c Divi...

Page 134: ...ince the stack can retain only two complex numbers at a time perform the calculation as z1 1 z2 z3 Keys Display Description 1 Ï 2 z Ï 3 z Ï 4 c Ù Add z2 z3 displays real part c 1 z2 z3 13 Ï 23 c z1 z2 z3 Result is 2 5 i 9 Evaluate 4 i 2 5 3 i 2 3 Do not use complex operations when calculating just one part of a complex number Keys Display Description Ë 2 Ë 5 z Ï Enters imaginary part of first comp...

Page 135: ...esult of 1 i 2 c Final result is 0 8776 i 0 4794 Using Complex Numbers in Polar Notation Many applications use real 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 33s s complex operations work on numbers in rectangular form convert polar form to rectangular form ...

Page 136: ...will first need to convert 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 Ý Sets Degrees mode 62 Ï 185 º Enters L1 and converts it to rectangular form 143 Ï 170 º Enters and converts L2 c Ù Adds vectors 261 Ï 100 º Enters and converts L3 ...

Page 137: ...Operations with Complex Numbers 9 7 c Ù Adds L1 L2 L3 Converts vector back to polar form displays r θ ...

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Page 139: ... Octal mode OCT annunciator on Converts numbers to base 8 uses integers only The 8 9 and unshifted top row keys are inactive Binary mode BIN annunciator on Converts numbers to base 2 uses integers only Digit keys other than 0 and 1 and the unshifted top row functions are inactive If a number is longer than 12 digits then the Ö and Õ keys are active for viewing windows See Windows for Long Binary N...

Page 140: ... Bases 2 8 and 16 You can perform arithmetic operations using Ù Ã and in any base The only function keys that are actually deactivated outside of Decimal mode a r e r e e and However you should realize that most operations other than arithmetic will not produce meaningful results since the fractional parts of numbers are truncated Arithmetic in bases 2 8 and 16 is in 2 s complement form and uses i...

Page 141: ...s 12F16 E9A16 Keys Display Description Sets base 16 HEX annunciator on 12F Ï E9A Ù Result 77608 43268 Sets base 8 OCT annunciator on Converts displayed number to octal 7760 Ï 4326 Ã Result 1008 58 100 Ï 5 Integer part of result 5A016 10011002 5A0 _ Set base 16 HEX annunciator on 1001100 _ Changes to base 2 BIN annunciator on This terminates digit entry so no Ï is needed between the numbers Ù Resul...

Page 142: ...ber For example the binary representation of 12510 is displayed as 1111101 which is the same as these 36 digits 000000000000000000000000000001111101 Negative Numbers The leftmost most significant or highest bit of a number s binary representation is the sign bit it is set 1 for negative numbers If there are undisplayed leading zeros then the sign bit is 0 positive A negative number is the 2 s comp...

Page 143: ... 367 34 359 738 368 When you key in numbers the calculator will not accept more than the maximum number of digits for each base For example if you attempt to key in a 10 digit hexadecimal number digit entry halts and the â annunciator appears If a number entered in decimal base is outside the range given above then it produces the message in the other base modes In RPN mode the original decimal va...

Page 144: ...ch 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 Ö or Õ to view the obscured window Press to display left window Press to display right window ...

Page 145: ... x and y Weighted mean x weighted by y Summation statistics n Σx Σy Σx2 Σy2 and Σxy Entering Statistical Data One and two variable statistical data are entered or deleted in similar fashion using the or key Data values are accumulated as summation statistics in six statistics registers 28 through 33 whose names are displayed in the SUMS menu Press º and see Note Always clear the statistics registe...

Page 146: ...ntered press Í Entering Two Variable Data In RPN mode 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 Ï x so that y ends up in the Y register and X in the X register 1 Press Σ to clear existing statistical data 2 Key in the y value first and press Ï 3 Key in the corresponding x value and press 4 ...

Page 147: ...egister Example Key in the x y values on the left then make the corrections shown on the right Initial x y Corrected x y 20 4 20 5 400 6 40 6 Keys Display Description Clears existing statistical data 4 Ï 20 Enters the first new data pair 6 Ï 400 Display shows n the number of data pairs you entered Í Brings back last x value Last y is still in Y register Deletes the last data pair 6 Ï 40 Reenters t...

Page 148: ...viation later in this chapter SUMS º The summation menu See Summation Statistics later in this chapter Mean Mean is the arithmetic average of a group of numbers Press º for the mean of the x values Press º for the mean of the y values Press º for the weighted mean of the x values using the y values as weights or frequencies The weights can be integers or non integers Example Mean One Variable Prod...

Page 149: ...ighted 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 60 4 70 4 10 Number of Parts y 250 800 900 1000 Find the average price weighted for the purchase quantity for this part Remember to enter y the weight frequency before x the price Keys Display Description Clears the statistics registers 250 Ï 4 25 800 Ï 4 ...

Page 150: ...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 deviation of the times Treat all the data as x values Keys Display Description Clears the statistics registers 15 5 Enters the first time 9 25 10 12 5 12 8 5 Enters the remaining data six data points entered º σ σ Calculates the standard deviation time Population Standa...

Page 151: ...cal method for finding a straight line that best fits a set of x y data Note To avoid a message enter your data before executing any of the functions in the L R menu L R Linear Regression Menu Menu Key Description Estimates predicts x for a given hypothetical value of y based on the line calculated to fit the data Estimates predicts y for a given hypothetical value of x based on the line calculate...

Page 152: ...r the following data determine the linear relationship the correlation coefficient the slope and the y intercept X Nitrogen Applied kg per hectare 0 00 20 00 40 00 60 00 80 00 Y Grain Yield metric tons per hectare 4 63 5 78 6 61 7 21 7 78 Keys Display Description Clears all previous statistical data 4 63 Ï 0 5 78 Ï 20 6 61 Ï 40 7 21 Ï 60 Enters data displays n 7 78 Ï 80 Five data pairs entered º D...

Page 153: ...to the rice field Predict the grain yield based on the above statistics Keys Display Description Å 70 _ Enters hypothetical x value º 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 ...

Page 154: ...Again scaling the data can avoid this problem Effect of Deleted Data Executing 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 have a magnitude that is enormous compared with the correct data in such a case it would be wise to clear and reenter all the data Summation ...

Page 155: ...1 Stores the first data pair 1 2 4 Ï 3 Stores the second data pair 3 4 u Displays VAR catalog and views n register Views Σxy register Views Σy2 register Views Σx2 register Views Σy register Views Σx register Å Leaves VAR catalog The Statistics Registers in Calculator Memory The memory space for the statistics registers is automatically allocated if it doesn t already exist when you press or The re...

Page 156: ...es Σxy 33 Sum of products of accumulated x and y values You can load a statistics register with a summation by storing the number 28 through 33 of the register you want in i number e Ñ and then storing the summation value e Ò Similarly you can press º È Ò to view a register value the display is labeled with the register name The SUMS menu contains functions for recalling the register values See In...

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Page 159: ...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 formula A π r2 and press RPN mode 5 º j ALG mode 5...

Page 160: ...the following Keys In RPN mode Display Description Clears memory Activates Program entry mode PRGM annunciator on r Ë Ë Resets program pointer to PRGM TOP Radius 2 º j π Area πx2 Exits Program entry mode Try running this program to find the area of a circle with a radius of 5 Keys In RPN mode Display Description r Ë Ë This sets the program to its beginning 5 The answer We will continue using the a...

Page 161: ...n program memory then a program needs a label to mark its beginning such as and a return to mark its end such as Notice that the line numbers acquire an to match their label Program Labels Programs and segments of programs called routines should start with a label To record a label press Ó letter key The label is a single letter from A through Z The letter keys are used as they are for variables a...

Page 162: ...ns and ALG Operations Use less memory Easier to write and 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 t evaluates an equation in the equation list For program evaluation in an equation is essentially treated as There s no programmable equivalent to Ï for an assignment equation other than wri...

Page 163: ...ed before all other program lines If you don t need any other programs that might be in memory clear program memory by pressing To confirm that you want all programs deleted press after the message 3 Give the program a label a single letter A through Z Press Ó letter Choose a letter that will remind you of the program such as A for area If the message is displayed use a different letter You can cl...

Page 164: ... The equation does not become part of the equation list After you ve entered an equation you can press º Î to see its checksum and length Hold the Î 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 Õ and Ö to scroll the display Keys That Clear Note these special conditions during program entry Å always ca...

Page 165: ...gram 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 to delete the current program line then reenter the line correctly Keys In RPN mode Display Description Activates Program entry mode PRGM on Clears all of program memory Ó A Labels this program routine A for a...

Page 166: ...N mode Display Description r Ë Ë Activates Program entry mode sets pointer to top of memory Ó E Labels this program routine E for equation e R Stores radius in variable R º d º j h R 2 Ï π Selects Equation entry mode enters the equation returns to Program entry mode º Î º Ô Ends the program u Displays label E and the length of the program in bytes º Î Checksum and length of equation Å Å Cancels pr...

Page 167: ...efore executing A or E Keys In RPN mode Display Description 5 t A Enters the radius then starts program A The resulting area is displayed 2 5 t E Calculates area of the second circle using program E 2 º j t 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 executi...

Page 168: ... 4 The program pointer moves to the next line Repeat step 3 until you find an error an incorrect result occurs or reach the end of the program If Program entry mode is active then Ø or simply changes the program pointer without executing lines Holding down a cursor key during program entry makes the lines roll by automatically Example Testing a Program Step through the execution of the program lab...

Page 169: ...g 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 the X register In a displayed equation if enabled by flag 10 set The equation is usually a me...

Page 170: ...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 to recall the variable at a later time you could INPUT it and use it when you need it You might be able to save some memory space this way However in a long program it is simpler to just input all your data up front and then recall individ...

Page 171: ...can press 2 Ï 5 To calculate with the displayed number press Ï before typing another number To cancel the INPUT prompt press Å The current value for the variable remains in the X register If you press to resume the program the canceled INPUT prompt is repeated If you press Å during digit entry it clears the number to zero Press Å again to cancel the INPUT prompt Using VIEW for Displaying Data The ...

Page 172: ...ecked for valid syntax until they re evaluated This means you can enter almost any sequence of characters into a program as an equation you enter it just as you enter any equation On any program line press º d to start the equation Press number and math keys to get numbers and symbols Press h before each letter Press Ï to end the equation If flag 10 is set equations are displayed instead of being ...

Page 173: ...mpt for radius and height º d º j h R 2 h H Ï π Calculates the volume º Î Checksum and length of equation e V Store the volume in V º d 2 º j h R º y h R Ù h H º Ï π Calculates the surface area º Î Checksum and length of equation e S Stores the surface area in S º Ë 0 Sets flag 10 to display equations º d h V h O h L Ù h A h R h E h A Ï Displays message in equations º Ë 0 Clears flag 10 ...

Page 174: ...hatever value happens to be in R 2 Ë 1 Ë 2 value Enters 2 1 2 as a fraction Prompts for H 8 Message displayed Volume in cm3 Surface area in cm2 Displaying Information without Stopping Normally a program stops when it displays a variable with VIEW or displays an equation message You normally have to press to resume execution If you want you can make the program continue while the information is dis...

Page 175: ...ram entry inserts a PSE pause instruction This will suspend a running program and display the contents of the X register for about 1 second with the following exception If PSE immediately follows a VIEW instruction 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 interru...

Page 176: ...ssing r Ë label nnnn moves the program pointer there 2 Delete the line you want to change if it contains an equation press otherwise press 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 Å or To insert a program lin...

Page 177: ...es is circular so you can wrap the program pointer from the bottom to the top and reverse While program entry is active there are three ways to change the program pointer the displayed line Use the cursor keys and Pressing at the last line moves the pointer to while pressing at moves the pointer to the last program line To move more than one line at a time scrolling continue to hold the Ø or key P...

Page 178: ... 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 t or while the label is displayed Display a labeled program Press while the label is displayed Delete specific programs Press while the label is displayed See the checksum associated with a given program segment Press º Î The catalo...

Page 179: ...ctly entered all the lines of the program To see your checksum 1 Press u for the catalog of program labels 2 Display the appropriate label by using the cursor keys if necessary 3 Press and hold º Î to display checksum and length For example to see the checksum for the current program the cylinder program Keys In RPN mode Display Description u Displays label C which takes 67 bytes º Î hold Checksum...

Page 180: ...s that use numbers in a base other than 10 set the base mode both as the current setting for the calculator and in the program as an instruction Selecting a Base Mode in a Program Insert a BIN OCT or HEX instruction into the beginning of the program You should usually include a DEC instruction at the end of the program so that the calculator s setting will revert to Decimal mode when the program i...

Page 181: ...d right columns All non decimal numbers are right justified in the calculator s display Notice how the number 13 appears as D in Hexadecimal mode Decimal mode set Hexadecimal mode set PRGM PRGM PRGM HEX PRGM HEX Polynomial Expressions and Horner s Method Some expressions such as polynomials use the same variable several times for their solution For example the expression Ax4 Bx3 Cx2 Dx E uses the ...

Page 182: ...Ë Ë Ó A Ç X 5 5 h X 5x 4 5x4 Ù 5x4 2 5x4 2 h X 5x4 2x 3 5x4 2x3 Ï º Ô u Displays label A which takes 93 bytes º Î Checksum and length Å Å Cancels program entry Now evaluate this polynomial for x 7 Keys In ALG mode Display Description t A value Prompts for x 7 Result ...

Page 183: ...Simple Programming 12 25 A more general form of this program for any equation Ax4 Bx3 Cx2 Dx E would be Checksum and length E41A 54 ...

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Page 185: ... 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 read understand and alter For example look at the program for Normal and Inverse Normal Distributions in chapter 16 Rou...

Page 186: ...ns to the line after the originating XEQ 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 instruction that sends program execution back to routine D to store and display the result at line D0004 See the flow diagrams below The flow diagrams in this chapter use ...

Page 187: ...ested subroutines is as shown below MAIN program top level End of program Attempting to execute a subroutine nested more than seven levels deep causes an error Example A Nested Subroutine The following subroutine labeled S calculates the value of the expression 2 2 2 2 d c b a as part of a larger calculation in a larger program The subroutine calls upon another subroutine a nested subroutine label...

Page 188: ...n routine 135 Nested subroutine Adds x2 246 Returns to subroutine S Branching GTO As we have seen with subroutines it is often desirable to transfer execution to a part of the program other than the next line This is called branching Unconditional branching uses the GTO go to instruction to branch to a program label It is not possible to branch to a specific line number during a program ...

Page 189: ...o GTO is not used for subroutines For example consider the Curve Fitting program in chapter 16 The instruction branches execution from any one of three independent initializing routines to LBL Z the routine that is the common entry point into the heart of the program Can start here 1 Branches to Z Can start here 1 Branches to Z Can start here 1 Branches to Z 1 Branch to here Using GTO from the Key...

Page 190: ... compares the contents of the X register with zero If the X register does contain zero then the program goes on to the next line If the X register does not contain zero then the program skips the next line thereby branching to line A0007 This rule is commonly known as Do if true Do next if true 2 Skip next if false 1 2 1 The above example points out a common technique used with conditional tests t...

Page 191: ... 0 for tests comparing x and 0 Remember that x refers to the number in the X register and y refers to the 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 e...

Page 192: ...ulated correction with 0 0001 If the value is less than 0 0001 Do If True the program executes line T0014 if the value is equal to or greater than 0 0001 the program skips to line T0015 Flags A flag is an indicator of status It is either set true or clear false Testing a flag is another conditional test that follows the Do if true rule program execution proceeds directly if the tested flag is set ...

Page 193: ...lf It has no effect but can be tested Flags 5 and 6 allow you to control overflow conditions that occur during a program Setting flag 5 stops a program at the line just after the line that caused the overflow By testing flag 6 in a program you can alter the program s flow or change a result anytime an overflow occurs Flags 7 8 and 9 control the display of fractions Flag 7 can also be controlled fr...

Page 194: ...ffect automatic prompting during keyboard execution When flag 11 is clear the default state evaluation SOLVE and FN of equations in programs proceed without interruption The current value of each variable in the equation is automatically recalled each time the variable is encountered INPUT prompting is not affected When flag 11 is set each variable is prompted for when it is first encountered in t...

Page 195: ...n Clear flag Clears flag n n Is flag set Tests the status of flag n A flag test is a conditional test that affects program execution just as the comparison tests do The FS n instruction tests whether the given flag is set If it is then the next line in the program is executed If it is not then the next line is skipped This is the Do if True rule illustrated under Conditional Instructions earlier i...

Page 196: ...uts for a Straight line model curve Line L0003 sets flag 0 so that line W0007 takes the natural log of the X input for a Logarithmic model curve Line E0004 sets flag 1 so that line W0011 takes the natural log of the Y input for an Exponential model curve Lines P0003 and P0004 set both flags so that lines W0007 and W0011 take the natural logarithms of both the X and Y inputs for a Power model curve...

Page 197: ...r 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 1 the indicator for In Y Sets flag 0 the indicator for ln X Sets flag 1 the indicator for In Y If flag 0 is set takes the natural log of the X input If flag 1 is set takes the natural log of the Y input ...

Page 198: ...The program also contains examples of how the three fraction display flags 7 8 and 9 and the message display flag 10 are used Messages in this program are listed as MESSAGE and are entered as equations 1 Set Equation entry mode by pressing º d the EQN annunciator turns on 2 Press h letter for each alpha character in the message press the key for each space character 3 Press Ï to insert the message...

Page 199: ...ts decimal base Prompts for a number Prompts for denominator 2 4095 Displays message then shows the decimal number Sets c value and sets flag 7 Displays message then shows the fraction Sets flag 8 Displays message then shows the fraction Sets flag 9 Displays message then shows the fraction Goes to beginning of program Checksum and length 6F14 123 ...

Page 200: ...umber Message indicates the fraction format denominator is no greater than 16 then shows the fraction indicates that the numerator is a little below 8 Message indicates the fraction format denominator is factor of 16 then shows the fraction Message indicates the fraction format denominator is 16 then shows the fraction Å º Ë 0 Stops the program and clears flag 10 Loops Branching backwards that is ...

Page 201: ...oops GTO When you want to perform an operation until a certain condition is met but you don t know how many times the loop needs to repeat itself you can create a loop with a conditional test and a GTO instruction For example the following routine uses a loop to diminish a value A by a constant amount B until the resulting A is less than or equal to B Program lines In RPN mode Description Checksum...

Page 202: ...DSE instruction is like a FOR NEXT loop with a negative increment After pressing a shifted key for ISG or DSE ª or º you will be prompted for a variable that will contain the loop control number described below The Loop Control Number The specified variable should contain a loop control number ccccccc fffii where ccccccc is the current counter value 1 to 12 digits This value changes with loop exec...

Page 203: ...f current value final value exit loop 1 2 1 2 If current 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 b...

Page 204: ... to another variable or label It holds a number just like any other variable A through Z Ò 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 Ñ and Ò are used together to create an indirect address See the examples below By itself i is just another variable By itself Ò is eithe...

Page 205: ... 28 n register 29 Σx register 30 Σy register 31 Σx2 register 32 Σy2 register 33 Σxy register 34 or 34 or 0 error 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 the statistics registers However yo...

Page 206: ...er 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 stored and then indirectly addressed in widely separated parts of the program The fir...

Page 207: ...used by the program Solutions of Simultaneous Equations Matrix Inversion Method in chapter 15 This program uses the looping instructions and in conjunction with the indirect instructions and to fill and manipulate a matrix The first part of this program is routine A which stores the initial loop control number in i Program lines In RPN mode Description The starting point for data input Loop contro...

Page 208: ...s the inversion of the 3 3 matrix Program Lines In RPN mode Description This routine completes inverse by dividing by determinant Divides element 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 indirectly Notice that means the variable specified by the number in variable i ...

Page 209: ...ing Sets counter for 1 to 26 Stores counter Initializes sum Checksum and length AEC5 42 Starts summation loop Equation to evaluate the ith square Press º d to start the equation Ckecksum and length of equation F09C 5 Adds ith square to sum Tests for end of loop Branches for next variable Ends program Checksum and length of program E005 23 ...

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Page 211: ...program for SOLVE below 2 Select the program to solve press º s label You can skip this step if you re re solving the same program 3 Solve for the unknown variable press Û 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 Å or The current best estimate of the root is in the unknown va...

Page 212: ...ram 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 the program with a RTN Program execution should end with the value of the function in the X register If the program contains a VIEW or STOP instruction or a message for display an equation with Flag 10 set then the instruction ...

Page 213: ... Program mode Type in the program Program Lines In ALG mode Description Identifies the programmed function Stores P Stores V Stores N Stores R Stores T Pressure Pressure volume Pressure volume Pressure volume Number of moles of gas Pressure volume Moles gas constant Pressure volume Moles gas constant temp Gets the result Ends the program Checksum and length EB2A 42 Press Å to cancel Program entry ...

Page 214: ... Stores 0821 in R prompts for T 24 Ù 273 1 Ï Calculates T 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 In RPN mode Display Description r Ë Ë Selects Program entry mode Moves program pointer to top of the list of programs Ó H Labels the program º Ë 1 Enables equation prompting º d h P h V º...

Page 215: ... previous example Keys In RPN mode Display Description e L Stores previous pressure º s H Selects program H Û P Selects variable P prompts for V Retains 2 in V prompts for N Retains 005 in N prompts for R Retains 0821 in R prompts for T Ï 10 Ã Calculates new T Stores 287 1 in T solves for new P h L Ã Calculates pressure change of the gas when temperature drops from 297 1 K to 287 1 K negative resu...

Page 216: ...e since this might not 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 result displayed add a VIEW variable instruction after the SOLVE instruction If no solution is found for the unknown variable then the next program line is skipped in accordance with the Do if True rule explained in chapter 13...

Page 217: ...x y Include INPUT or equation prompting as required Integrating a Program In chapter 8 you saw how you can enter an equation or expression it s added to the list of equations and then integrate it with respect to any variable You can also enter a program that calculates a function and then integrate it with respect to any variable This is especially useful if the function you re integrating change...

Page 218: ...an INPUT instruction for each variable including the variable of integration INPUT instructions enable you to integrate with respect to any variable in a multi variable function INPUT for the variable of integration is ignored by the calculator so you need to write only one program that contains a separate INPUT instruction for every variable including the variable of integration If you include no...

Page 219: ...al function with respect to x from 0 to 2 t 2 Keys In RPN mode Display Description Ý Selects Radians mode º s S Selects label S as the integrand 0 Ï 2 _ Enters lower and upper limits of integration º X Integrates function from 0 to 2 displays result Ý Restores Degrees mode Using Integration in a Program Integration can be executed from a program Remember to include or prompt for the limits of inte...

Page 220: ...e the program is called by FN However if VIEW or a message is followed by PSE then the value or message will be displayed for one second each time the program is called STOP followed by PSE is ignored Example FN in a Program The Normal and Inverse Normal Distributions program in chapter 16 includes an integration of the equation of the normal density function e 2 dD 2 S 1 2 S M D D M π The 2 2 S M...

Page 221: ...in an 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 contains an FN instruction produces a error just as FN cannot call a routine that contains a SOLVE instruction produces an error The SOLVE variable and FN d variable instructions in a program use one of the seven pending subroutine returns...

Page 222: ......

Page 223: ...ross 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 This program uses the following equations Coordinate conversion X R sin P cos T R 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 ...

Page 224: ...1 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 ...

Page 225: ...ccepts input of Z Checksum and length 8E7D 12 Defines beginning of rectangular to polar conversion process θ Calculates Y X 2 2 and arctan Y X Saves T arctan Y X θ Calculates Z Y X 2 2 2 and P Saves R Saves P Checksum and length E230 36 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 θ Calculates ...

Page 226: ...ksum and length 5F1D 48 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 1961 24 Defines beginning of vector exchange routine Exchanges X Y and Z with U V and W respectively Loops back for polar conversion and display input Checksum and length CE3C 33 Defines beginning of vec...

Page 227: ...or polar conversion and display input Checksum and length 6ED7 33 Defines the beginning of the vector subtraction routine Multiplies X Y and Z by 1 to change the sign Goes to the vector addition routine Checksum and length 5FC1 30 Defines the beginning of the cross product routine Calculates YW ZV which is the X component ...

Page 228: ... the Y component Stores XV YU which is the Z component Stores X component Stores Y component Loops back for polar conversion and display input Checksum and length 6F95 81 Defines beginning of dot product and vector angle routine Stores the dot product of XU YV ZW Displays the dot product θ ...

Page 229: ...ar 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 coordinate input it would not have been available for cross product Program Instructions 1 Key in the progra...

Page 230: ...rectangular form press t R then press 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 t E before keying in a new vector 10 Go to step 2 to continue vector calculations Variables Used X Y Z The rectangular components of v1 U V W The re...

Page 231: ...value Sets X equal to 7 3 15 7 value Sets Y equal to 15 7 76 z Sets Z equal to 0 76 and calculates R the radius Calculates T the angle in the x y plane Calculates P the angle from the z axis Example 2 What is the moment at the origin of the lever shown below What is the component of force along the lever What is the angle between the resultant of the force vectors and the lever ...

Page 232: ...Display Description t P value Starts polar input routine 17 value Sets radius equal to 17 215 value Sets T equal to 215 17 Sets P equal to 17 t E Enters vector by copying it into v2 23 Sets radius of v1 equal to 23 80 Sets T equal to 80 74 Sets P equal to 74 t A Adds the vectors and displays the resultant R Displays T of resultant vector ...

Page 233: ...LG mode Display Description 1 07 Sets R equal to 1 07 125 Sets T equal to 125 63 Sets P equal to 63 t C Calculates cross product and displays R of result Displays T of cross product Displays P of cross product t R Displays rectangular form of cross product The dot product can be used to resolve the force still in v2 along the axis of the lever Keys In ALG mode Display Description t P Starts polar ...

Page 234: ...o 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 Specifics regardin...

Page 235: ...ariable Checksum and length 35E7 21 Starts the input loop Prompts for and stores the variable addressed by i 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 51AB 15 This routine inverts a 3 3 matrix Calculates determinant and saves value for the division loop J Calculates E determinant AI CG Calculates F determinan...

Page 236: ...gram Lines In RPN mode Description Calculates H determinant BG AH Calculates I determinant AE BD Calculates A x determinant EI FH Calculates B determinant CH BI Calculates C determinant BF CE Stores B Calculates D determinant FG DI ...

Page 237: ...determinant Checksum and length 0FFB 222 This routine completes inverse by dividing by determinant Divides element Decrements index value so it points closer to A Loops for next value Returns to the calling program or to Checksum and length 1FCF 15 This routine multiplies a column matrix and a 3 3 matrix Sets index value to point to last element in first row Sets index value to point to last eleme...

Page 238: ... 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 Gets result back Stores result Displays result Returns to the calling program or to Checksum and length DFF4 54 This routine multiples and adds values within a row Gets next column value Sets index value to point to next row value Mul...

Page 239: ...e Description Calculates A E I Calculates A E I D H C Calculates A E I D H C G F B A E I D H C G F B G E C A E I D H C G F B G E C A F H A E I D H C G F B G E C A F H D B I Returns to the calling program or to Checksum and length 7957 75 Flags Used None ...

Page 240: ...s to see the value of Y then press 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 to store the determinant X through Z Output vector values also used for scratch i Loop control value index variable also used for scratch Remarks For 2 2 solutions use zero for coefficients C F H...

Page 241: ... 15 value Sets D equal to 15 Continues entry for E through L 14 Returns to first coefficient entered t I Calculates the inverse and displays the determinant t M Multiplies by column vector to compute X Calculates and displays Y Calculates and displays Z t A Begins review of the inverted matrix Displays next value Displays next value Displays next value Displays next value Displays next value ...

Page 242: ... 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 1 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 least one real root After one root is fou...

Page 243: ...s x2 J L x K M 0 x2 J L x K M 0 where J a3 2 K y0 2 L 0 2 2 y a J the sign of JK a1 2 M 0 2 a K Roots of the fourth degree polynomial are found by 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 ...

Page 244: ...lect root finding routine Starts root finding routine Checksum and length 588B 21 Evaluates polynomials using Horner s method and synthetically reduces the order of the polynomial using the root Uses pointer to polynomial as index Starting value for Horner s method Checksum and length 0072 24 Starts the Horner s method loop Saves synthetic division coefficient Multiplies current sum by next power ...

Page 245: ... order polynomial Generates DIVIDE BY 0 error if no real root found Checksum and length 15FE 54 Starts quadratic solution routine Exchanges a0 and a1 a1 2 a1 2 Saves a1 2 Stores real part if complex root a1 2 2 a0 a1 2 2 ao Initializes flag 0 Discriminant d 0 Sets flag 0 if d 0 complex roots d d Stores imaginary part if complex root Complex roots Returns if complex roots Calculates a1 2 d Calculat...

Page 246: ...polynomial on stack Discards polynomial function value Solves remaining second order polynomial and stores roots Displays real root of cubic Displays remaining roots Checksum and length 7A4B 33 Starts fifth 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 polyno...

Page 247: ...a0 a3 2 a1 2 Stores b0 a2 b2 a2 Stores b2 a3 a3 a1 4a0 b1 a3a1 4a0 Stores b1 To enter lines D0021 and D0022 press 4 º Î 3 Creates 7 004 as a pointer to the cubic coefficients 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 ...

Page 248: ...th order polynomial If not complex roots determine largest real root y0 Stores largest real root of cubic Checksum and length C8B3 180 Starts fourth order solution routine J a3 2 K y0 2 Creates 10 9 as a lower bound for M2 K K2 M2 K2 a0 If M2 10 9 use 0 for M2 M 0 2 a K Stores M J JK a1 a1 2 JK a1 2 Use 1 if JK a1 2 0 ...

Page 249: ...er polynomial J J L K K M Checksum and length 539D 171 Starts routine to calculate and display two roots Uses quadratic routine to calculate two roots Checksum and length 410A 6 Starts routine to display two real roots or two complex roots Gets the first real root Stores the first real root Displays real root or real part of complex root Gets the second real root or imaginary part of complex root ...

Page 250: ...ry part of the second complex root Displays the imaginary part of the second complex root Checksum and length 748D 24 Flags Used Flag 0 is used to remember if the root is real or complex that is to remember the sign of d If d is negative then flag 0 is set Flag 0 is tested later in the program to assure that both the real and imaginary parts are displayed if necessary Remarks The program accommoda...

Page 251: ...Key in the program routines press Å when done 3 Press t P to start the polynomial root finder 4 Key in F the order of the polynomial and press 5 At each prompt key in the coefficient and press You re not prompted for the highest order coefficient it s assumed to be 1 You must enter 0 for coefficients that are 0 Coefficient A must not be 0 Terms and Coefficients Order x5 x4 x3 x2 x Constant 5 1 E D...

Page 252: ...1 Find the roots of x5 x4 101x3 101x2 100x 100 0 Keys In RPN mode Display Description t P value Starts the polynomial root finder prompts for order 5 value Stores 5 in F prompts for E 1 z value Stores 1 in E prompts for D 101 z value Store 101 in D prompts for C 101 value Stores 101 in C prompts for B 100 value Stores 100 in B prompts for A 100 z Stores 100 in A calculates the first root Calculate...

Page 253: ...mpts for order 4 value Stores 4 in F prompts for D 8 z Ï 4 value Stores 8 4 in D prompts for C 13 z Ï 4 value Stores 13 4 in C prompts for B 10 z Ï 4 value Stores 10 4 in B prompts for A 22 Ï 4 Stores 22 4 in A calculates the first root Calculates the second root Displays the real part of the third root Displays the imaginary part of the third root Displays the real part of the fourth root Display...

Page 254: ...ates the second root Coordinate Transformations This program provides two dimensional coordinate translation and rotation The following formulas are used to convert a point 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 x m sinθ The inverse transformation is accomplished with the formulas below x u cos...

Page 255: ...Mathematics Programs 15 33 y y x x m n New coordinate system Old coordinate system 0 0 x P u y v θ ...

Page 256: ...X to the X register Pushes X and Y up and recalls N to the X register Pushes N X and Y up and recalls M Calculates X M and Y N Pushes X M and Y N up and recalls T Changes the sign of T because sin T equals sin T Sets radius to 1 for computation of cos T and sin T θ Calculates cos T and sin T in X and Y registers Calculates X M cos T Y N sin T and Y N cos T X M sin T Stores x coordinate in variable...

Page 257: ...ores the y coordinate in variable Y Swaps the positions of the coordinates back Halts the program to display X Halts the program to display Y Goes back for another calculation Checksum and length 8C82 66 Flags Used None Program Instructions 1 Key in the program routines press Å when done 2 Press t D to start the prompt sequence which defines the coordinate transformation 3 Key in the x coordinate ...

Page 258: ...her new to old transformation press and go to step 13 For an old to new transformation go to step 7 Variables Used M The x coordinate of the origin 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 of 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...

Page 259: ...ode Display Description Ý Sets Degrees mode since T is given in degrees t D value Starts the routine that defines the transformation 7 value Stores 7 in M 4 z value Stores 4 in U 27 Stores 27 in T t N value Starts the old to new routine 9 z value Stores 9 in X 7 Stores 7 in Y and calculates U Calculates V ...

Page 260: ...oblem 5 z Stores 5 in X 4 z Stores 4 in Y Calculates V Resumes the old to new routine for next problem 6 Stores 6 in X 8 Stores 8 in Y and calculates U Calculates V t O Starts the new to old routine 2 7 Stores 2 7 in U 3 6 z Stores 3 6 in V and calculates X Calculates Y ...

Page 261: ...e 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 regression functions of the HP 33s are used t...

Page 262: ... 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 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 in Precision of Data in chapter 11 ...

Page 263: ...X Clears flag 1 the indicator for ln Y Branches to common entry point Z Checksum and length F78E 27 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 293B 27 This routine sets the status for the power mod...

Page 264: ...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 C95E 57 Defines the beginning of the undo routine Recalls the most recent data pair Deletes this pair from the statistical accumulation Loops for another X Y pair Checksum and leng...

Page 265: ...changed stores y value in Y Adjusts index value to address the appropriate subroutine Calls subroutine to compute x Stores x in X for next loop Loops for another estimate Checksum and length 9B34 42 This subroutine calculates y for the straight line model Calculates y MX B Returns to the calling routine Checksum and length F321 15 This subroutine calculates x for the straight line model Restores i...

Page 266: ...e Calculates x e Y B M Returns to the calling routine Checksum and length 5117 21 This subroutine calculates y for the exponential model Calculates y BeMX Returns to the calling routine Checksum and length 1F92 18 This subroutine calculates x for the exponential model Restores index value to its original value Calculates x ln Y B M Returns to the calling routine Checksum and length CC13 21 This su...

Page 267: ...o the calling routine Checksum and length 3040 24 Flags Used Flag 0 is set if a natural log is required of the X input Flag 1 is set if a natural log is required of the Y input Program instructions 1 Key in the program routines press Å when done 2 Press t and select the type of curve you wish to fit by pressing S for a straight line L for a logarithmic curve E for an exponential curve or P for a p...

Page 268: ...d on x key in x at the value prompt then press to see y 11 If you wish to estimate x based on y press until you see the value prompt key in y then press to see x 12 For more estimations go to step 10 or 11 13 For a new case go to step 2 Variables Used B Regression coefficient y intercept of a straight line also used for scratch M Regression coefficient slope of a straight line R Correlation coeffi...

Page 269: ...Keys In RPN mode Display Description t S Starts straight line routine 40 5 value Enters x value of data pair 104 5 Enters y value of data pair 38 6 Enters x value of data pair 102 Enters y value of data pair Now intentionally enter 379 instead of 37 9 so that you can see how to correct incorrect entries Keys In RPN mode Display Description 379 Enters wrong x value of data pair Retrieves prompt t U...

Page 270: ...sion coefficient B Calculates regression coefficient M Prompts for hypothetical x value 37 Stores 37 in X and calculates y 101 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 starting execution label and the results the correlation and regression coefficients and the x and y estimates for...

Page 271: ... 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 upper tail area Q x This program also provides the inverse given a value Q x the program calculates the corresponding value x x y Upper tail area x Q x x x x x dx e x Q 2 2 2 1...

Page 272: ...sum and length D72F 48 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 X Checksum and length EA54 18 This routine calculates X given Q X Prompts for and stores Q X Recalls the mean Stores the mean as the guess for X called Xguess Checksum and length 79B9 12 This label...

Page 273: ...E12 63 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 Integrates the normal function using the dummy variable D π Calculates S π 2 Stores result temporarily for inverse routine Adds half the area under the curve since we integrated using the mean as the lower limi...

Page 274: ...s Computation time is significantly less with a lower number of displayed digits In routine Q the constant 0 5 may be replaced by 2 and You do not need to key in the inverse routine in routines I and T if you are not interested in the inverse capability Program Instructions 1 Key in the program routines press Å when done 2 Press t S 3 After the prompt for M key in the population mean and press If ...

Page 275: ...andard deviation default value of 1 T Variable used temporarily to pass the value S π 2 to the inverse program X Input value that defines the left side of the upper tail area Example 1 Your good friend informs you that your blind date has 3σ intelligence You interpret this to mean that this person is more intelligent than the local population except for people more than three standard deviations a...

Page 276: ...t the program may be rerun simply by pressing Keys In RPN mode Display Description Resumes program 2 Enters X value of 2 and calculates Q X 10000 Multiplies by the population for the revised estimate Example 2 The mean of a set of test scores is 55 The standard deviation is 15 3 Assuming that the standard normal curve adequately models the distribution what is the probability that a randomly selec...

Page 277: ...iption t I Starts the inverse routine 0 1 Stores 0 1 10 percent in Q X and calculates X Resumes the inverse routine 0 8 Stores 0 8 100 percent minus 20 percent in Q X and calculates X Grouped Standard Deviation The standard deviation of grouped data Sxy is the standard deviation of data points x1 x2 xn occurring at positive integer frequencies f1 f2 fn 1 2 2 f f f x f x S i i i i i i xg This progr...

Page 278: ...N Checksum and length EF85 24 Input statistical data points Stores data point in X Stores data point frequency in F Enters increment for N Recalls data point frequency fi Checksum and length 184C 30 Accumulate summations Stores index for register 28 Updates i f in register 28 i if x Stores index for register 29 Updates i if x in register 29 i 2 i f x Stores index for register 31 ...

Page 279: ...put Checksum and length 3080 117 Calculates statistics for grouped data Grouped standard deviation Displays grouped standard deviation Weighted mean Displays weighted mean Goes back for more points Checksum and length 7246 24 Undo data entry error Enters decrement for N Recalls last data frequency input Changes sign of fi Adjusts count and summations Checksum and length E469 33 Flags Used None ...

Page 280: ...o step 3 to enter the correct data 7 When the last data pair has been input press t G to calculate and display the grouped standard deviation 8 Press to display the weighted mean of the grouped data 9 To add additional data points press and continue at step 3 To start a new problem start at step 2 Variables Used X Data point F Data point frequency N Data pair counter S Grouped standard deviation M...

Page 281: ...ores 17 in F displays the counter Prompts for the second xi 8 Prompts for second fi 26 Displays the counter Prompts for the third xi 14 Prompts for the third fi 37 Displays the counter You erred by entering 14 instead of 13 for x3 Undo your error by executing routine U t U Removes the erroneous data displays the revised counter Prompts for new third xi 13 Prompts for the new third fi Displays the ...

Page 282: ...ounter Prompts for the fifth xi 22 Prompts for the fifth fi 73 Displays the counter Prompts for the sixth xi 37 Prompts for the sixth fi 115 Displays the counter t G Calculates and displays the grouped standard deviation sx of the six data points Calculates and displays weighted mean x Å Clears VIEW ...

Page 283: ... 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 sign while money that you pay has a negative sign Note that any problem can be viewed from two...

Page 284: ... º y 1 Ù h I 100 _ º Ã h N º h I Ù h F º y 1 Ù h I 100 º Ã h N Ù h B Ï Terminates the equation º Î hold Checksum and length Remarks The TVM equation requires that I must be non zero to avoid a error If you re solving for I and aren t sure of its current value press 1 e I before you begin the SOLVE calculation Û I The order in which you re prompted for values depends upon the variable you re solvin...

Page 285: ...the values of the four known variables as they are prompted for press after each value 5 When you press the last the value of the unknown variable is calculated and displayed 6 To calculate a new variable or recalculate the same variable using different data go back to step 2 SOLVE works effectively in this application without initial guesses Variables Used N The number of compounding periods I Th...

Page 286: ...2 Converts your annual interest rate input to the equivalent monthly rate value Stores 0 88 in I prompts for N 36 value Stores 36 in N prompts for F 0 value Stores 0 in F prompts for B 7250 Ï 1500 Ã Calculates B the beginning loan balance Stores 5750 in B calculates monthly payment P The answer is negative since the loan has been viewed from the borrower s perspective Money received by the borrowe...

Page 287: ...ns 36 in N prompts for F Retains 0 in F prompts for B Retains 5750 in B calculates monthly interest rate 12 Calculates annual interest rate Part 3 Using the calculated interest rate 6 75 assume that you sell the car after 2 years What balance will you still owe In other words what is the future balance in 2 years Note that the interest rate I from part 2 is not zero so you won t get a error when y...

Page 288: ...y 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 larger than the input The program identifies non prime numbers by exhaustively trying all possible factors If a number is not prime the program adds 2 as...

Page 289: ...Miscellaneous Programs and Equations 17 7 LBL Y VIEW Prime LBL Z P 2 x LBL P x P 3 D LBL X x 0 yes no Start no yes Note x is the value in the X register ...

Page 290: ...outine adds 2 to P Checksum and length 8696 21 This routine stores the input value for P Tests for even input Increments P if input an even number Stores 3 in test divisor D Checksum and length D0B8 87 This routine tests P to see if it is prime Finds the fractional part of P D Tests for a remainder of zero not prime If the number is not prime tries next possibility ...

Page 291: ...ksum and length 161E 57 Flags Used None Program Instructions 1 Key in the program routines press Å when done 2 Key in a positive integer greater than 3 3 Press t P to run program Prime number P will be displayed 4 To see the next prime number press 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 ensure that the input ...

Page 292: ...17 10 Miscellaneous Programs and Equations Keys In ALG mode Display Description 789 t P Calculates next prime number after 789 Calculates next prime number after 797 ...

Page 293: ...Part 3 Appendixes and Reference ...

Page 294: ......

Page 295: ... 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 Ý function page 1 18 Q How do l change the number of decimal places in the display A Use the Þ menu page 1 19 Q How do I clear all or portions of memory A displays the CLEAR menu whi...

Page 296: ...hing 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 É Environmental Limits To maintain product reliability observe the following temperature and humidity limits Operating temperature 0 to 45 C 32 to 113 F Storage temperature 20 to 65 C 4 to 149 F Operating and storage humidity 90 relative humidity at 40 C 104 F m...

Page 297: ...ery terminals handle batteries only by their edges 2 Make sure the calculator is OFF Do not press ON Å 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 Turn the calculator over and slide off the battery cover 4 Never remove two old batteries at the same time to prevent memory los...

Page 298: ...ration has been restored If your calculator requires service refer to page A 7 The calculator won t turn on steps 1 4 or doesn t respond when you press the keys steps 1 3 1 Reset the calculator Hold down the Å key and press It may be necessary to repeat these reset keystrokes several times 2 Erase memory Press and hold down Å then press and hold down both and Memory is cleared and the message is d...

Page 299: ... row and so on until you ve pressed Ù Then continue to press these keys in order _ Ý Ö Õ Û Ø Þ If you press the keys in the proper order and they are functioning properly the calculator displays 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 se...

Page 300: ...nable time to repair or replace any product to a condition as warranted you will be entitled to a refund of the purchase price upon prompt return of the product 4 HP products may contain remanufactured parts equivalent to new in performance or may have been subject to incidental use 5 Warranty does not apply to defects resulting from a improper or inadequate maintenance or calibration b software i...

Page 301: ...re set forth in the express warranty statements accompanying such products and services Nothing herein should be construed as constituting an additional warranty HP shall not be liable for technical and editorial errors or omissions contained herein FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND THE WARRANTY TERMS CONTAINED IN THIS STATEMENT EXCEPT TO THE EXTENT LAWFULLY PERMITTED DO NOT E...

Page 302: ...urg 32 2 7126219 Other European countries 420 5 41422523 Asia Pacific Country Telephone numbers Australia 61 3 9841 5211 Singapore 61 3 9841 5211 L America Country Telephone numbers Argentina 0 810 555 5520 Brazil Sao Paulo 3747 7799 ROTC 0 800 157751 Mexico Mx City 5258 9922 ROTC 01 800 472 6684 Venezuela 0800 4746 8368 Chile 800 360999 Columbia 9 800 114726 Peru 0 800 10111 Central America Carib...

Page 303: ...d television reception The calculator complies with the limits for a Class B digital device pursuant to Part 15 of the FCC Rules These limits are designed to provide reasonable protection against harmful interference in a residential installation However there is no guarantee that interference will not occur in a particular installation In the unlikely event that there is interference to radio or ...

Page 304: ...n この装置は情報処理装置等電波障害自主規制協議会 VCCI の基準に基づく第二情報技術装置ですこの装置は家庭環境で使用することを目的としていますがこの装置がラジオやテレビジョン受信機に近接して使用されると受信障害を引き起こすことがあります取扱説明書に従って正しい取り扱いをしてください Noise Declaration In the operator position under normal operation per ISO 7779 LpA 70dB ...

Page 305: ...n 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 any or all equations see Editing and Clearing Equations in chapter 6 Clear any or all programs see Clearing One or More...

Page 306: ...alculation that has been interrupted press º Ô This deallocation is done automatically whenever you execute a program or another SOLVE or FN calculation Resetting the Calculator If the calculator doesn t respond to keystrokes or if it is otherwise behaving unusually attempt to reset it Resetting the calculator halts the current calculation and cancels program entry digit entry a running program a ...

Page 307: ...old down the Å key 2 Press and hold down 3 Press You will be pressing three keys simultaneously When you release all three keys the display shows if the operation is successful Category CLEAR ALL MEMORY CLEAR Default Angular mode Unchanged Degrees Base mode Unchanged Decimal Contrast setting Unchanged Medium Decimal point Unchanged Denominator c value Unchanged 4095 Display format Unchanged FIX 4 ...

Page 308: ...ions except those in the following two lists will enable stack lift Disabling Operations The four operations ENTER Σ Σ and CLx disable stack lift A number keyed in after one of these disabling operations writes over the number currently in the X register The Y Z and T registers remain unchanged In addition when Å and act like CLx they also disable stack lift The INPUT function disables stack lift ...

Page 309: ...ARS PSE SHOW RADIX RADIX CLΣ Ä and STOP and Ø Å and u u r Ë Ë r Ë label nnnn EQN FDISP Errors and program entry Switching binary windows Digit entry Except when used like CLx Including all operations performed while the catalog is displayed except Ï and t which enable stack lift ...

Page 310: ...ACOSH ATANH IP FP SGN INTG RND ABS CHG Σ Σ RCL y x θ r θ r y x HR HMS DEG RAD nCr nPr 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 not affect the LAST X register The recall arithmetic sequence x h Ù variable stores a different value in the LAST X register than the sequence x h variable Ù does The former stores x in LAST X the latter stores the recalle...

Page 311: ...and 16 Entering statistical two variable data Press º Ú to set the calculator to ALG mode When the calculator is in ALG mode the ALG annunciator is on In ALG mode operations are performed in the following order 1 Expression in parenthesis 2 Function that require inputting values before pressing the function key for example COS SIN TAN ACOS ASIN ATAN LOG LN x2 1 x x π 3 x X CMPLX RND RAND IP FP INT...

Page 312: ...arithmetic Power functions Percentage calculations m or º p Permutations and Combinations x Quotient and Remainder of Division b º Simple Arithmetic Here are some examples of simple arithmetic In ALG mode you enter the first number press the operator Ù Ã enter the second number and finally press the Ï key To Calculate Press Display 12 3 12 Ù 3 Ï 12 3 12 Ã 3 Ï 12 3 12 3 Ï 12 3 12 3 Ï Power Function...

Page 313: ...ed with Ù or Ã it adds or subtracts percentages To Calculate Press Display 27 of 200 200 27 m Ï 200 less 27 200 Ã 27 m Ï 12 greater than 25 25 Ù 12 m Ï To Calculate Press x of y y x m Ï Percentage change from y to x y 0 y º p x Ï Compare these keystrokes in RPN and ALG modes RPN Mode ALG Mode 27 of 200 200 Ï 27 m 200 27 m Ï 200 less 27 200 Ï 27 m Ã 200 Ã 27 m Ï ...

Page 314: ...4 women and 10 men is forming a six person safety committee How many different combinations of people are possible Keys Display Description 24 x 6 Ï Total number of combinations possible Quotient and Remainder Of Division You can use b and º to produce either the quotient or remainder of division operations involving two integers Integer 1 b Integer 2 Integer 1 º Integer 2 Example To display the q...

Page 315: ...eys Display Description 30 º y 85 Ã No calculation is done 12 º Calculates 85 12 9 _ Calculates 30 73 Ï Calculates 30 85 12 9 You can omit the multiplication sign before a left parenthesis Implied multiplication is not available in Equation mode For example the expression 2 5 4 can be entered as 2 º y 5 Ã 4 º without the key inserted between 2 and the left parenthesis Chain Calculations To do a ch...

Page 316: ...s you key it in Keys Display 456 Ã 75 Ï 18 5 68 1 9 Ï Reviewing the Stack The or º key produces a menu in the display X1 X2 X3 X4 registers to let you review the entire contents of the stack The difference between the and the º key is the location of the underline in the display Pressing the º displays the underline on the X4 register pressing the displays the underline on the X2 register Pressing...

Page 317: ...tween rectangular and polar coordinates 1 Enter the coordinates in rectangular or polar form that you want to convert In ALG mode the order is y w x or θ w r 2 Execute the conversion you want press rectangular to polar or º polar to rectangular The converted coordinates occupy the X and Y registers 3 The resulting display the X register shows either r polar result or x rectangular result Press Ø t...

Page 318: ...se the required order of operations w 4 5 º Calculates x Ø Displays y Integrating an Equation 1 Key in an equation see Entering Equations into the Equation List in chapter 6 and leave Equation mode 2 Enter the limits of integration key in the lower limit and press w then key in the upper limit 3 Display the equation Press º d and if necessary scroll through the equation list press or Ø to display ...

Page 319: ...x Operations Use the complex operations as you do real operations but follow the imaginary part with c To do an operation with one complex number 1 Enter the complex number z Use parentheses for z if the real part exists 2 Select the complex function 3 Press Ï to calculate To do an arithmetic operation with two complex numbers 1 Enter the first complex number z1 Use parentheses for z if the real p...

Page 320: ...play Description º y 2 Ù 3 c º k Ø Result is 9 1545 i 4 1689 Examples Evaluate the expression z 1 z2 z3 where z1 23 i 13 z2 2 i z3 4 i 3 Keys Display Description º y 23 Ù 13 c º º y 2 z Ù 1 c Ù 4 Ã 3 c º Ï Real part of result Ø Result is 2 5000 i 9 0000 ...

Page 321: ...urrent expression in the first line does not fit in the display the rightmost digits are replaced with an ellipsis to indicate it is too long to be displayed Here are some examples of arithmetic in Hexadecimal Octal and Binary modes Example 12F16 E9A16 Keys Display Description Sets base 16 HEX annunciator on 12F Ù E9A Ï Result 77608 43268 Sets base 8 OCT annunciator on 7760 Ã 4326 Ï Converts displ...

Page 322: ...r an x y pair in reverse order y w x so that y ends up in the Y register and X in the X register 1 Press Σ to clear existing statistical data 2 Key in the y value first and press w 3 Key in the corresponding x value and press 4 The display shows n the number of statistical data pairs you have accumulated 5 Continue entering x y pairs n is updated with each entry Example Key in the x y values on th...

Page 323: ...w 400 Display shows n the number of data pairs you entered Í Brings back last x value Last y is still in Y register Deletes the last data pair 6 w 40 Reenters the last data pair 4 w 20 Deletes the first data pair 5 w 20 Reenters the first data pair There is still a total of two data pairs in the statistics registers ...

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Page 325: ... 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 search occurs SOLVE always fi...

Page 326: ...ituations 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 ...

Page 327: ...e 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 see the previous estimate of the root x which was left in the Y register Press again to see the value of f x which was left in the Z register...

Page 328: ...Initial guesses for the root º d Selects Equation mode displays the left end of the equation Û X Solves for X displays the result Final two estimates are the same to four decimal places 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 x2 x 6 0 Enter the equation as an expression Keys Display Description º d Select...

Page 329: ...tain 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 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 operat...

Page 330: ... of the equation IP x 1 5 Enter the equation Keys Display Description º d Selects Equation mode º h X º º Ð 1 5 Ï Enter the equation º Î Checksum and length Å Cancels Equation mode Now solve to find the root Keys Display Description 0 e X 5 _ Your initial guesses for the root º d Selects Equation mode displays the equation ...

Page 331: ...e 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 Find the root of the equation 0 1 6 2 x x As x approaches 6 f x becomes a very large positive or negative number Enter the equation as an expression Keys Display Description º d Selects Equation mode h X º y h X 2 Ã 6 º Ã 1 Ï ...

Page 332: ... below If the ending value of f x stored in the Z register is relatively close to zero it is possible that a root has been found the number stored in the unknown variable might be a 12 digit number very close to a theoretical root The search halts because SOLVE is working on a horizontal asymptote an area where f x is essentially constant for a wide range of x see figure b below The ending value o...

Page 333: ...Is Found Example A Relative Minimum Calculate the root of this parabolic equation x2 6x 13 0 It has a minimum at x 3 Enter the equation as an expression Keys Display Description º d Selects Equation mode h X 2 Ã 6 h X Ù 13 Ï Enters the equation º Î Checksum and length ...

Page 334: ...stimate of x º Î Previous estimate was not the same Final value for f x is relatively large Example An Asymptote Find the root of the equation 0 1 10 X Enter the equation as an expression Keys Display Description º d Selects Equation mode 10 Ã h X º Ï Enters the equation º Î Checksum and length Å Cancels Equation mode 005 e X 5 _ Your positive guesses for the root º d Selects Equation mode display...

Page 335: ...s the result Example Find the root of the equation 0 5 0 0 3 x x Enter the equation as an expression Keys Display Description º d Selects Equation mode h X º y h X Ù Ë 3 º º Ã Ë 5 Ï Enters the equation º Î Checksum and length Å Cancels Equation mode First attempt to find a positive root Keys Display Description 0 e X 10 _ Your positive guesses for the root º d Selects Equation mode displays the le...

Page 336: ...ve numerator causing a negative square root Keys Display Description 0 e X 10 z _ º d Selects Equation mode displays the left end of the equation Û X No root found for f x Å Clears error message cancels Equation mode º È 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 In RPN mode enter th...

Page 337: ...t 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 the answer 1 0000 due to round off error Round off error can also cause SOLVE to fail to find a root The equation 0 7 x2 has a root at 7 However no 12 digit number exactly equals 7 so the calculator can never ...

Page 338: ... 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 infinity anyway ...

Page 339: ...alculated 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 integral that is as accurate as is justified...

Page 340: ...mely 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 algorithm in the HP 33s is one of the best available in certain situations it like all other algori...

Page 341: ...eral 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 of the interval of integration at some iteration the algorithm will likely detect the fluctuation When this happens the number of sample points is increased until successive iterations yield approximations that take into account the ...

Page 342: ...escription Þ 3 0 Ï 499 _ Specifies accuracy level and limits of integration º d Selects Equation mode displays the equation º X Approximation of the integral The answer returned by the calculator is clearly incorrect since the actual integral of f x xe x from zero to is exactly 1 But the problem is not that was represented by 10499 since the actual integral of this function from zero to 10499 is v...

Page 343: ... problems such as this see the next topic Conditions That Prolong Calculation 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 ...

Page 344: ...than if they 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 ...

Page 345: ...tions over the subintervals Conditions That Prolong Calculation Time In the 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 v...

Page 346: ...dually in a predictable manner The algorithm 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 ...

Page 347: ...of integration includes mostly regions 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 integra...

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Page 349: ...nother integration calculation was running A running program attempted to solve a program while an integration calculation was running The catalog of variables u 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 verify clearing all programs in memory O...

Page 350: ...iable name when solving an equation Attempted a factorial or gamma operation with x as a negative integer 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 Attempted an operation with an indirect address but the number in the inde...

Page 351: ...r to handle The calculator returns 9 99999999999E499 in the current display format See Range of Numbers and Overflow on page 1 16 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 after the last line ...

Page 352: ...l 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 instruction is true Occurs only when executed from the keyboar...

Page 353: ...cters are alphabetized before all the letters function 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 z Changes the sign of a number 1 14 1 Ù Addition Returns y x 1 17 1 Ã Subtraction Returns y x 1 17 1 Multiplication Returns y x 1 17 1 Division Returns y x 1 17 1...

Page 354: ...3 12 9 12 18 Ö or Õ Scrolls the display to show more digits to the left and right displays the rest of an equation or binary number goes the next menu page in the CONST and SUMS menus 1 11 6 4 10 6 Goes to the top line of the equation or program list 6 3 Goes to the last line of the equation or program list 6 3 å Separates the two arguments of a function 6 5 2 1 x Reciprocal 1 17 1 10x Common expo...

Page 355: ...e sum of squares of x values 11 10 1 Σxy º Returns the sum of products of x and y values 11 10 1 Σy º Returns the sum of y values 11 10 1 Σy2 º Returns the sum of squares of y values 11 10 1 σx º σ Returns population standard deviation of x values n x xi 2 11 6 1 σy º σ Returns population standard deviation of y values n y yi 2 11 6 1 θ r y x º Polar to rectangular coordinates Converts r θ to x y ...

Page 356: ...ted with a function in an equation 6 6 2 º Close parenthesis Ends a quantity associated with a function in an equation 6 6 2 A through Z h variable or e variable Value of named variable 6 4 2 ABS Absolute value Returns x 4 16 1 ACOS l Arc cosine Returns cos 1x 4 4 1 ACOSH l Hyperbolic arc cosine Returns cosh 1 x 4 6 1 º Ú Activates Algebraic mode 1 10 ALOG Common exponential Returns 10 raised to t...

Page 357: ...10 1 BIN Selects Binary base 2 mode 10 1 Å Turns 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 4 1 9 1 24 6 3 12 6 12 17 c º Ê Denominator Sets denominator limit for displayed fractions to x If x 1 displays current c value 5 5 C Converts F to C 4 13 1 CB Cub...

Page 358: ...n Program mode 12 20 Clears the displayed equation calculator in Program mode 12 6 CLΣ Clears statistics registers 11 11 CLVARS Clears all variables to zero 3 4 CLx Clears x the X register to zero 2 2 2 6 12 6 CM Converts inches to centimeters 4 13 1 c Displays the CMPLX_ prefix for complex functions 9 2 CMPLX c z Complex change sign Returns zx i zy 9 2 CMPLX c Ù Complex addition Returns z1x i z1y...

Page 359: ...COS c n Complex cosine Returns cos zx i zy 9 2 CMPLXex c Complex natural exponential Returns iz z y x e 9 2 CMPLXLN c Complex natural log Returns log e zx i zy 9 2 CMPLXSIN c k Complex sine Returns sin zx i zy 9 2 CMPLXTAN c q Complex tangent Returns tan zx i zy 9 2 CMPLXyx c Complex power Returns iz z 1y 1x 2y 2x iz z 9 2 Cn r x Combinations of n items taken r at a time Returns n r n r 4 14 2 COS...

Page 360: ...ariable 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 result fff final value skips the next program line 13 18 Begins entry of exponents and adds E to the number being entered Indicates that a power of 10 follows 1 14 1 ENG n Þ n Selects Engineering display with n digits following the first d...

Page 361: ...d Activates or cancels 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 15 2 F º Converts C to F 4 13 1 É Turns on and off Fraction display mode 5 1 FIX n Þ n Selects Fixed display with n decimal places 0 n 11 1 19 º Displays the menu to set clear and test flags 13 11 FN label º s lab...

Page 362: ...of program label in program memory 13 4 13 17 r Ë label nnnn Sets program pointer to line nnnn of program label 12 19 r Ë Ë Sets program pointer to PRGM TOP 12 19 HEX Selects Hexadecimal base 16 mode 10 1 Displays the HYP_ prefix for hyperbolic functions 4 6 HMS º Hours to hours minutes seconds Converts x from a decimal fraction to hours minutes seconds format 4 12 1 HR Hours minutes seconds to ho...

Page 363: ...t integer equal to or less than given number 4 16 1 INPUT variable Ç variable Recalls the variable to the X register displays the variable s name and value and halts program execution Pressing to resume program execution or Ø to execute the current program line stores your input in the variable Used only in programs 12 11 INV Reciprocal of argument 6 15 2 IP º Integer part of x 4 16 1 ISG variable...

Page 364: ...XEQ GTO or FN operations Used only in programs 12 3 LN Natural logarithm Returns log e x 4 1 1 LOG Common logarithm Returns log10 x 4 1 1 º Displays menu for linear regression 11 4 m º Returns the slope of the regression line Σ xi x yj y Σ xi x 2 11 7 1 u Displays the amount of available memory and the catalog menu 1 24 u Begins catalog of programs 12 20 u Begins catalog of variables 3 3 Ý Display...

Page 365: ...display x variable or equation then resumes Used only in programs 12 16 12 17 r º Returns the correlation coefficient between the x and y values 2 2 y y x x y y x x i i i i 11 7 1 RAD Ý Selects Radians angular mode 4 4 RAD º µ Degrees to radians Returns 2π 360 x 4 13 1 RADIX Ý Selects the comma as the radix mark decimal point 1 18 RADIX Ý Selects the period as the radix mark decimal point 1 18 RAN...

Page 366: ...involving two integers 6 15 2 RND f 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 16 5 7 1 ä Activates Reverse Polish notation 1 10 RTN º Ô Return Marks the end of a program the program pointer returns to the top or to the calling routine 12 3 13 2 R Rol...

Page 367: ...rough 11 1 19 SEED º Restarts the random number sequence with the seed x 4 14 SF n n Sets flag n n 0 through 11 13 11 SGN º a Indicates the sign of x 4 16 1 º Î Shows the full mantissa all 12 digits of x or the number in the current program line displays hex checksum and decimal byte length for equations and programs 6 18 12 21 SIN k Sine Returns sin x 4 3 1 SINH k Hyperbolic sine Returns sinh x 4...

Page 368: ...le 3 4 STO variable e Ã variable Stores variable x into variable 3 4 STO variable e variable Stores variable x into variable 3 4 STO variable e variable Stores variable x into variable 3 4 STOP Run stop Begins program execution at the current program line stops a running program and displays the X register 12 17 º Displays the summation menu 11 4 sx º Returns sample standard deviation of x values ...

Page 369: ...s the displayed equation 6 12 XEQ label t label Executes the program identified by label 13 2 x2 Square of x 4 2 1 x3 Cube of x 4 2 1 x Square root of x 4 2 1 3 x Cube root of x 4 2 1 X y The xth root of y 4 2 1 x º Returns the mean of x values Σ xi n 11 4 1 x º Given a y value in the X register returns the x estimate based on the regression line x y b m 11 10 1 x Factorial or gamma Returns x x 1 ...

Page 370: ...rison tests menu 13 7 x y If x y executes next program line if x y skips next program line 13 7 x y If x y executes next program line if x y skips next program line 13 7 x y If x y executes next program line if x y skips next program line 13 7 x y If x y executes next program line if x y skips next program line 13 7 x y If x y executes next program line if x y skips next program line 13 7 x y If x...

Page 371: ...t program line 13 7 x 0 º If x 0 executes next program line if x 0 skips next program line 13 7 x 0 º If x 0 executes next program line if x 0 skips next program line 13 7 x 0 º If x 0 executes next program line if x 0 skips next program lire 13 7 y º Returns the mean of y values Σyi n 11 4 1 y º Given an x value in the X register returns the y estimate based on the regression line y m x b 11 10 1...

Page 372: ...G 20 Operation Index Name Keys and Description Page yx Power Returns y raised to the xth power 4 2 1 Notes 1 Function can be used in equations 2 Function appears only in equations ...

Page 373: ... 22 ALG 1 10 compared to equations 12 4 in programs 12 4 Algebraic mode 1 10 ALL format See display format in equations 6 5 in programs 12 6 setting 1 20 alpha characters 1 3 angles between vectors 15 1 converting format 4 13 converting units 4 13 implied units 4 4 A 2 angular mode 4 4 A 2 B 3 annunciators alpha 1 3 battery 1 1 A 2 descriptions 1 11 flags 13 11 list of 1 7 low power 1 1 A 2 shift ...

Page 374: ... numbers arithmetic 10 2 converting to 10 1 range of 10 5 scrolling 10 6 typing 10 1 viewing all digits 3 3 10 6 borrower finance 17 1 branching 13 2 13 16 14 7 C CHG arguments 4 7 Å adjusting contrast 1 1 canceling prompts 1 5 6 13 12 13 canceling VIEW 3 3 clearing messages 1 5 F 1 clearing X register 2 2 2 6 interrupting programs 12 17 leaving catalogs 1 5 3 3 leaving Equation mode 6 3 6 4 leavi...

Page 375: ...conditional tests 13 6 13 7 13 8 13 11 13 17 constant filling stack 2 6 Continuous Memory 1 1 contrast adjustment 1 1 conversion functions 4 9 conversions angle format 4 13 angle units 4 13 coordinates 4 9 9 5 15 1 length units 4 13 mass units 4 13 number bases 10 1 temperature units 4 13 time format 4 12 volume units 4 13 coordinates converting 4 5 4 9 15 1 transforming 15 32 correlation coeffici...

Page 376: ...quation list 6 4 6 6 in Program mode 12 6 EQN LIST TOP 6 7 F 1 equality equations 6 9 6 10 7 1 equation list adding to 6 4 displaying 6 6 editing 6 8 EQN annunciator 6 4 in Equation mode 6 3 operation summary 6 3 Equation mode backspacing 1 5 6 8 during program entry 12 6 leaving 1 5 6 3 shows equation list 6 3 starting 6 3 6 6 equation entry cursor backspacing 1 5 6 8 12 19 operation 6 5 equation...

Page 377: ... 1 variables in 6 3 7 1 with i 13 24 error messages F 1 errors clearing 1 5 correcting 2 7 F 1 estimation statistical 11 7 16 1 executing programs 12 9 exponential curve fitting 16 1 exponential functions 1 15 4 1 9 3 exponents of ten 1 14 1 15 expression equations 6 9 6 10 7 1 F FN See integration É not programmable 5 9 toggles display mode 1 23 5 1 A 2 toggles flag 13 9 factorial function 4 14 f...

Page 378: ...t of G 1 names in display 4 17 12 7 nonprogrammable 12 22 one number 1 17 2 8 9 2 real number 4 1 two number 1 17 2 8 9 3 future balance finance 17 1 G r finds PRGM TOP 12 5 12 19 13 6 finds program labels 12 9 12 19 13 5 finds program lines 12 18 12 19 13 5 gamma function 4 14 go to See GTO grads angle units 4 4 A 2 Grandma Hinkle 11 7 Greatest integer 4 16 grouped standard deviation 16 17 GTO 13...

Page 379: ...f result 8 2 8 5 8 6 E 2 using 8 2 C 8 variable of 8 2 C 8 intercept curve fit 11 7 16 1 interest finance 17 3 intermediate results 2 11 inverse function 1 17 9 3 inverse hyperbolic functions 4 6 inverse trigonometric functions 4 4 inverse normal distribution 16 11 ISG 13 18 K keys alpha 1 3 letters 1 3 shifted 1 3 L LAST X register 2 7 B 6 LASTx function 2 7 lender finance 17 1 length conversions...

Page 380: ...s example of using 1 9 general operation 1 7 leaving 1 5 1 9 list of 1 7 messages clearing 1 5 1 23 displaying 12 14 12 16 in equations 12 14 responding to 1 23 F 1 summary of F 1 minimum of function D 8 modes See angular mode base mode Equation mode Fraction display mode Program entry mode MODES menu angular mode 4 4 setting radix 1 18 money finance 17 1 N negative numbers 1 14 9 3 10 4 nested ro...

Page 381: ... 3 10 5 setting response 13 9 F 3 testing occurrence 13 9 P π A 2 parentheses in arithmetic 2 11 in equations 6 5 6 6 6 14 pause See PSE payment finance 17 1 percentage functions 4 6 periods in numbers 1 18 A 1 permutations 4 14 Physics constants 4 8 polar to rectangular coordinate conversion 4 10 9 5 15 1 poles of functions D 5 polynomials 12 23 15 20 population standard deviations 11 6 power ann...

Page 382: ... deleting 1 24 deleting all 1 6 deleting equations 12 6 12 18 deleting lines 12 18 designing 12 3 13 1 editing 1 5 12 6 12 18 editing equations 12 6 12 18 entering 12 5 equation evaluation 13 10 equation prompting 13 10 equations in 12 4 12 6 errors in 12 17 executing 12 9 flags 13 8 13 11 for integration 14 7 for SOLVE 14 1 D 1 fractions with 5 8 12 13 13 9 functions not allowed 12 22 indirect ad...

Page 383: ...2 14 8 stopping SOLVE 7 7 14 1 R and R 2 3 C 6 radians angle unit 4 4 angle units A 2 converting to degrees 4 13 radix mark 1 18 A 1 random numbers 4 14 B 3 RCL 3 2 12 12 RCL arithmetic 3 5 B 6 real numbers integration with 8 1 operations 4 1 SOLVE with 14 2 real part complex numbers 9 1 9 2 recall arithmetic 3 5 B 6 rectangular to polar coordinate conversion 4 10 9 5 15 1 regression linear 11 7 1...

Page 384: ...ys 1 3 sign of numbers 1 14 1 17 9 3 10 4 sign conventions finance 17 1 Sign value 4 16 simultaneous equations 15 12 sine trig 4 4 9 3 A 2 single step execution 12 9 slope curve fit 11 7 16 1 SOLVE asymptotes D 8 base mode 12 22 14 11 checking results 7 6 D 3 discontinuity D 5 evaluating equations 7 1 7 6 evaluating programs 14 1 flat regions D 8 how it works 7 5 D 1 in programs 14 6 initial guess...

Page 385: ...earing 1 6 11 2 correcting 11 2 entering 11 1 initializing 11 2 one variable 11 2 precision 11 9 sums of variables 11 10 two variable 11 2 statistics calculating 11 4 curve fitting 11 8 16 1 distributions 16 11 grouped data 16 17 one variable data 11 2 operations 11 1 two variable data 11 2 statistics menus 11 1 11 4 statistics registers See statistical data accessing 11 11 clearing 1 6 11 2 11 11...

Page 386: ...es 3 1 number storage 3 1 of integration 8 2 14 7 C 8 polynomials 12 23 program input 12 12 program output 12 13 12 16 recalling 3 2 3 3 separate from stack 3 2 showing all digits 3 3 12 13 solving for 7 1 14 1 14 6 D 1 storing 3 2 storing from equation 6 11 typing name 1 3 viewing 3 3 12 13 12 16 vectors application program 15 1 coordinate conversions 4 11 9 6 15 1 operations 15 1 VIEW displaying...

Page 387: ...Index 15 clearing in programs 12 6 displayed 2 2 during programs pause 12 17 exchanging with variables 3 6 exchanging with Y 2 4 not clearing 2 5 part of stack 2 1 testing 13 7 unaffected by VIEW 12 14 ...

Page 388: ...ies are delivered with this product when empty do not throw them away but collect 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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