HP 35s HP 35s scientific calculator - User Guide
HP 35s - Scientific Calculator Manual
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- HP 35s | HP 35s scientific calculator - User Guide - Page 1
HP 35s scientific calculator user's guide H Edition 1 HP part number F2215AA-90001 - HP 35s | HP 35s scientific calculator - User Guide - Page 2
Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF - HP 35s | HP 35s scientific calculator - User Guide - Page 3
Shifted Keys 1-2 Alpha Keys 1-3 Cursor Keys 1-3 Backspacing and Clearing 1-4 Using Menus 1-6 Exiting Menus 1-8 RPN and ALG Modes 1-9 Undo key 1-11 The Display and Annunciators 1-12 Keying in Numbers 1-15 Making Numbers Negative 1-15 Exponents of Ten 1-15 Understanding Entry Cursor 1-17 - HP 35s | HP 35s scientific calculator - User Guide - Page 4
Complex number display format 1-24 SHOWing Full 12-Digit Precision 1-25 Fractions 1-26 Entering Fractions 1-26 Messages 1-27 Calculator Memory 1-28 Checking Available Memory 1-28 Clearing All of Memory 1-29 2. RPN: The Automatic Memory Stack 2-1 What the Stack Is 2-1 The X and Y-Registers - HP 35s | HP 35s scientific calculator - User Guide - Page 5
Trigonometry 4-3 Entering 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 4-10 Rectangular/Polar Conversions 4-10 Time Conversions 4-13 Angle Conversions 4-13 Unit Conversions 4-14 - HP 35s | HP 35s scientific calculator - User Guide - Page 6
Entering Equations into the Equation List 6-4 Variables in Equations 6-4 Numbers in Equations 6-5 Functions in Equations 6-5 Parentheses in Equations 6-6 Displaying and Selecting Equations 6-6 Editing and Clearing Equations 6-8 Types of Equations 6-9 Evaluating Equations 6-10 Using ENTER - HP 35s | HP 35s scientific calculator - User Guide - Page 7
of Integration 8-6 Specifying Accuracy 8-6 Interpreting Accuracy 8-6 For More Information 8-8 9. Operations with Complex Numbers 9-1 The Complex Stack 9-2 Complex Operations 9-2 Using Complex Numbers in Polar Notation 9-5 Complex Numbers in Equations 9-7 Complex Number in Program 9-8 10 - HP 35s | HP 35s scientific calculator - User Guide - Page 8
Binary Numbers 11-8 Using base in program and equations 11-8 12.Statistical Operations 12-1 Entering Statistical Data 12-1 Entering One-Variable Data 12-2 Entering Two-Variable Data 12-2 Correcting Errors in Data Entry 12-2 Statistical Calculations 12-4 Mean 12-4 Sample Standard Deviation - HP 35s | HP 35s scientific calculator - User Guide - Page 9
13-3 Selecting a Mode 13-3 Program Boundaries (LBL and RTN 13-4 Using RPN, ALG and Equations in Programs 13-4 Data Input and Output 13-5 Entering a Program 13-6 Clear functions and backspace key 13-7 Function Names in Programs 13-8 Running a Program 13-10 Executing a Program (XEQ 13-10 - HP 35s | HP 35s scientific calculator - User Guide - Page 10
14-2 Branching (GTO 14-4 A Programmed GTO Instruction 14-5 Using GTO from the Keyboard 14-5 Conditional Instructions 14-6 Tests of Comparison (x?y, x?0 14-7 Flags 14-9 Loops 14-16 Conditional Loops (GTO 14-17 Loops with Counters (DSE, ISG 14-18 Indirectly Addressing Variables and Labels 14 - HP 35s | HP 35s scientific calculator - User Guide - Page 11
16-11 Grouped Standard Deviation 16-18 17.Miscellaneous Programs and Equations 17-1 Time Value of Money 17-1 Prime Number Generator 17-7 Cross Product in Vectors 17-11 Part 3. Appendixes and Reference A. Support, Batteries, and Service A-1 Calculator Support A-1 Answers to Common - HP 35s | HP 35s scientific calculator - User Guide - Page 12
Parentheses Calculations C-4 Exponential and Logarithmic Functions C-5 Trigonometric Functions C-6 Hyperbolic functions C-6 Parts of numbers C-7 Reviewing the Stack C-7 Integrating an Equation C-8 Operations with Complex Numbers C-8 Arithmetic in Bases 2, 8, and 16 C-10 Entering Statistical - HP 35s | HP 35s scientific calculator - User Guide - Page 13
Interpreting Results D-3 When SOLVE Cannot Find a Root D-8 Round-Off Error D-13 E. More about Integration E-1 How the Integral Is Evaluated E-1 Conditions That Could Cause Incorrect Results E-2 Conditions That Prolong Calculation Time E-7 F. Messages F-1 G. Operation Index G-1 Contents 11 - HP 35s | HP 35s scientific calculator - User Guide - Page 14
12 Contents - HP 35s | HP 35s scientific calculator - User Guide - Page 15
Basic Operation Part 1 - HP 35s | HP 35s scientific calculator - User Guide - Page 16
- HP 35s | HP 35s scientific calculator - User Guide - Page 17
margin. It identifies examples or keystrokes that are shown in RPN mode and must be performed differently in ALG mode. Appendix C explains how to use your calculator in ALG mode. Important Preliminaries Turning the Calculator On and Off To turn the calculator on, press . ON is printed on the bottom - HP 35s | HP 35s scientific calculator - User Guide - Page 18
a right-shifted function (blue). The shifted function names are printed in yellow above and in blue on the bottom of each key. Press the appropriate shift key ( or ) before pressing the key for the desired function. For example, to turn the calculator off, press and release the shift key, then - HP 35s | HP 35s scientific calculator - User Guide - Page 19
a letter in their bottom right corner, 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 t he alpha keys are "active". Variables are covered in chapter 3; labels are covered in chapter 13 - HP 35s | HP 35s scientific calculator - User Guide - Page 20
the entire equation. Program-entry mode: If a program line is in the process of being entered or edited, erases the character to the left of the insert cursor; otherwise, if the program line has been entered, deletes the entire line. Clear or Cancel. Clears the displayed number to zero or - HP 35s | HP 35s scientific calculator - User Guide - Page 21
contains options for clearing x (the number in the X-register), all direct variables, all of memory, all statistical data, all stacks and indirect variables. If you press a new menu is displayed so you can verify your decision before erasing everything in memory. During program entry is replaced - HP 35s | HP 35s scientific calculator - User Guide - Page 22
; weighted mean of statistical x-values Sample standard deviation, population standard deviation. Menu to access the values of 41 physics constants- refer to "Physics constants" on page 4-8. Statistical data summations. Base conversions (decimal, hexadecimal, octal, and binary). Sign value - HP 35s | HP 35s scientific calculator - User Guide - Page 23
memory available); catalog of variables; catalog of programs (program labels 14 14 1, 3, 12 4, 1 Angular modes and operation mode 1 Fixed, scientific, engineering, full floating point numerical display formats; radix symbol options (. or ,); complex number display format (in RPN mode - HP 35s | HP 35s scientific calculator - User Guide - Page 24
: In this example, we use the DISPLAY menu to fix the display of numbers to 4 decimal places and then compute 6÷7. The example closes using the DISPLAY menu to return to full floating point display of numbers. Keys: 8 or 8 Display Description: Initial display Enter the DISPLAY menu The - HP 35s | HP 35s scientific calculator - User Guide - Page 25
; hence, you do not have to use parentheses. In Algebraic mode (ALG), you perform arithmetic operations using the standard order of operations. To select RPN mode: Press 9 to set the calculator to RPN mode. When the calculator is in RPN mode, the RPN annunciator is on. Getting Started 1-9 - HP 35s | HP 35s scientific calculator - User Guide - Page 26
To select ALG mode: Press 9 to set the calculator to ALG 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 key, enter the second number, and finally press the arithmetic operator - HP 35s | HP 35s scientific calculator - User Guide - Page 27
that you just deleted using an expression you were editing but cleared using a character in an equation or program that you just deleted using (while in equation or program mode) Please note also that the Undo operation is limited by the amount of available memory. Getting Started 1-11 - HP 35s | HP 35s scientific calculator - User Guide - Page 28
and annunciators. Entries with more than 14 characters will scroll to the left. During input, the entry is displayed in the first line in ALG mode and the second line in RPN mode. Every calculation is displayed in up to 14 digits, including an sign (exponent), and exponent value up to three digits - HP 35s | HP 35s scientific calculator - User Guide - Page 29
Annunciator RPN ALG PRGM EQN 0 1 2 3 4 RAD or GRAD HEX OCT BIN HYP HP 35s Annunciators Meaning The " (Busy)" annunciator appears while an operation, equation, or program is executing. When in Fraction-display mode (press ), only one of the " " or " " halves of the " "' annunciator will be - HP 35s | HP 35s scientific calculator - User Guide - Page 30
keys are active for stepping through an equation list, a catalog of variables, lines of a program, menu pages, or programs in the program catalog. 1, 6, 13 The alphabetic keys are active. 3 Attention! Indicates a special condition or an 1 error. Battery power is low. A 1-14 Getting Started - HP 35s | HP 35s scientific calculator - User Guide - Page 31
the exponent of 10. Thus 4.2x10-5 is entered and displayed as 4.2E-5. A number whose magnitude is too large or too small for the display format will automatically be displayed in exponential form. For example, in FIX 4 format for four decimal places, observe the effect of the following keystrokes - HP 35s | HP 35s scientific calculator - User Guide - Page 32
Description: Shows number being entered. Rounds number to fit the display format. Automatically uses scientific notation because otherwise no significant digits would appear. Keying in Powers of Ten The key is used to enter powers of ten quickly. For example, instead of entering one million - HP 35s | HP 35s scientific calculator - User Guide - Page 33
terminated (no cursor), acts like and clears the entire number. Try it! Range of Numbers and OVERFLOW The smallest number available on the calculator is -9.99999999999 × 10499,while the largest number is 9.99999999999 × 10499. If a calculation produces a result that exceeds the largest possible - HP 35s | HP 35s scientific calculator - User Guide - Page 34
Operations Some of the numerical operations of the HP 35s require a single number for input, such as and k. These single argument operations are entered differently, depending on whether the calculator is in RPN or ALG mode. In RPN mode, the number is entered first and then the operation is applied - HP 35s | HP 35s scientific calculator - User Guide - Page 35
Example: Calculate 3.42, first in RPN mode and then in ALG mode. Keys: 9 9 Display: Description: Enter RPN mode (if necessary) Enter the number Press the square operator Switch to ALG mode Enter the square operation Insert the number between the parentheses Press the Enter - HP 35s | HP 35s scientific calculator - User Guide - Page 36
Example Calculate 2+3 and 6C4, first in RPN mode and then in ALG mode. Keys: 9 x 9 x Õ Display: _ Description: Switch to RPN mode (if necessary) Enter 2, then place 3 in the x-register. Note the flashing cursor after the 3; don't press Enter! Press the addition key to - HP 35s | HP 35s scientific calculator - User Guide - Page 37
or . 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 (1011) or too small (10-11) to display in the current decimal-place setting will automatically be displayed in scientific format - HP 35s | HP 35s scientific calculator - User Guide - Page 38
the prompt type in the number of decimal places to be displayed. For 10 or 11 places, press or . (The mantissa part of the number will always be less than 10.) For example, in the number the "2", "3", "4", and "6" are the decimal digits you see when the calculator is set to SCI 4 display mode - HP 35s | HP 35s scientific calculator - User Guide - Page 39
illustrates the behavior of the Engineering format using the number 12.346E4. It also shows the use of the @ and 2 functions. This example uses RPN mode. Keys: 8 ) or 2 @ 2 Display: _ Description: Choose Engineering format Enter 4 (for 4 significant digits after the 1st - HP 35s | HP 35s scientific calculator - User Guide - Page 40
Example Enter the number 12,345,678.90 and change the decimal point to the comma. Then choose to have no thousand separator. Finally, return to the default settings. This example uses RPN mode. Keys: 8 ) 8() 8 ) 8 8 ) Display: Description: Select full floating point - HP 35s | HP 35s scientific calculator - User Guide - Page 41
Description: Enable ALG mode Enter the complex number. It displays as 3i4, the default format. Change to x+yi format. Change to rθ a format. The radius is 5 and the angle is approximately 53.13°. SHOWing Full 12-Digit Precision Changing the number of displayed decimal places affects what you - HP 35s | HP 35s scientific calculator - User Guide - Page 42
full precision until you release Fractions The HP 35s allows you to enter and operate on fractions, displaying them as either decimals or fractions. The HP 35s displays fractions in the form a b/c, where a is an integer and both b and c are counting numbers. In addition, b is such that 0≤b - HP 35s | HP 35s scientific calculator - User Guide - Page 43
example uses RPN mode. Keys: É Display Description: The decimal point is interpreted in the normal way. When is pressed the 2nd time, the display switches to fraction mode. Upon entry, the number is displayed using the current display format. Switch to fraction display mode. Enter - HP 35s | HP 35s scientific calculator - User Guide - Page 44
". Calculator Memory The HP 35s has 30KB of memory in which you can store any combination of data (variables, equations, or program lines). Checking Available Memory Pressing displays the following menu: Where is the amount of used indirect variables is the number of bytes of memory - HP 35s | HP 35s scientific calculator - User Guide - Page 45
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 clear settings as well as data, see "Clearing Memory" in appendix B.) To clear all of memory: 1. Press You will then see the confirmation prompt which - HP 35s | HP 35s scientific calculator - User Guide - Page 46
1-30 Getting Started - HP 35s | HP 35s scientific calculator - User Guide - Page 47
manipulate and organize data for programs. What the Stack Is Automatic storage of intermediate results is the reason that the HP 35s easily processes complex calculations, and does so without parentheses. The key to automatic storage is the automatic, RPN memory stack. HP's operating logic is based - HP 35s | HP 35s scientific calculator - User Guide - Page 48
2 and part 3 will be null in this case. A complex number or a 2-D vector will occupy part 1 and part 2; part 3 will be null in this case. A 3-D vector will occupy part 1, part 2, and part 3. In programming, the stack is used to perform calculations, to temporarily store intermediate results, to pass - HP 35s | HP 35s scientific calculator - User Guide - Page 49
. 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 key, in contrast, is context-sensitive. It either clears or cancels the current display - HP 35s | HP 35s scientific calculator - User Guide - Page 50
contents are displayed. R calculate this expression from left-to-right are: Note Understand 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. 2-4 RPN: The Automatic Memory - HP 35s | HP 35s scientific calculator - User Guide - Page 51
movements of the stack, you do not need to clear the X-register before doing a new calculation. Most functions prepare the stack to lift its contents when the next number enters the X-register. See appendix B for lists of functions that disable stack lift. RPN: The Automatic Memory Stack 2-5 - HP 35s | HP 35s scientific calculator - User Guide - Page 52
is simply to separate two sequentially entered numbers. You can use the replicating effect of to clear the stack quickly: press 0 . All stack registers now contain zero. Note, however, that you don't need to clear the stack before doing calculations. Using a Number Twice in a Row You can use - HP 35s | HP 35s scientific calculator - User Guide - Page 53
Press 2. Press 3. Press Mainly used during program entry.) 4. Press to clear the X-, Y-, Z-, and T-registers to zero. For example, if you intended to enter 1 and 3 but mistakenly entered 1 and 2, this is what you should do to correct your error: RPN: The Automatic Memory Stack 2-7 - HP 35s | HP 35s scientific calculator - User Guide - Page 54
or numbers, such as .) Pressing returns this value into the X-register. This ability to retrieve the "last x" has two main uses: 1. Correcting errors. 2. Reusing a number in a calculation. See appendix B for a comprehensive list of the functions that save x in the LAST X register. 2-8 RPN: The - HP 35s | HP 35s scientific calculator - User Guide - Page 55
number, key in the correct one and execute the function. If you had used the wrong first number, key in the correct first number, press to recover the second number, and execute the function again. (Press first if you want to clear the incorrect result from the stack.) RPN: The Automatic Memory - HP 35s | HP 35s scientific calculator - User Guide - Page 56
) 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 . Example: Calculate 96.704 + 52.3947 52.3947 2-10 RPN: The Automatic Memory Stack - HP 35s | HP 35s scientific calculator - User Guide - Page 57
Keys: Display Description: Enters first number. Intermediate result. Brings back display from before . Final result. Example: Two close stellar neighbors of Earth are Rigel yr × (9.5 × 1015 m/yr). To Sirius: 8.7 yr × (9.5 × 1015 m/yr). RPN: The Automatic Memory Stack 2-11 - HP 35s | HP 35s scientific calculator - User Guide - Page 58
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 Evaluate the expression in the same way on the HP 35s, starting inside the parentheses. Keys: Display: Description - HP 35s | HP 35s scientific calculator - User Guide - Page 59
results to get the answer. Work through the problem the same way with the HP 35s, except that you don't have to write down intermediate answers-the calculator remembers them for you. Keys: Display Description: First adds (3+4) Then adds (5+6) RPN: The Automatic Memory Stack 2-13 - HP 35s | HP 35s scientific calculator - User Guide - Page 60
) × 4] = 0.2500 Solution: or 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: 2-14 RPN: The Automatic Memory Stack - HP 35s | HP 35s scientific calculator - User Guide - Page 61
example, when solved left-to-right, needed all registers in the stack at one point: Keys: Display _ Description: Saves 4 and 14 as intermediate numbers in the stack. At this point the stack is full with numbers for this calculation. Intermediate result. Intermediate result. RPN - HP 35s | HP 35s scientific calculator - User Guide - Page 62
result. Final result. More Exercises Practice using RPN by working through the following problems: Calculate: (14 + 12) × (18 - 12) ÷ (9 - 7) = 78.0000 A Solution: Calculate: 232 - (13 × 9) + 1/7 = 412.1429 A Solution: Calculate: (5.4 × 0.8) ÷ (12.5 − 0.73) = 0.5961 Solution: or - HP 35s | HP 35s scientific calculator - User Guide - Page 63
A Solution: RPN: The Automatic Memory Stack 2-17 - HP 35s | HP 35s scientific calculator - User Guide - Page 64
2-18 RPN: The Automatic Memory Stack - HP 35s | HP 35s scientific calculator - User Guide - Page 65
HP 35s has 30 KB of memory, in which you can store numbers, equations, and programs. Numbers Example: This example shows you how to store the value 3 in the variable A, first in RPN mode and then in ALG mode. Keys: 9 A 9 A Display: Description: Switch to RPN mode (if necessary) Enter - HP 35s | HP 35s scientific calculator - User Guide - Page 66
real or complex, decimal or fraction, base 10 or other as supported by the HP 35s. To store a copy of a displayed number (X-register) to a direct variable: Press letter-key . To recall a copy of a number from a direct variable to the display: Press letter-key . Example: Storing Numbers. Store - HP 35s | HP 35s scientific calculator - User Guide - Page 67
the Recall command. The display of this command differs slightly from RPN to ALG mode, as the following example illustrates. Example: In this example, we recall the value of 1.75 that we stored in the variable G in the last example. This example assumes the HP 35s is still in ALG mode at the start - HP 35s | HP 35s scientific calculator - User Guide - Page 68
(u) provides information about the amount of available memory. The catalog display has the following format: where mm,mmm is the number of bytes of available memory and nnn is the amount of used indirect variables. For more information on indirect variables, see Chapter 14. The VAR - HP 35s | HP 35s scientific calculator - User Guide - Page 69
we view these variables via the VAR Catalog and clear them as well. This example uses RPN mode. Keys: ) C D E u Display: Description: Clear all direct variables Store 3 in C, 4 in D, and 5 in E. Enter the VAR catalog. Note the and annunciators indicating that - HP 35s | HP 35s scientific calculator - User Guide - Page 70
to enter the VAR catalog will display the error message If the value of a variable has too many digits to display completely, you can use Õ and Ö to view the missing digits. Arithmetic with Stored Variables Storage arithmetic and recall arithmetic allow you to do calculations with a number - HP 35s | HP 35s scientific calculator - User Guide - Page 71
For example, suppose you want to divide the number in the X-register (3, displayed) by the value in A(12). Press A. Now x = 0.25, while 12 is still in A. Recall arithmetic saves memory in programs: using A (one instruction) uses half as much memory as A, (two instructions). A 12 - HP 35s | HP 35s scientific calculator - User Guide - Page 72
D, E, and F. Displays the current value of D. Clears the VIEW display; displays Xregister again. Suppose the variables D, E, and F contain the values 2, 3, and 4 from the last example. Divide 3 by D, multiply it by E, and add F to the result. Keys: D E F Display Description: Calculates - HP 35s | HP 35s scientific calculator - User Guide - Page 73
Example: Keys: A A Display A Description: Stores 12 in variable A. Displays x. Exchanges contents of the X-register and variable on the key. This is a programming technique called indirect addressing that is covered under "Indirectly Addressing Variables and Labels" in chapter 14. - HP 35s | HP 35s scientific calculator - User Guide - Page 74
3-10 Storing Data into Variables - HP 35s | HP 35s scientific calculator - User Guide - Page 75
). Arithmetic functions and calculations were covered in chapters 1 and 2. Advanced numeric operations (root-finding, integrating, complex numbers, base conversions, and statistics) are described in later chapters. The examples in this chapter all assume the HP 35s is in RPN mode. Exponential and - HP 35s | HP 35s scientific calculator - User Guide - Page 76
. (Do not press .) 4. Press the function key. Example: To display the quotient and remainder produced by 58 ÷ 9 Keys: Display Description: Displays the quotient. Displays the remainder. Power Functions In RPN mode, to calculate a number y raised to a power x, key in y x, then press - HP 35s | HP 35s scientific calculator - User Guide - Page 77
Press: Result In RPN mode, to calculate a root x of a number y (the xth root of y), key in y x, then press . For y < 0, x must be an integer. To Calculate: 196 3 − 125 4 625 −1.4 .37893 Press: Result Trigonometry Entering π Press to place the first 12 digits - HP 35s | HP 35s scientific calculator - User Guide - Page 78
not convert numbers already present (see "Conversion Functions" later in this chapter). 360 degrees = 2π radians = 400 grads To set an angular mode, press 9. A menu will be displayed from which you can select an option. Option Description Sets degree mode, which uses decimal degrees rather - HP 35s | HP 35s scientific calculator - User Guide - Page 79
significant digits). Keys: 9 9 Display: Description: Sets Radians mode; RAD annunciator on. 5/7 in decimal format. Cos (5/7)π. Switches to Degrees mode (no annunciator). Calculates cos 128.57°, which is the same as cos (5/7)π. Programming Note: Equations using inverse trigonometric - HP 35s | HP 35s scientific calculator - User Guide - Page 80
carry out subsequent calculations using both the base number and the result without reentering the base number. To Calculate: x% of y Percentage change from y to x. (y≠ 0) Example: Press: y x y x Find the sales tax at 6% and the total cost of a $15.76 item. Use FIX 2 display format so - HP 35s | HP 35s scientific calculator - User Guide - Page 81
Keys: 8 Display: Description: Rounds display to two decimal places. Calculates 6% tax. Total cost (base price + 6% tax). Suppose that the $15.76 item cost $16.12 last year. What is the percentage change from last year's price to this year's? Keys: 8 Display Description: - HP 35s | HP 35s scientific calculator - User Guide - Page 82
CONST Menu Items ε Description Speed of light in vacuum Standard acceleration of gravity Newtonian constant of gravitation Molar volume of ideal gas Avogadro constant ×10-27 J T-1 1.410606633×10-26 J T-1 -9.28476362×10-24 J T-1 -9.662364×10-27 J T-1 4-8 Real-Number Functions - HP 35s | HP 35s scientific calculator - User Guide - Page 83
Standard atmosphere γ Proton gyromagnetic ratio First radiation constant Second radiation constant Conductance quantum The base number No.6,1999 and Reviews of Modern inserted. 2. Press to display the physics constants menu. 3. Press equations, and programs. Real-Number Functions 4-9 - HP 35s | HP 35s scientific calculator - User Guide - Page 84
Functions The HP 35s supports four types of conversions. You can convert between: rectangular and polar formats for complex numbers degrees, radians, and gradients for angle measures decimal and hexagesimal formats for time (and degree angles) various supported units (cm/in, kg/lb, etc) With - HP 35s | HP 35s scientific calculator - User Guide - Page 85
by the mode setting. Here are the steps required to set a complex number format: 1. Press 8 and then choose either or in RPN mode (in ALG mode, you may also choose 2. Input your desired coordinate value (x 6 y, x y 6 or r ?a) 3. press Example: Polar to Rectangular Conversion. In the - HP 35s | HP 35s scientific calculator - User Guide - Page 86
8 6 Sets complex coordinate mode. Convert xiy (rectangular) to rθ a (polar). 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 - HP 35s | HP 35s scientific calculator - User Guide - Page 87
Time Conversions The HP 35s can convert between decimal and hexagesimal formats for numbers. This is especially useful for time and angles measured in degrees. For example, in decimal format an angle measured in degrees is expressed as D.ddd..., while in hexagesimal the same angle is represented as - HP 35s | HP 35s scientific calculator - User Guide - Page 88
radians: Example In this example, we convert an angle measure of 30° to π/6 radians. Keys: Display: Description: µ Enter the angle in degrees. Convert to radians. Read the result as 0.5236, a decimal approximation of π/6. Unit Conversions The HP 35s has ten unit-conversion functions - HP 35s | HP 35s scientific calculator - User Guide - Page 89
1). The value for x cannot be a negative integer. Probability Combinations To calculate the number of possible sets of n items taken r at a time, enter n first, x, then r (nonnegative integers only). No item occurs more than once in a set, and different orders of the same r items are not counted - HP 35s | HP 35s scientific calculator - User Guide - Page 90
Therefore, a sequence of random numbers can be repeated by starting with the same seed. You can store a new seed with the SEED function. If memory is cleared, the seed is reset to zero. A seed of zero will result in the calculator generating its own seed. Example: Combinations of People. A company - HP 35s | HP 35s scientific calculator - User Guide - Page 91
with zeros, press For example, the fractional part of 14.2300 is 0.2300) Absolute value To replace a number in the x-register with its absolute value, press . For complex numbers and vectors, the absolute value of: 1. a complex number in rθa format is r 2. a complex number in xiy format is - HP 35s | HP 35s scientific calculator - User Guide - Page 92
Greatest integer To obtain the greatest integer equal to or less than given number, press Example: This example summarizes many of the operations that extract parts of numbers. To calculate: Press: Display: The integer part of 2.47 The fractional part of 2.47 The absolute value of - HP 35s | HP 35s scientific calculator - User Guide - Page 93
off Fraction-display mode, if active. Functions work the same with fractions as they do with decimal numbers - except for RND, which is discussed later in this chapter. The examples in this chapter all utilize RPN mode unless otherwise noted. Entering Fractions You can type almost any number as - HP 35s | HP 35s scientific calculator - User Guide - Page 94
. (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 - HP 35s | HP 35s scientific calculator - User Guide - Page 95
fraction is indicated by the and annunciators at the right of the display. The calculator compares the value of the fractional part of the internal 12-digit number with the value of the displayed fraction: If no indicator is lit, the fractional part of the internal 12-digit value exactly matches - HP 35s | HP 35s scientific calculator - User Guide - Page 96
In its default condition, the calculator displays a fractional number according to certain rules. However, you can change the rules according to how you want fractions displayed: You can set the maximum denominator that's used. You can select one of three fraction formats. The next few topics - HP 35s | HP 35s scientific calculator - User Guide - Page 97
fraction. To see the number's decimal representation, press and then hold . Example: This example illustrates the steps required to set the maximum denominator to 3125 and then show a fraction that is too long for the display. Keys: Õ Display: Description: Set the maximum denominator to - HP 35s | HP 35s scientific calculator - User Guide - Page 98
. For example, if you're working with time measurements, you might want to see c value is 60 ). There are three flags that control the fraction format. These flags are numbered 7, 8, and 9. Each flag is either clear or set. Their purposes are as follows: Flag 7 toggles fraction-display mode on or - HP 35s | HP 35s scientific calculator - User Guide - Page 99
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 or to clear the or response.) Example: This example illustrates the display of fractions in the - HP 35s | HP 35s scientific calculator - User Guide - Page 100
indicatior turns off if the fraction matches the decimal representation exactly. Otherwise, the accuracy indicatior stays on, (See "Accuracy Indicators" earlier in this chapter.) In an equation or program, the RND function does fractional rounding if Fraction- display mode is active. 5-8 Fractions - HP 35s | HP 35s scientific calculator - User Guide - Page 101
. The cumulative round off error. Clears flag 8. Turns off Fraction-display mode. Fractions in Equations You can use a fraction in an equation. When an equation is displayed, all numerical values in the equation are shown in their entered form. Also, fractiondisplay mode is available for operations - HP 35s | HP 35s scientific calculator - User Guide - Page 102
using Fraction- display mode if it's active. If you're prompted for values by INPUT instructions, you may enter fractions. The program's result is displayed using the current display format. A program can control the fraction display using the /c function and by setting and clearing flags 7, 8, and - HP 35s | HP 35s scientific calculator - User Guide - Page 103
pipe (78.5398 cubic inches). However, by storing the equation, you get the HP 35s to "remember" the relationship between diameter, length, and volume - so you can use it many times. Put the calculator in Equation mode and type in the equation using the following keystrokes: Entering and Evaluating - HP 35s | HP 35s scientific calculator - User Guide - Page 104
Equation mode, shown by or the current equation in the EQN annunciator. line 2 Begins a new equation, turns on the A..Z annunciator so you can enter a variable name. types Digit entry uses the "_" entry cursor. ends the number. types . Terminates and displays the equation - HP 35s | HP 35s scientific calculator - User Guide - Page 105
or bottom of the equation list. Shows the displayed equation's checksum (verification value) and length (bytes of memory). Recovers the most recently deleted element or equation. Leaves Equation mode. You can also use equations in programs - this is discussed in chapter 13. Entering and Evaluating - HP 35s | HP 35s scientific calculator - User Guide - Page 106
calculator is in its normal operating mode, usually with a number in the display. For example, you can't be viewing the catalog of variables or programs. 2. Press . The EQN annunciator shows that Equation mode is active, and an entry from the equation list is displayed. 3. Start typing the equation - HP 35s | HP 35s scientific calculator - User Guide - Page 107
complex, and fractional numbers. Numbers are always shown using ALL display format, which displays up to 12 characters. To enter a number in an equation, you can use the standard number-entry keys, including , , and . Do not use for subtraction. Functions in Equations You can enter many HP 35s - HP 35s | HP 35s scientific calculator - User Guide - Page 108
the equation list. Starts a new equation with variable R. Enters a number Enters infix operators. Enters a prefix function with a left parenthesis. Enters the argument and right parenthesis. Terminates the equation and displays it. Shows its checksum and length. Leaves Equation mode. Displaying and - HP 35s | HP 35s scientific calculator - User Guide - Page 109
. Example: Viewing an Equation. View the last equation you entered. Keys: Display Õ Ö Description: Displays the current equation in the equation list. Activates cursor to the left of the equation Activates cursor to the right of the equation Leaves Equation mode. Entering and - HP 35s | HP 35s scientific calculator - User Guide - Page 110
, selecting a setting menu (such as 9, 8, or ), will end the equation edit status. 2. When editing an equation, selecting an insert or view menu (such as and ), the equation will still be in edit mode after inserting the item. 3. The menus are disabled in equation mode. 6-8 Entering and - HP 35s | HP 35s scientific calculator - User Guide - Page 111
the previous example. Keys: Ö Display Description: Shows the current equation in the equation list. Activates cursor at the end of the equation Deletes the number 25. Shows the end of edited equation in the equation list. Leaves Equation mode. Types of Equations The HP 35s works - HP 35s | HP 35s scientific calculator - User Guide - Page 112
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 - HP 35s | HP 35s scientific calculator - User Guide - Page 113
it uses only numbers in the equation and variable values. The value of the equation is returned to the X- register. Using ENTER for Evaluation If an equation is displayed in the equation list, you can press to evaluate the equation. (If you're in the process of typing the equation, pressing only - HP 35s | HP 35s scientific calculator - User Guide - Page 114
to liters (but doesn't change V. Using XEQ for Evaluation If an equation is displayed in the equation list, you can press to evaluate the equation. The entire equation is evaluated, regardless of the type of equation. The result is returned to the X-register. 6-12 Entering and Evaluating - HP 35s | HP 35s scientific calculator - User Guide - Page 115
If the unnamed indirect variable (I) or (J) is in an equation, you will not be prompted to for its value, as the current value stored in the unnamed indirect variable will be used automatically. (See chapter 14) To leave the number unchanged, just press . Entering and Evaluating Equations 6-13 - HP 35s | HP 35s scientific calculator - User Guide - Page 116
in the X-register. You can enter a number as a fraction if you want. If you need to calculate a number, use normal keyboard calculations, then press . For example, you can press 2 5 in RPN mode, or press 2 5 in ALG mode. Before pressing , the expression will display in line 2, and after - HP 35s | HP 35s scientific calculator - User Guide - Page 117
Equality Example 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 Entering and Evaluating Equations 6-15 - HP 35s | HP 35s scientific calculator - User Guide - Page 118
, display a left parenthesis when you enter them. The prefix functions that require two arguments are %CHG, XROOT, IDIV, RMDR, nCr and nPr. Separate the two arguments with a comma. In an equation, the XROOT function takes its arguments in the opposite order from RPN usage. For example, -83 to - HP 35s | HP 35s scientific calculator - User Guide - Page 119
^ IDIV 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 ( 1 + 1 ) sinθ sinφ a h θ φ b The following equation obeys the syntax rules for HP 35s equations: Entering and - HP 35s | HP 35s scientific calculator - User Guide - Page 120
instead of the 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 = 1 n d 2 cos(π /n) 4 sin(π/n) d 2π/n You can specify this - HP 35s | HP 35s scientific calculator - User Guide - Page 121
. The length is the number of bytes of calculator memory used by the equation. The checksum and length allow you to verify that equations you type are correct. The checksum and length of the equation you type in an example should match the values shown in this manual. Example: Checksum and Length of - HP 35s | HP 35s scientific calculator - User Guide - Page 122
Keys: ( ×as required) (hold) (release) Display Description: Displays the desired equation. Display equation's checksum and length. Redisplays the equation. Leaves Equation mode. 6-20 Entering and Evaluating Equations - HP 35s | HP 35s scientific calculator - User Guide - Page 123
equation equals zero. Solving an Equation To solve an equation (excluding built-in equations) for an unknown variable: 1. Press and display the desired equation. If necessary, type the equation as explained in chapter 6 under "Entering Equations into the Equation List." Solving Equations - HP 35s | HP 35s scientific calculator - User Guide - Page 124
unknown variable. For example, press X to solve for x. The equation then prompts for a value for every other variable in the equation. 3. For each prompt, enter the desired value: If the displayed value is the one you want, press . If you want a different value, type or calculate the value and - HP 35s | HP 35s scientific calculator - User Guide - Page 125
Description: Clears memory. Selects Equation mode. Starts the equation. Terminates the equation and displays the left end. Checksum and length. g (acceleration due to gravity) is included as a variable so you can change it for different units (9.8 m/s2 or 32.2 ft/s2 ). Calculate how many - HP 35s | HP 35s scientific calculator - User Guide - Page 126
number of moles of gas, R is the universal gas constant (0.0821 liter-atm/mole-K or 8.314 J/mole-K), and T is temperature (Kelvins: K=°C + 273.1). Enter the equation: Keys: P Display: _ Description: Selects Equation mode and starts the equation. Terminates and displays the equation - HP 35s | HP 35s scientific calculator - User Guide - Page 127
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 solving for P: Keys: Display: Description: P value value value value Solves for P; prompts - HP 35s | HP 35s scientific calculator - User Guide - Page 128
x, y, and z. The calculator can detect cases with infinitely many solutions or no solutions. Example: solve the x,y in simultaneous equations Keys: Display value value value value value Description: Enters equation mode. Displays the built-in equation Prompts for A. Stores 1 in - HP 35s | HP 35s scientific calculator - User Guide - Page 129
, the calculator displays See appendix D for more information about how SOLVE works. Verifying the Result After the SOLVE calculation ends, you can verify that the result is indeed a solution of the equation by reviewing the values left in the stack: The X-register (press to clear the viewed - HP 35s | HP 35s scientific calculator - User Guide - Page 130
, the root given was only an approximation; this number should be close to zero. If a calculation ends with the the calculator could not converge on a root. (You can see the value in the X-register - the final estimate of the root - by pressing or to clear the message.) The values in the X- and - HP 35s | HP 35s scientific calculator - User Guide - Page 131
variable, the second guess will be the same value since the display also holds the number you just stored in the variable. (If such is the case, the calculator changes one guess slightly so that it has two different guesses.) Entering your own guesses has the following advantages: By narrowing the - HP 35s | HP 35s scientific calculator - User Guide - Page 132
Example: Using Guesses to Find a Root. Using a rectangular piece of sheet 2H ) × (40 - 2H ) × H which you can simplify and enter as Type in the equation: Keys: V= ( 40 - H ) × ( 20 - H ) × 4 × H Display: _ Description: Selects Equation mode and starts the equation 4 HÕ 7-10 Solving - HP 35s | HP 35s scientific calculator - User Guide - Page 133
40 cm wide. Initial estimates of 10 and 20 cm are therefore appropriate. Keys: H H Display: value Description: Leaves Equation mode. Stores lower and upper limit guesses. Displays current equation. Solves for H; prompts for V. Stores 7500 in V; solves for H. Now check the quality of - HP 35s | HP 35s scientific calculator - User Guide - Page 134
of the unknown. For each point on the graph, display the equation and press - at the prompt for x enter the x-coordinate, and then obtain the corresponding value of the equation, the y-coordinate. For the problem above, you would always set V = 7500 and vary the value of H to produce different - HP 35s | HP 35s scientific calculator - User Guide - Page 135
8 Integrating Equations Many problems in mathematics, science, and engineering require calculating the definite integral of a function. If the function is denoted by f(x) and the interval of integration is a to b, then the integral can be expressed mathematically as f (x) I = ∫ b a f (x) - HP 35s | HP 35s scientific calculator - User Guide - Page 136
the equation list, key it in (see "Entering Equations into the Equation List" in chapter 6) and leave Equation mode. The equation usually contains just an expression. 2. Enter the limits of integration: key in the lower limit and press , then key in the upper limit. 3. Display the equation: Press - HP 35s | HP 35s scientific calculator - User Guide - Page 137
function for x-values of 2 and 3. Enter the expression that defines the integrand's function: cos (x sin t ) Keys: X Display: Description: Clears memory. Selects Equation mode. Types the equation. Terminates the expression and displays its left end. Checksum and - HP 35s | HP 35s scientific calculator - User Guide - Page 138
the limits of integration (lower limit first). Displays the current equation. Prompts for the variable of integration. Prompts for value of X. x = 3. Starts integrating and calculates the result for π ∫ f (t) . 0 The final result for J0(3). Example: Sine Integral. Certain problems in communications - HP 35s | HP 35s scientific calculator - User Guide - Page 139
and length. Leaves Equation mode. Now integrate this function with respect to x (that is, X) from zero to 2 (t = 2). Keys: 9 X X Display: _ Description: Selects Radians mode. Enters limits of integration (lower first). Displays the current equation. Calculates the result for Si - HP 35s | HP 35s scientific calculator - User Guide - Page 140
-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 to view the value of the uncertainty. For example - HP 35s | HP 35s scientific calculator - User Guide - Page 141
. With the display format set to SCI 2, calculate the integral in the expression for Si(2) (from the previous example). Keys: 8 X Display Description: Sets scientific notation with two decimal places, specifying that the function is accurate to two decimal places. Rolls down - HP 35s | HP 35s scientific calculator - User Guide - Page 142
Description: Specifies accuracy to four decimal places. The uncertainty from the last example is still in the display. Rolls down the limits of integration from the Z- and T-registers into the X- and Y-registers. Displays the current equation. Calculates the result. Note that the uncertainty - HP 35s | HP 35s scientific calculator - User Guide - Page 143
enter a complex number: Form: 1. Type the real part. 2. Press6. 3. Type the imaginary part. Form: 1. Type the real part. 2. Press 3. Type the imaginary part. 4. Press6. Form: 1. Type the value of r. 2. Press?. 3. Type the value of θ. The examples in this chapter all utilize RPN mode - HP 35s | HP 35s scientific calculator - User Guide - Page 144
r t 3 X2iY2 X Y2 or a2 (Display in line 2) or X2 or r2 r2θ a2 Complex Stack Complex Result,Z Complex Operations Use the complex operations as you do real operations in ALG and RPN mode. To do an operation with one complex number: 1. Enter the complex number z as described before. 2. Select - HP 35s | HP 35s scientific calculator - User Guide - Page 145
an arithmetic operation with two complex numbers: 1. Enter the first complex number, z1 as described before. 2. Enter the second complex number z2 as described before. 3. Select the arithmetic operation: Arithmetic With Two Complex Numbers, z1 and z2 To Calculate: Addition, z1 + z2 Subtraction, z1 - HP 35s | HP 35s scientific calculator - User Guide - Page 146
are some examples of trigonometry and arithmetic with complex numbers: Evaluate sin (2i3) Keys: 8 6 Display: Description: Sets display format. Result is 9.1545 i -4.1689. Evaluate the expression z 1 ÷ (z2 + z3), where z1 = 23 i 13, z2 = -2i1 z3 = 4 i- 3 Perform the calculation as Keys - HP 35s | HP 35s scientific calculator - User Guide - Page 147
Keys: 6 Display Description: ENTER 1i1Intermediate result of Z-2,result is 0i-5 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 - HP 35s | HP 35s scientific calculator - User Guide - Page 148
: Display: 9 8 Õ Description: Sets Degrees mode. Sets complex mode Enters L1 Enters L2. Enters L3 and adds L2 + L3 Adds L1 + L2 + L3. Scrolls the screen to see the rest of the answer You can do a complex operation with numbers whose complex - HP 35s | HP 35s scientific calculator - User Guide - Page 149
equation and are prompted for variable values, you may enter complex numbers. The values and format of the result are controlled by the display setting. This is the same as calculating in ALG mode. Equations that contain complex numbers can be solved and integrated. Operations with Complex Numbers - HP 35s | HP 35s scientific calculator - User Guide - Page 150
For example, 1i2+3θ 10+5 θ 30 in program is: Program lines: (ALG mode Description Begins the program When you are running a program and are prompted for values by INPUT instructions, you can enter complex numbers. The values and format of the result are controlled by the display setting. The - HP 35s | HP 35s scientific calculator - User Guide - Page 151
momentum, angular velocity and acceleration, etc. To enter a vector: 1. Press 3 2. Enter the first number for the vector. 3. Press and enter a second number for a 2-D or 3-D vector. 4. Press and enter a third number for a 3-D vector. The HP 35s cannot handle vectors with more than 3 dimensions - HP 35s | HP 35s scientific calculator - User Guide - Page 152
Calculate [1.5,-2.2]+[-1.5,2.2] Keys: 9 Display: 3 3 Description: Switches to RPN mode(if necessary) Enters [1.5,-2.2] Enters [-1.5,2.2] Adds two vectors Calculate [-3.4,4.5]-[2.3,1.4] Keys: 9 3 3 Display Description: Switches to ALG mode Enters [-3.4,4.5] Enters - HP 35s | HP 35s scientific calculator - User Guide - Page 153
[3,4]x5 Keys: Display: 9 3 Description: Switches to RPN mode Enters [3,4] Enters 5 as a scalar _ Performs multiplication Calculate [-2,4]÷2 Keys: 9 3 Display Description: Switches to ALG mode Enters [-2,4] Enters 5 as a scalar Performs - HP 35s | HP 35s scientific calculator - User Guide - Page 154
for dot product, and enters the second vector The dot product of two vectors is 11 Calculate the dot product of two vectors, [9,5] and [2.2] Keys: Display: 9 3 3 Description: Switches to RPN mode Enters the first vector [9,5] and enters the second vector [2,2] 10 - HP 35s | HP 35s scientific calculator - User Guide - Page 155
Display: Description: 9 9 3 Switches to ALG mode Sets Degrees mode Arc cosine function Enters vector A [1,0] Õ 3 3 3 Enters vector 9 9 3 3 3 Display: Description: Switches to RPN mode Sets Degrees mode Finds the dot product of two vectors Finds - HP 35s | HP 35s scientific calculator - User Guide - Page 156
be used in equations and in equation variables exactly like real numbers. A vector can be entered when prompted for a variable. Equations containing vectors can be solved, however the solver has limited ability if the unknown is a vector. Equations containing vectors can be integrated, however the - HP 35s | HP 35s scientific calculator - User Guide - Page 157
as real and complex numbers For example, [5, 6] +2 x [7, 8] x [9, 10] in a program is: Program lines Description: Begins the program [5,6] A vector can be entered when prompted for a value for a variable. Programs that contain vectors can be used for solving and integrating. Vector Arithmetic - HP 35s | HP 35s scientific calculator - User Guide - Page 158
It is possible to create vectors containing the contents of memory variables, stack registers, or values from the indirect registers, in run or program modes. In ALG mode, begin entering the vector by pressing 3. RPN mode works similarly to ALG mode, except that the d key must be pressed first - HP 35s | HP 35s scientific calculator - User Guide - Page 159
. BASE Menu Menu label Description Decimal mode. This is the normal calculator mode Hexadecimal mode. The HEX annunciator is displayed when this mode is active. Numbers are displayed in hexadecimal format. In RPN mode, the keys and act as shortcut to enter the digits A to F. In ALG - HP 35s | HP 35s scientific calculator - User Guide - Page 160
number. To enter a binary number, type the number followed by "" Examples: Converting the Base of a Number. The following keystrokes do various base conversions. Convert 125.9910 to hexadecimal, octal, and binary numbers. Keys: Display: Description: Converts the decimal number - HP 35s | HP 35s scientific calculator - User Guide - Page 161
. you can use menu to enter base-n sign b/o/d/h following the operand to represent 2/8/10/16 base number in any base mode. A number without a base sign is a decimal number Note: In ALG mode: 1. The result's base mode is determined by the current base mode setting. 2. If there is no active command - HP 35s | HP 35s scientific calculator - User Guide - Page 162
any base. The only function keys that are actually deactivated in HEX mode are 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 - HP 35s | HP 35s scientific calculator - User Guide - Page 163
negative number possible. Example: Here are some examples of arithmetic in Hexadecimal, Octal, and Binary modes: 12F16 + E9A16 = ? Keys: Display Description: Sets base 16; HEX annunciator on. Result. 77608 - 43268 Sets base 8; OCT annunciator on. Converts displayed number to - HP 35s | HP 35s scientific calculator - User Guide - Page 164
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 complement of its positive binary number. Keys: Display Description: Enters a positive, decimal number; then converts it to hexadecimal - HP 35s | HP 35s scientific calculator - User Guide - Page 165
377777777777o 400000000000o Binary 0111111111111111111111 10000000000000000000000 11111111111111b 0000000000000b Decimal 34,359,738,367 -34,359,738,368 Numbers outside of this range can not be entered when a non decimal base is selected. Base Conversions and Arithmetic and Logic 11-7 - HP 35s | HP 35s scientific calculator - User Guide - Page 166
in program and equations Equations and program are affected by the base setting and binary, octal and hexadecimal numbers can be entered in equation and in program as well as when the calculator prompts for a variable. Results will be displayed according to the current base. 11-8 Base Conversions - HP 35s | HP 35s scientific calculator - User Guide - Page 167
HP 35s provide functions to statistically analyze a set of one- or two-variable data(real numbers): Mean, sample and population standard deviations. Linear regression and linear estimation ( xˆ and yˆ ). Weighted mean (x weighted by y). Summation statistics: n, Σx, Σy, Σx2, Σy2, and Σxy. Entering - HP 35s | HP 35s scientific calculator - User Guide - Page 168
One-Variable Data 1. Press ()to clear existing statistical data. 2. Key in each x-value and press . 3. The display shows n, the number of statistical data values now accumulated. Pressing actually enters two variables into the statistics registers because the value already in the - HP 35s | HP 35s scientific calculator - User Guide - Page 169
Example: Key in the x, y-values on the left, then make the corrections shown on the right: Initial x, y 20, 4 400, 6 Corrected x, y 20, 5 40, 6 Keys: () Display: Description: Clears existing statistical data. Enters the first new data pair. Display shows n, the number - HP 35s | HP 35s scientific calculator - User Guide - Page 170
Statistical Calculations Once you have entered your standard-deviation menu See "Sample Standard Deviation" and "Population Standard Deviation" later in this chapter. The summation menu See "Summation Statistics" later in this chapter. Mean Mean is the arithmetic average of a group of numbers - HP 35s | HP 35s scientific calculator - User Guide - Page 171
all data as x-values.) Keys: Display: Description: () Clears the statistics registers. Enters the first time. Enters the remaining data; six data points accumulated. Calculates the mean time to complete the process. Example: Weighted Mean (Two Variables - HP 35s | HP 35s scientific calculator - User Guide - Page 172
8.5 Calculate the standard deviation of the times. (Treat all the data as x-values.) Keys: () Display: Description: Clears the statistics registers. Enters the first time. Enters the remaining data; six data points entered. Calculates the standard deviation - HP 35s | HP 35s scientific calculator - User Guide - Page 173
cm. Find the population standard deviation of their heights. Keys: () Display: Description: Clears the statistics registers. Enters data. Four data points accumulated. Calculates the population standard deviation. Linear Regression Linear regression - HP 35s | HP 35s scientific calculator - User Guide - Page 174
is a number in the range -1 through +1 that measures how closely the calculated line fits the data. Slope of the calculated line. y-intercept of the calculated line. To 5.78 6.61 7.21 7.78 Keys: () Display: Description: Clears all previous statistical data. 12-8 Statistical Operations - HP 35s | HP 35s scientific calculator - User Guide - Page 175
Õ Õ y Enters data; displays n. Five data pairs entered. Displays linear-regression menu. Correlation coefficient; data closely approximate a straight line. Slope of the line. y-intercept. 8.50 7.50 r = 0.9880 X (70, y) 6.50 5.50 m = 0.0387 b = 4.8560 4. - HP 35s | HP 35s scientific calculator - User Guide - Page 176
rounding. Here are two examples: Normalizing Close, Large Numbers The calculator might be unable to correctly calculate the standard deviation and linear regression for a variable whose data values differ by a relatively small amount. To avoid this, normalize the data by entering each value as the - HP 35s | HP 35s scientific calculator - User Guide - Page 177
in addition to those provided by the calculator. If you've entered statistical data, you can see the contents of the statistics registers. Press then use × and Ø to view the statistics registers. Example: Viewing the Statistics Registers. Use to store data pairs (1,2) and (3,4) in the - HP 35s | HP 35s scientific calculator - User Guide - Page 178
Registers The statistics register assignments in the HP 35s are shown in the following table. Summation registers should be referred to by names and not by numbers in expression, equations and programs. Register n Σx Σy Σx2 Σy2 Σxy Statistics Registers Number -27 -28 -29 -30 -31 -32 Description - HP 35s | HP 35s scientific calculator - User Guide - Page 179
can press 7 or A (or 7 or A ) to view (or recall)a register value - the display is labeled with the register name. The SUMS menu contains functions for recalling the register values. See "Indirectly Addressing Variables and Labels" in chapter 14 for more information. Statistical Operations 12 - HP 35s | HP 35s scientific calculator - User Guide - Page 180
12-14 Statistical Operations - HP 35s | HP 35s scientific calculator - User Guide - Page 181
Programming Part 2 - HP 35s | HP 35s scientific calculator - User Guide - Page 182
- HP 35s | HP 35s scientific calculator - User Guide - Page 183
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 ALG mode: 5 to get the result for this - HP 35s | HP 35s scientific calculator - User Guide - Page 184
Keys: (In RPN mode) 5 Display Description: This sets the program to its beginning. The answer! In ALG mode, to enter this program into program memory, do the following: Keys: (In ALG mode) Display: Description: Clears memory. Activates Program-entry mode (PRGM annunciator - HP 35s | HP 35s scientific calculator - User Guide - Page 185
mode) X Display: Description: This sets the program to its beginning. Stores 5 into X The answer! We will continue using the above program for the area of a circle to illustrate programming concepts and methods. Designing a Program The following topics show what instructions - HP 35s | HP 35s scientific calculator - User Guide - Page 186
should end with a return instruction. The keystrokes are: When a program finishes running, the last RTN instruction returns the program pointer to the top of program memory. Using RPN, ALG and Equations in Programs You can calculate in programs the same ways you calculate on the keyboard: 13 - HP 35s | HP 35s scientific calculator - User Guide - Page 187
to for an assignment equation - other than writing the equation as an expression, then using STO to store the value in a variable.) For both types of calculations, you can include RPN instructions to control input, output, and program flow. Data Input and Output For programs that need more than - HP 35s | HP 35s scientific calculator - User Guide - Page 188
to activate Program-entry mode. 2. Press to display This sets the program pointer to a known spot, before any other programs. As you enter program lines, they are inserted before all other program lines. If you don't need any other programs that might be in memory, clear program memory by - HP 35s | HP 35s scientific calculator - User Guide - Page 189
number is shortened in the display, press to view all digits.) To enter an equation in a program line: 1. Press to activate Equation-entry mode. The EQN annunciator turns on. 2. Enter the equation as you would in the equation list. See chapter 6 for details. Use to correct errors as you type - HP 35s | HP 35s scientific calculator - User Guide - Page 190
. Keys: (In RPN mode) A Display: (2 13-8 Simple Programming Description: Activates Program-entry mode (PRGM on). Clears all of program memory. Labels this program routine A (for "area"). Enters the three program lines. Ends the program. Displays label A and - HP 35s | HP 35s scientific calculator - User Guide - Page 191
Example: Entering a Program with an Equation. The following program calculates the area of a circle using an equation, rather than using RPN operations like the previous program. Keys: (In RPN mode) Display E Description: Activates Program-entry mode; sets pointer to top of memory - HP 35s | HP 35s scientific calculator - User Guide - Page 192
of 5, 2.5, and 2π. Remember to enter the radius before executing A or E. Keys: (In RPN mode) A Display: E Description: Enters the radius, then starts program A. The resulting area is displayed. Calculates area of the second circle using program E. Calculates area of the third - HP 35s | HP 35s scientific calculator - User Guide - Page 193
roll by automatically. Example: Testing a Program. Step through the execution of the program labeled A. Use a radius of 5 for the test data. Check that Program-entry mode is not active before you start: Keys: (In RPN mode) hold) (release) Ø (hold) (release) Display: Description: Moves - HP 35s | HP 35s scientific calculator - User Guide - Page 194
of π. 25π. End of program. Result is correct. Entering and Displaying Data The calculator's variables are used to store equation prompting (if enabled by flag 11 set). (This is also handy if you're using equations.) In a program, you can display information in these ways: With a VIEW instruction - HP 35s | HP 35s scientific calculator - User Guide - Page 195
given variable. If you have not changed the displayed value, then that value is retained in the X-register. The area-of-a-circle program with an INPUT instruction looks like this: RPN mode ALG mode To use the INPUT function in a program: 1. Decide which data values you will need, and - HP 35s | HP 35s scientific calculator - User Guide - Page 196
in the X-register. You can enter a number as a fraction if you want. If you need to calculate a number, use normal keyboard calculations, then press . For example, you can press in RPN mode, or press in ALG mode (Before you press , the expression will be displayed in line 2. After you press - HP 35s | HP 35s scientific calculator - User Guide - Page 197
prompt. Using VIEW for Displaying Data The programmed VIEW instruction ( variable ) stops a running program and displays and identifies the contents of the given variable, such as This is a display only, and does not copy the number to the X-register. If Fraction- display mode is active, the - HP 35s | HP 35s scientific calculator - User Guide - Page 198
area), V (volume), R (radius), and H (height). Use these formulas: V = πR2H Keys: (In RPN mode) R ÇH S = 2π R2 + 2π RH = 2π R ( R + H ) Display: Description: Program, entry; clears the program memory. Labels program. Instructions to prompt for radius and height. 13-16 Simple - HP 35s | HP 35s scientific calculator - User Guide - Page 199
and length of equation. Store the volume in V. Calculates the surface area. Checksum and length of equation. Stores the surface area in S. Sets flag 10 to display equations. Displays message in equations. Clears flag 10. Displays volume. Displays surface area. Ends program. Displays label C and the - HP 35s | HP 35s scientific calculator - User Guide - Page 200
a 1-second pause. In this case, no scrolling or keyboard input is allowed. The display is cleared by other display operations, and by the RND operation if flag 7 is set (rounding to a fraction). Press to enter PSE in a program. The VIEW and PSE lines - or the equation and PSE lines - are treated - HP 35s | HP 35s scientific calculator - User Guide - Page 201
number). Error Stops If an error occurs in the course of a running program, program execution halts and an error message appears in the display. (There is a list of messages and conditions in appendix F.) To see the line in the program containing the error-causing instruction, press . The program - HP 35s | HP 35s scientific calculator - User Guide - Page 202
line A004, then key in the instruction or instructions. Subsequent program lines, starting with the original line A005, are moved down and renumbered accordingly. To edit operand, expression or equation in a program line: 1. Locate or display the program line that you want to edit. 2. Press Õ or - HP 35s | HP 35s scientific calculator - User Guide - Page 203
which mode it was entered in. Program Memory Viewing Program Memory Pressing toggles the calculator into and out of program entry (PRGM annunciator on, program lines displayed). When Program-entry mode is active, the contents of program memory are displayed. Program memory starts at The list of - HP 35s | HP 35s scientific calculator - User Guide - Page 204
line number. Canceling Program-entry mode does not change the position of the program pointer. Memory Usage If during program entry you encounter the message then there is not enough room in program memory for the line you just tried to enter. You can make more room available by clearing programs - HP 35s | HP 35s scientific calculator - User Guide - Page 205
is the number of bytes used by the program. Clearing One or More Programs To clear a specific program from memory 1. Press 2 and display (using Ø and × ) the label of the program. 2. Press . 3. Press to cancel the catalog or to back out. To clear all programs from memory: 1. Press - HP 35s | HP 35s scientific calculator - User Guide - Page 206
an equation in a program line" earlier in this chapter. Nonprogrammable Functions The following functions of the HP 35s are not programmable: label line number Programming with BASE You can program instructions to change the base mode - HP 35s | HP 35s scientific calculator - User Guide - Page 207
calculator's setting will revert to Decimal mode when the program is done. An instruction in a program to change the base mode will determine how input is interpreted and how output looks during and after program execution, but it does not affect the program lines as you enter them. Numbers Entered - HP 35s | HP 35s scientific calculator - User Guide - Page 208
Ax4 + Bx3 + Cx2 + Dx + E uses the variable x four different times. A program to calculate such an expression using RPN operations could repeatedly recall a stored copy of x from a variable. Example: Write a program using RPN operations for 5x4 + 2x3, then evaluate it for x = 7. 13-26 Simple - HP 35s | HP 35s scientific calculator - User Guide - Page 209
Keys: (In RPN mode) A X X X Display: Now evaluate this polynomial for x = 7. Keys: (In RPN mode) Display: A value Description: 5 x4 5x4 x3 2x3 5x4 + 2x3 Displays label A, which takes 46 bytes. Checksum and length. Cancels program entry. Description - HP 35s | HP 35s scientific calculator - User Guide - Page 210
A more general form of this program for any equation Ax4 + Bx3 + Cx2 + Dx + E would be: Checksum and length: 9E5E 51 13-28 Simple Programming - HP 35s | HP 35s scientific calculator - User Guide - Page 211
conditional instructions (comparisons and flags) to determine which instructions or subroutines should be used. Using loops with counters to execute a set of instructions a certain number of times. Using indirect addressing to access different variables using the same program instruction. Routines - HP 35s | HP 35s scientific calculator - User Guide - Page 212
line. The example below show you to call a subroutine to change the sign of the number you input. Subroutine E that is called from routine D by line changes sign of the number. Subroutine E ends with a RTN instruction that sends program execution back to routine D (to store and display the result - HP 35s | HP 35s scientific calculator - User Guide - Page 213
nested more than 20 levels deep causes an error. Example: A Nested Subroutine. The following subroutine, labeled S, calculates the value of the expression a2 + b2 + c2 + d2 as part of a larger calculation in a larger program. The subroutine calls upon another subroutine (a nested subroutine - HP 35s | HP 35s scientific calculator - User Guide - Page 214
In RPN mode, 1 2 3 4 5 6 Starts subroutine here. Enters A. Enters B. Enters C. Enters D. program other than the next line. This is called branching. Unconditional branching uses the GTO (go to) instruction to branch to a specific program line (label and line number). 14-4 Programming - HP 35s | HP 35s scientific calculator - User Guide - Page 215
GTO label instruction (press label line number) transfers the execution of a running program to the specified program line. The program continues running from the new location, and never automatically returns to its point of origination, so GTO is not used for subroutines. For example, consider - HP 35s | HP 35s scientific calculator - User Guide - Page 216
line of a label, for example. A001: (press and hold), the display will show Conditional Instructions Another way to alter the sequence of program execution is by a conditional test, a true/false test that compares two numbers and skips the next program instruction if the proposition is false - HP 35s | HP 35s scientific calculator - User Guide - Page 217
These check the status of flags, which can be either set or clear. Loop counters. These are usually used to loop a specified number of times. Tests of Comparison (x?y, x?0) There are 12 comparisons available for programming. Pressing or displays a menu for one of the two categories of tests - HP 35s | HP 35s scientific calculator - User Guide - Page 218
In RPN mode In ALG mode Keys: Display: Example: The "Normal and Inverse-Normal Distributions" program in chapter 16 uses the x - HP 35s | HP 35s scientific calculator - User Guide - Page 219
flag is clear. Meanings of Flags The HP 35s has 12 flags, numbered 0 through 11. All flags can be set, cleared, and tested from the keyboard or by a program instruction. The default state of all 12 flags is clear. The three-key memory clearing operation described in appendix B clears all flags - HP 35s | HP 35s scientific calculator - User Guide - Page 220
Flag Status Clear (Default) Set 7 Fraction display off; display real numbers in the current display format. Fraction display on; display real numbers as fractions. Fraction-Control Flags 8 9 Fraction denominators not greater than the /c value. Reduce fractions to smallest form. Fraction - HP 35s | HP 35s scientific calculator - User Guide - Page 221
pointer moves to the next program line. 3. The equation is displayed without affecting the stack. You can clear the display by pressing or . Pressing any other key executes that key's function. 4. If the next program line is a PSE instruction, execution continues after a 1-second pause. The - HP 35s | HP 35s scientific calculator - User Guide - Page 222
flag number (0- 11). For example, press to set flag 0; press to set flag 10; press to set flag 11. Menu Key n n n FLAGS Menu Description Set flag. Sets flag n. Clear flag. Clears flag n. Is flag set? Tests the status of flag n. A flag test is a conditional test that affects program - HP 35s | HP 35s scientific calculator - User Guide - Page 223
, and that it will be set only if something in the program sets it. You should make sure of this by clearing the flag before the condition arises that might set it. See the example below. Example: Using Flags. Program Lines: (In RPN mode) Description: Clears flag 0, the indicator for In - HP 35s | HP 35s scientific calculator - User Guide - Page 224
for a fractional number and a denominator (the /c value). 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 - HP 35s | HP 35s scientific calculator - User Guide - Page 225
(In RPN mode) Description: Begins the fraction program. Clears three fraction flags. Displays messages. Selects 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 - HP 35s | HP 35s scientific calculator - User Guide - Page 226
above program to see the different forms of fraction display: Keys: (In RPN mode) Display: Description: F value value Executes label F; prompts for a fractional number (V). Stores 2.53 in V; prompts for denominator (D). Stores 16 as the /c value. Displays message, then the decimal - HP 35s | HP 35s scientific calculator - User Guide - Page 227
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: It is easier to - HP 35s | HP 35s scientific calculator - User Guide - Page 228
, ISG) When you want to execute a loop a specific number of times, use the (increment; skip if greater than) or (decrement; skip if less than or equal to) conditional function keys. Each time a loop function is executed in a program, it automatically decrements or increments a counter value - HP 35s | HP 35s scientific calculator - User Guide - Page 229
at zero, count up to 50, and increase the number by 1 each loop. If the loop-control number is a complex number or vector, it will use the real part or first part to control the loop. The following program uses ISG to loop 10 times in RPN mode. The loop counter (1.010) is stored in the variable - HP 35s | HP 35s scientific calculator - User Guide - Page 230
Press L, then press Z to see that the loop-control number is now 11.0100. Indirectly Addressing Variables and Labels Indirect addressing is a technique used in advanced programming to specify a variable or label without specifying beforehand exactly which one. This is determined when the - HP 35s | HP 35s scientific calculator - User Guide - Page 231
variables or labels) can use (I) or (J) to refer to A through Z (variables or labels) or statistics registers indirectly. The function (I) or (J) uses the value in variable I to J to determine which variable, label, or register to address. The following table shows how. Programming Techniques 14-21 - HP 35s | HP 35s scientific calculator - User Guide - Page 232
(J)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, you must use indirect addressing to do other operations, such as STO, VIEW, and INPUT. The functions listed below can use - HP 35s | HP 35s scientific calculator - User Guide - Page 233
which variable or program label will be needed. Indirect addressing is very useful for counting and controlling loops. The variable I or J serves as an index, holding the address of the variable that contains the loop- control number for the functions DSE and ISG. Equations with (I)/(J) You can - HP 35s | HP 35s scientific calculator - User Guide - Page 234
Program Lines: (In RPN mode Description: Defined the storage address range "0-100" and saved "12345" into address 100. Saves "67890" into address 150. The defined indirect storage range is now "0-150". Stores 0 into indirect register 100. The defined range is still "0-150". Display " - HP 35s | HP 35s scientific calculator - User Guide - Page 235
how you can enter an equation - it's added to the equation list - and then solve it for any variable. You can also enter a program that calculates a function, and then solve it for any variable. This is especially useful if the equation you're solving changes for certain conditions or if it requires - HP 35s | HP 35s scientific calculator - User Guide - Page 236
or entered at equation prompts. 3. Enter the instructions to evaluate the function. A function programmed as a multi-line RPN or ALG sequence must be in the form of an expression that goes to zero at the solution. If your equation is f(x) = g(x), your program should calculate f(x) - g(x). "=0" is - HP 35s | HP 35s scientific calculator - User Guide - Page 237
pointer to the top of program memory. Keys: (In ALG mode) Display: Description: Sets Program mode. Type in the program: Program Lines: (In ALG mode) Description: Identifies the programmed function. Stores P for pressure Stores V for volume Stores N for number of moles of gas - HP 35s | HP 35s scientific calculator - User Guide - Page 238
equation prompting. Evaluates the equation, clearing flag 11. (Checksum and length: EDC8 9). Ends the program. Cancels Program-entry mode. Now calculate the change in pressure of the carbon dioxide if its temperature drops by 10 °C from the previous example. 15-4 Solving and Integrating Programs - HP 35s | HP 35s scientific calculator - User Guide - Page 239
Keys: (In RPN mode) L H P L Display: Description: Stores previous pressure. Selects program "H." 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. Calculates new T. Stores 287.1 in T; - HP 35s | HP 35s scientific calculator - User Guide - Page 240
an equation for an unknown variable appear in programs as: label variable The programmed SOLVE instruction does not produce a labeled display (variable = value) since this might not be the significant output for your program (that is, you might want to do further calculations with this number - HP 35s | HP 35s scientific calculator - User Guide - Page 241
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 changes for certain conditions or if it - HP 35s | HP 35s scientific calculator - User Guide - Page 242
include no INPUT instructions, the program uses the values stored in the variables or entered at equation prompts. 3. Enter the instructions to evaluate the function. A function programmed as a multi-line RPN or ALG sequence must calculate the function values you want to integrate. 15-8 Solving and - HP 35s | HP 35s scientific calculator - User Guide - Page 243
= 2). Keys: (In RPN mode) 9 (2 S X 9 (1) Display: Description: _ Selects Radians mode. Selects label S as the integrand. Enters lower and upper limits of integration. Integrates function from 0 to 2; displays result. Restores Degrees mode. Solving and Integrating Programs 15-9 - HP 35s | HP 35s scientific calculator - User Guide - Page 244
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 PSE or STOP () instruction to display the result in the X-register after the ∫ FN instruction. If the PSE instruction immediately follows an equation - HP 35s | HP 35s scientific calculator - User Guide - Page 245
The SOLVE variable and ∫ FN d variable instructions cannot call a routine that contains another SOLVE or ∫ FN instruction. That is, neither of these instructions can be used recursively. For example, attempting to calculate a multiple integral will result in an error. Also, SOLVE and ∫ FN - HP 35s | HP 35s scientific calculator - User Guide - Page 246
15-12 Solving and Integrating Programs - HP 35s | HP 35s scientific calculator - User Guide - Page 247
coefficients, m and b. The program includes a routine to calculate the estimates xˆ and yˆ . (For definitions of these values, see "Linear Regression" in chapter 12.) Samples of the curves and the relevant equations are shown below. The internal regression functions of the HP 35s are used to compute - HP 35s | HP 35s scientific calculator - User Guide - Page 248
. 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 - HP 35s | HP 35s scientific calculator - User Guide - Page 249
Program Listing: Program Lines: (In RPN mode) Description This routine sets, the status for the straight-line model. Clears flag 0, the indicator for ln X. Clears flag 1, the indicator for In Y. Branches to common entry point Z. Checksum and length: 8E85 12 This routine sets the - HP 35s | HP 35s scientific calculator - User Guide - Page 250
b. If flag 1 is set takes the natural antilog of b. Stores b in B. Displays value. Calculates coefficient m. Stores m in M. Displays value. Checksum and length: 850C 36 Defines the beginning of the estimation (projection) loop. 16-4 Statistics Programs - HP 35s | HP 35s scientific calculator - User Guide - Page 251
Program Lines: (In RPN mode) Description Displays, prompts for, and, if changed, stores x-value in X. If flag 0 is set . . . Branches to K001 Branches to M001 Stores yˆ -value in Y. Displays, prompts for, and, if changed, stores y-value in Y. If flag 0 is set . . . Branches to - HP 35s | HP 35s scientific calculator - User Guide - Page 252
Program Lines: (In RPN mode) Checksum and length: 889C 18 Description This subroutine calculates xˆ for the logarithmic model. Calculates xˆ = e(Y - B) ÷ M Returns to the calling routine. Checksum and length: 0DBE 18 This subroutine calculates yˆ for the exponential - HP 35s | HP 35s scientific calculator - User Guide - Page 253
Program Lines: (In RPN mode) Description Calculates xˆ= (Y/B ) 1/M Goes to O005 Checksum and length: 8524 21 Determines if D001 or B001 should be run If flag 1 is set . . . Executes D001 Executes B001 Goes to Y006 Checksum and length: 4BFA 15 Determines if C001 - HP 35s | HP 35s scientific calculator - User Guide - Page 254
set in routine N, then I001 is executed. If flag 1 is clear, G001 is executed. Program instructions: 1. Key in the program routines; press when done. 2. Press and select the type visible), press again (displaying the value prompt) and press 4, press U. In either case, continue at step 3. 6. - HP 35s | HP 35s scientific calculator - User Guide - Page 255
routine. Also, estimate y for an x value of 37. Estimate x for a y value of 101. X 40.5 38.6 37.9 36.2 35.1 34.6 Y 104.5 102 100 97.5 95.5 94 Keys: (In RPN mode) S Display: value Description: Starts straight-line routine. Enters x-value of data pair. Statistics Programs 16-9 - HP 35s | HP 35s scientific calculator - User Guide - Page 256
Keys: (In RPN mode) Display: Description: U R Enters wrong x-value of data pair. Retrieves prompt. Deletes the last pair. Now proceed with the correct data entry. Enters correct x-value of data pair. Enters y-value of data pair. Enters x-value of data pair. Enters y-value of data - HP 35s | HP 35s scientific calculator - User Guide - Page 257
model assumes that the sample distribution is symmetric about the mean, M, with a standard deviation, S, and approximates the shape of the bell- shaped curve shown below. Given a value x, this program calculates the probability that a random selection from the sample data will have a higher value - HP 35s | HP 35s scientific calculator - User Guide - Page 258
y "Upper tail" area Q [x] x x ∫ Q(x) = 0.5 − 1 e dx x −((x −x )÷σ )2 ÷2 σ 2π x This program uses the built-in integration feature of the HP 35s to integrate the equation of the normal frequency curve. The inverse is obtained using Newton's method to iteratively search for a value of x which - HP 35s | HP 35s scientific calculator - User Guide - Page 259
Listing: Program Lines: (In RPN mode) Description This routine initializes the normal distribution program. Stores default value for mean. Prompts for and stores mean, M. Stores default value for standard deviation. Prompts for and stores standard deviation, S. Stops displaying - HP 35s | HP 35s scientific calculator - User Guide - Page 260
Program Lines: (In RPN mode) Description Adds the correction to yield a new Xguess. Tests to see if the correction is significant. Goes back to start of loop if correction is significant. Continues if correction is not significant. Displays the calculated value of X. Loops to - HP 35s | HP 35s scientific calculator - User Guide - Page 261
Lines: (In RPN mode) Description Returns to the calling routine. Checksum and length: B3EB 31 Flags Used: None. Remarks: The accuracy of this program is dependent on the display setting. For inputs in the area between ±3 standard deviations, a display of four or - HP 35s | HP 35s scientific calculator - User Guide - Page 262
10,000 possible blind dates. How many people fall into the "3σ" band? Since this problem is stated in terms of standard deviations, use the default value of zero for M and 1 for S. Keys: (In RPN mode) S Display: 16-16 Statistics Programs Description: Starts the initialization routine. - HP 35s | HP 35s scientific calculator - User Guide - Page 263
rerun simply by pressing . Keys: (In RPN mode) Display: Example 2: Description: Resumes program. Enters X-value of 2 and calculates Q(X). Multiplies by the population for the revised estimate. The mean of a set of test scores is 55. The standard deviation is 15.3. Assuming that the - HP 35s | HP 35s scientific calculator - User Guide - Page 264
mean. Stores 15.3 for the standard deviation. Starts the distribution program and prompts for X. Enters 90 for X and calculates Q(X). Thus, we would expect that only about 1 percent of the students would do better than score 90. Keys: (In RPN mode) Display: Description: I Starts the - HP 35s | HP 35s scientific calculator - User Guide - Page 265
input data, correct entries, and calculate the standard deviation and weighted mean of the grouped data. Program Listing: Program Lines: (In ALG mode) Description Start grouped standard deviation program. Clears statistics registers (-27 through -32). Clears the count N. Checksum and - HP 35s | HP 35s scientific calculator - User Guide - Page 266
F6CB 84 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: DAF2 24 Undo data-entry error. Enters decrement for - HP 35s | HP 35s scientific calculator - User Guide - Page 267
frequency. Data-pair counter. Grouped standard deviation. Weighted mean. Index variable used to indirectly address the correct statistics register. Summation Σfi. Summation Σxifi. Summation Σxi2fi. Enter the following data and calculate the grouped standard deviation. Statistics Programs 16-21 - HP 35s | HP 35s scientific calculator - User Guide - Page 268
xi fi 1 2 3 4 5 6 5 8 13 15 22 37 17 26 37 43 73 115 Keys: (In ALG mode) S Display: value value Description: Prompts for the first xi. Stores 5 in X; prompts for first fi. Stores 17 in F; displays the counter. Prompts for the second xi. Prompts for second fi - HP 35s | HP 35s scientific calculator - User Guide - Page 269
fifth xi. Prompts for the fifth fi. Displays the counter. Prompts for the sixth xi. Prompts for the sixth fi. Displays the counter. Calculates and displays the grouped standard deviation (sx) of the six data points. Calculates and displays weighted mean ( x ). Clears VIEW. Statistics Programs 16-23 - HP 35s | HP 35s scientific calculator - User Guide - Page 270
16-24 Statistics Programs - HP 35s | HP 35s scientific calculator - User Guide - Page 271
Programs and Equations Time Value of Money Given any four of the five values in the "Time-Value-of-Money equation" (TVM), you can solve for the fifth value. This equation is useful in a wide variety of financial applications such as consumer and home loans and savings accounts. The TVM equation - HP 35s | HP 35s scientific calculator - User Guide - Page 272
Entry: Key in this equation: Keys: (In RPN mode) P 4 4 I NÕ I F 4 I N B (hold) Display: Description: or current equation Selects Equation mode. Starts entering equation. Terminates the equation. Checksum and length. Remarks - HP 35s | HP 35s scientific calculator - User Guide - Page 273
for. SOLVE instructions: 1. If your first TVM calculation is to solve for interest rate, I, press I. 2. Press . If necessary, press × or Ø to scroll through the equation list until you come to the TVM equation. 3. Do one of the following five operations: a. Press N to calculate the number of - HP 35s | HP 35s scientific calculator - User Guide - Page 274
Used: N The number of compounding periods. I The periodic interest rate as a percentage. (For example, if the Display: (In RPN mode) 8 (Ø as needed P value value value Description: Selects FIX 2 display format. Displays the leftmost part of the TVM equation. - HP 35s | HP 35s scientific calculator - User Guide - Page 275
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 borrower (the beginning balance) is positive, while money paid out is negative. Miscellaneous Programs and Equations 17-5 - HP 35s | HP 35s scientific calculator - User Guide - Page 276
rate would reduce the monthly payment by $10? Keys: (In RPN mode) Display: Description: I Displays the leftmost hart of the TVM equation. Selects I; prompts for P. Rounds the payment to two decimal places. Calculates new payment. Stores -176.89 in P; prompts for N. Retains 36 - HP 35s | HP 35s scientific calculator - User Guide - Page 277
for B. Retains 5750 in B; calculates F, the future balance. Again, the sign is negative, indicating that you must, pay out this money. Sets FIX 4 display format. Prime Number Generator This program accepts any positive integer greater than 3. If the number is a prime number (not evenly divisible by - HP 35s | HP 35s scientific calculator - User Guide - Page 278
LBL Y Note: x is the value in the X-register. VIEW Prime LBL Z P+2 →x Start LBL P x→ P 3→ D LBL X yes x = 0? no yes no 17-8 Miscellaneous Programs and Equations - HP 35s | HP 35s scientific calculator - User Guide - Page 279
Program Listing: Program Lines: (In ALG mode) Description This routine displays prime number P. Checksum and length: 2CC5 6 This routine adds 2 to P. Checksum and length: EFB2 9 This routine stores the input value for P. Tests for even input Increments P - HP 35s | HP 35s scientific calculator - User Guide - Page 280
that the input is greater than 3. Example: What is the first prime number after 789? What is the next prime number? Keys: (In ALG mode) P Display: Description: Calculates next prime number after 789. Calculates next prime number after 797. 17-10 Miscellaneous Programs and Equations - HP 35s | HP 35s scientific calculator - User Guide - Page 281
the program function to calculate the cross product. Cross product: where v1 × v2 = (YW - ZV )i + (ZU - XW)j + (XV - YU)k v1 = X i + Y j + Z k and v2=U i + V j + W k Program Lines: (In RPN mode) Description Defines the beginning of the rectangular input/display routine. Displays or - HP 35s | HP 35s scientific calculator - User Guide - Page 282
Program Lines: (In RPN mode) Description Defines the beginning of the cross-product routine. Calculates (YW - ZV), which is the X component. Calculates (ZU - WX), which is the Y component. Stores (XV - YU), which is the Z component - HP 35s | HP 35s scientific calculator - User Guide - Page 283
Keys: R z E C Display: Description: Run R routine to input vector value Input v2 of x- C routine to calculate x- component of cross product Calculate y-component of cross product Calculate z-component of cross product Miscellaneous Programs and Equations 17-13 - HP 35s | HP 35s scientific calculator - User Guide - Page 284
17-14 Miscellaneous Programs and Equations - HP 35s | HP 35s scientific calculator - User Guide - Page 285
Part 3 Appendixes and Reference - HP 35s | HP 35s scientific calculator - User Guide - Page 286
- HP 35s | HP 35s scientific calculator - User Guide - Page 287
of memory? A: displays the CLEAR menu, which allows you to clear x (the number in the X-register), all direct variables, all of memory, all statistical data, all stack levels and all indirect variables Q: What does an "E" in a number (for example mean? Support, Batteries, and Service A-1 - HP 35s | HP 35s scientific calculator - User Guide - Page 288
mode (9 or Q: What does an annunciator in the display mean? A: It indicates something about the status of the calculator. See "Annunciators" in chapter 1. Q: Numbers show up as fractions. How do I get decimal numbers relative humidity at 40 °C (104 °F) maximum. A-2 Support, Batteries, and Service - HP 35s | HP 35s scientific calculator - User Guide - Page 289
removed, the contents of Continuous Memory will be erased. 用 BK+B 3. Turn the calculator over and slide off the battery cover. 4. To prevent memory loss, never remove two old batteries at the same time. Be sure to remove and replace the batteries one at a time. Support, Batteries, and Service A-3 - HP 35s | HP 35s scientific calculator - User Guide - Page 290
. Hold down the key and press . It may be necessary to repeat these reset keystrokes several times. 2. Erase memory. Press and hold down , then press and hold down both and 6. Memory is cleared and the message is displayed when you release all three keys. A-4 Support, Batteries, and Service - HP 35s | HP 35s scientific calculator - User Guide - Page 291
fails the self test, it requires service. 2. If the calculator passes the self-test, you may have made a mistake operating the calculator. Reread portions of the manual and check "Answers to Common Questions" (page A-1). 3. Contact the Calculator Support Department listed on page A-8. The Self-Test - HP 35s | HP 35s scientific calculator - User Guide - Page 292
fail message with the calculator when you ship it for service. 5. To exit the self-test, reset the calculator (hold down and press ). Pressing and 9 starts a continuous self-test that is used at the factory. You can halt this factory test by pressing any key. A-6 Support, Batteries, and Service - HP 35s | HP 35s scientific calculator - User Guide - Page 293
Warranty HP 35s Scientific Calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above. If HP receives notice of such - HP 35s | HP 35s scientific calculator - User Guide - Page 294
TO THE EXTENT LAWFULLY PERMITTED, DO NOT EXCLUDE, RESTRICT OR MODIFY AND ARE IN ADDITION TO THE MANDATORY STATUTORY RIGHTS APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU. Customer Support AP Country : Australia Telephone numbers 1300-551-664 or 03-9841-5211 A-8 Support, Batteries, and Service - HP 35s | HP 35s scientific calculator - User Guide - Page 295
574-2700 +65 6100 6682 6100 6682 2-561-2700 +852 2805-2563 +65 6100 6682 +65 6100 6682 Telephone numbers 01 360 277 1203 02 620 00 86 02 620 00 85 296 335 612 82 33 28 44 09 8171 23500027 021 318 0093 495 228 3050 0800980410 913753382 08 5199 2065 022 827 8780 Support, Batteries, and Service A-9 - HP 35s | HP 35s scientific calculator - User Guide - Page 296
5308 0207 458 0161 LA Country : Telephone numbers Anguila Antigua Argentina Aruba Bahamas Barbados Bermuda 2881 + 800-711-2884 800-360-999 01-8000-51-4746-8368 (01-8000-51- HP INVENT) 0-800-011-0524 1-800-711-2884 1-800-711-2884 1-999-119 ♦ 800- 711-2884 A-10 Support, Batteries, and Service - HP 35s | HP 35s scientific calculator - User Guide - Page 297
800-711-2884 1-800-711-2884 01-800-711-2884 1-800-711-2884 0004-054-177 0-800-474-68368 (0-800 HP INVENT) NA Country : Canada USA Telephone numbers 800-HP-INVENT 800-HP INVENT Please logon to http://www.hp.com for the latest service and support information. Support, Batteries, and Service A-11 - HP 35s | HP 35s scientific calculator - User Guide - Page 298
used in accordance with the instructions, may cause harmful interference to by Hewlett-Packard Company may void the user's authority to operate the equipment. Declaration Operation is subject to the following two conditions: (1) this device may not cause harmful Support, Batteries, and Service - HP 35s | HP 35s scientific calculator - User Guide - Page 299
conformity to applicable harmonized European standards (European Norms) which are listed on the EU Declaration of number (used only if applicable - refer to the product label) Hewlett-Packard GmbH, HQ-TRE, Herrenberger Strasse 140, 71034 Boeblingen, Germany Support, Batteries, and Service - HP 35s | HP 35s scientific calculator - User Guide - Page 300
Equipment by Users in service or the shop where you purchased the product. Perchlorate Material - special handling may apply This calculator's Memory Backup battery may contain perchlorate and may require special handling when recycled or disposed in California. A-14 Support, Batteries, and Service - HP 35s | HP 35s scientific calculator - User Guide - Page 301
without affecting memory, How to clear (purge) all of user memory and reset the system defaults, and Which operations affect stack lift. Managing Calculator Memory The HP 35s has 30KB of user memory available to you for any combination of stored data (variables, equations, or program lines). SOLVE - HP 35s | HP 35s scientific calculator - User Guide - Page 302
Equation mode or the left end of the current equation will be displayed.) 2. If necessary, scroll through the equation list (press × or Ø ) until you see the desired equation. 3. Press to see the checksum (hexadecimal) and length (in bytes) of the equation. For example To see the total memory - HP 35s | HP 35s scientific calculator - User Guide - Page 303
unable to restore operation by resetting it or changing the batteries, try the following MEMORY CLEAR procedure. These keystrokes clear all of memory, reset the calculator, and restore all format and modes to their original, default settings (shown below): 1. Press and hold down the key. 2. Press - HP 35s | HP 35s scientific calculator - User Guide - Page 304
Category CLEAR ALL MEMORY CLEAR (Default) Angular mode Base mode Contrast setting Decimal point Thousand separator Denominator (/c value) Display format Flags Complex mode Fraction-display mode Random-number seed Equation pointer Equation list FN = label Program pointer Program memory Stack lift - HP 35s | HP 35s scientific calculator - User Guide - Page 305
for prompting (so any number then entered writes over the X-register), but it enables stack lift when the program resumes. Neutral Operations The following operations do not affect the status of stack lift: DEG, RAD, FIX, SCI, DEC, HEX, CLVARS GRAD ENG, ALL OCT, BIN PSE SHOW RADIX . RADIX - HP 35s | HP 35s scientific calculator - User Guide - Page 306
save x in the LAST X register in RPN mode: LN, LOG SIN, COS, TAN SINH, number in LASTx. In ALG mode, the LAST X register is a companion to the stack: it holds the number that is the result of last expression. It supports using the previous expression result in ALG mode. B-6 User Memory - HP 35s | HP 35s scientific calculator - User Guide - Page 307
. Pressing will place an instruction into a program or equation that recalls the value of the chosen stack register for further use. These are displayed as REGX, REGY, REGZ, and REGT. For example, a program line entered by first pressing d and then entering the instructions REGX x REGY x REGZ - HP 35s | HP 35s scientific calculator - User Guide - Page 308
B-8 User Memory and the Stack - HP 35s | HP 35s scientific calculator - User Guide - Page 309
Trigonometric functions Parts of numbers Reviewing the stack Operations with complex numbers Integrating an equation Arithmetic in bases 2, 8, and 16 Entering statistical two-variable data Press 9 to set the calculator to ALG mode. When the calculator is in ALG mode, the ALG annunciator is - HP 35s | HP 35s scientific calculator - User Guide - Page 310
{) Quotient and Remainder of Division Simple Arithmetic Here are some examples of simple arithmetic. In ALG mode, you enter the first number, press the operator enter the second number, and finally press the key. To Calculate: 12 + 3 12 - 3 12 × 3 12 ÷ 3 Press: Display C-2 ALG: Summary - HP 35s | HP 35s scientific calculator - User Guide - Page 311
Functions In ALG mode, to calculate a number y raised to a power x, key in y x, then press . To Calculate: 123 Press: Display 641/3 (cube root) Õ64 Percentage Calculations The Percent Function. The key divides a number by 100. To Calculate: Press: Display: 27% of - HP 35s | HP 35s scientific calculator - User Guide - Page 312
by 58 ÷ 9 Keys: 9 9 Display Parentheses Calculations Description: Displays the quotient. Displays the remainder. Use parentheses when you want to postpone calculating an intermediate result until you entered more numbers. For example, suppose you want to calculate: 30 × 9 85 − 12 - HP 35s | HP 35s scientific calculator - User Guide - Page 313
: No calculation is done. Calculates 85 − 12. Calculates 30/73. 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 - HP 35s | HP 35s scientific calculator - User Guide - Page 314
of x. Press: Display: Hyperbolic functions To Calculate: Hyperbolic sine key in a number, press key in a number,press key in a number, press key in a number,press key in a number,press key in a number,press C-6 - HP 35s | HP 35s scientific calculator - User Guide - Page 315
Parts of numbers To calculate: The integer part of 2.47 The fractional part of 2.47 The absolute value of -7 Press: The sign value of 9 The greatest integer equal to or less than -5.3 Display Reviewing the Stack The or key produces a menu in the display - HP 35s | HP 35s scientific calculator - User Guide - Page 316
scroll through the equation list (press × or Ø) to display the desired equation. 4. Select the variable of integration: Press variable. This starts the calculation. Operations with Complex Numbers To enter a complex number: Form: 1. Type the real part. 2. Press6. 3. Type the imaginary part - HP 35s | HP 35s scientific calculator - User Guide - Page 317
two complex numbers: 1. Enter the first complex number, z1. 2. Select the arithmetic operation. 3. Enter the second complex number, z2. 4. Press to calculate. 5. The calculated result will be displayed in Line 2 and the displayed form will be the one that you have set in 9. Here are some examples - HP 35s | HP 35s scientific calculator - User Guide - Page 318
Keys: 4 6Õ4 6 Display: Description: Result is 11.7333 i-3.8667 Arithmetic in Bases 2, 8, and 16 Here are some examples of arithmetic in Hexadecimal, Octal, and Binary modes: Example: Keys: 12F16 + E9A16 = ? Display: Description: Sets base 16; HEX annunciator on. C-10 ALG - HP 35s | HP 35s scientific calculator - User Guide - Page 319
on. Converts displayed number to octal. 1008 ÷ 58=? Integer part of result. 5A016 + 100110002 =? A0 Set base 16; HEX annunciator on. Result in hexadecimal base. Restores decimal base. Entering Statistical Two-Variable Data In ALG mode, remember to - HP 35s | HP 35s scientific calculator - User Guide - Page 320
4. After deleting the incorrect statistical data, the calculator will display the last statistical data entered in line 1 (top line of the display) and value of n in line 2. If there are no statistical data, the calculator will display n=0 in line 2. Example: After keying in the x, y-values on the - HP 35s | HP 35s scientific calculator - User Guide - Page 321
Linear Regression Linear regression, or L.R. (also called linear estimation), is a statistical method for finding a straight line that best fits a set of x,y-data. To find an estimated value for x (or y), key in a given hypothetical value for y (or x) ,press , then press or To find the values - HP 35s | HP 35s scientific calculator - User Guide - Page 322
C-14 ALG: Summary - HP 35s | HP 35s scientific calculator - User Guide - Page 323
SOLVE first attempts to solve the equation directly for the unknown variable. numbers of the calculator, and the function must be mathematically defined where the iterative search occurs. SOLVE always finds a root, provided one exists (within the overflow bounds), if one or more of these conditions - HP 35s | HP 35s scientific calculator - User Guide - Page 324
situations, the calculated root is an accurate estimate of the theoretical, infinitely precise root of the equation. An "ideal" solution is one for which f(x) = 0. However, a very small non-zero value for f(x) is often acceptable because it might result from approximating numbers with limited (12 - HP 35s | HP 35s scientific calculator - User Guide - Page 325
a solution under either of the following conditions: If it finds an estimate for which f(x) equals zero. (See figure a, below.) If it finds an estimate where f(x) is not equal to zero, but the calculated root is a 12-digit number adjacent to the place where the function's graph crosses the x-axis - HP 35s | HP 35s scientific calculator - User Guide - Page 326
mode; displays the left end of the equation. 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 - HP 35s | HP 35s scientific calculator - User Guide - Page 327
root. Selects Equation mode; displays the equation. Calculates the positive root using guesses 0 and 10. Final two estimates are the same. f(x) = 0. Your initial guesses for the negative root. Redisplays the equation. Calculates negative root using guesses 0 and -10. f(x) = 0. Certain cases require - HP 35s | HP 35s scientific calculator - User Guide - Page 328
the calculation to halt with an error message. f (x) f (x) x x a b Special Case: A Discontinuity and a Pole Example: A Discontinuous Function. Find the root of the equation: IP(x) = 1.5 Enter the equation: Keys: X Display: Description: Selects Equation mode. Enter the equation - HP 35s | HP 35s scientific calculator - User Guide - Page 329
sign for f(x). Example: Find the root of the equation x x2 − 6 − 1= 0 As x approaches 6 , f(x) becomes a very large positive or negative number. Enter the equation as an expression. Keys: Display: X4 X Description: Selects Equation mode. Enters the equation. More about - HP 35s | HP 35s scientific calculator - User Guide - Page 330
Equation mode. Description: Your initial guesses for the root. Selects Equation mode; displays the equation. No root found for f(x). When SOLVE Cannot Find a Root Sometimes SOLVE fails to find a root. The following conditions c, below). In these cases, the values in the stack will be same as - HP 35s | HP 35s scientific calculator - User Guide - Page 331
x c Case Where No Root Is Found Example: A Relative Minimum. Calculate the root of this parabolic equation: It has a minimum at x = 3. x2 - 6x + 13 = 0. Enter the equation as an expression: Keys: Display: X X Description: Selects Equation mode. Enters the equation. More about - HP 35s | HP 35s scientific calculator - User Guide - Page 332
: Display: X X Example: An Asymptote. Checksum and length. Cancels Equation mode. Description: Your initial guesses for the root. Selects Equation mode; displays the equation. Search fails with guesses 0 and 10 Find the root of the equation 10 − 1 = 0 X Enter the equation as - HP 35s | HP 35s scientific calculator - User Guide - Page 333
positive root: Keys: Display: X X Description: Selects Equation mode. Enters the equation. Checksum and length. Cancels Equation mode. Description: Your positive guesses for the root. Selects Equation mode; displays the left end of the equation. Calculates the root using guesses - HP 35s | HP 35s scientific calculator - User Guide - Page 334
Selects Equation mode; displays the left end of the equation. No root found for f(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 the function as the program Checksum - HP 35s | HP 35s scientific calculator - User Guide - Page 335
guesses of 10-8 and -10-8. Keys: (In RPN mode) Display: Description: X J X Enters guesses. Selects program "J" as the function. Solves for X; displays the result. Round-Off Error The limited (12-digit) precision of the calculator can cause errors due to rounding off, which - HP 35s | HP 35s scientific calculator - User Guide - Page 336
D-14 More about Solving - HP 35s | HP 35s scientific calculator - User Guide - Page 337
, 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 considering the inherent uncertainty - HP 35s | HP 35s scientific calculator - User Guide - Page 338
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 35s is one of the best available, in certain situations it - like all other - HP 35s | HP 35s scientific calculator - User Guide - Page 339
f (x) x With this number of sample points, the algorithm will calculate the same approximation for the integral of any of the functions shown. The actual integrals of the functions shown with solid blue and black lines are about the same, so the approximation will be fairly accurate if f(x) is one - HP 35s | HP 35s scientific calculator - User Guide - Page 340
accuracy level and limits of integration. Selects Equation mode; displays the equation. 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 - HP 35s | HP 35s scientific calculator - User Guide - Page 341
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 - HP 35s | HP 35s scientific calculator - User Guide - Page 342
the width of the interval of integration. With a given number of sample points, a function 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 - HP 35s | HP 35s scientific calculator - User Guide - Page 343
evaluate the integral by replacing ∞, the upper limit of integration, by a number not so large as 10499 - say 103. Rerun the previous integration problem with this new limit of integration: Keys: Display: _ Description: New upper limit. Selects Equation mode; displays the equation. More - HP 35s | HP 35s scientific calculator - User Guide - Page 344
larger interval is much greater than the number required over the smaller interval. Consequently, several more iterations are required over the larger interval to achieve an approximation with the same accuracy, and therefore calculating the integral requires considerably more time. E-8 More about - HP 35s | HP 35s scientific calculator - User Guide - Page 345
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 - HP 35s | HP 35s scientific calculator - User Guide - Page 346
E-10 More about Integration - HP 35s | HP 35s scientific calculator - User Guide - Page 347
) while another integration calculation was running. A running program attempted to solve a program while an integration calculation was running. The catalog of variables indicates no values stored. You set a wrong guess number (like a complex number or vector) when SOLVING equation for a variable - HP 35s | HP 35s scientific calculator - User Guide - Page 348
so is also the "equation" after the last equation in equation memory. The calculator is calculating the integral of an equation or program. This might take a while. A running CALCULATE,SOLVE or ∫ FN operation was interrupted by pressing or in ALG, RPN, EQN, or PGM mode. Data error: Attempted to - HP 35s | HP 35s scientific calculator - User Guide - Page 349
negative number. All of user memory has been erased (see page ). The calculator has insufficient memory available to do the operation (See appendix B). The condition checked by a test instruction is not true. (Occurs only when executed from the keyboard.) Attempted to refer to a nonexistent program - HP 35s | HP 35s scientific calculator - User Guide - Page 350
program line (the line following the instruction variable). Warning (displayed momentarily); the magnitude of a result is too large for the calculator to handle. The calculator returns ±9.99999999999E499 in the current display format. (See "Range of Numbers and Overflow" on page .) This condition - HP 35s | HP 35s scientific calculator - User Guide - Page 351
The condition checked by a test instruction is true. (Occurs only when executed from the keyboard.) Self-Test Messages: n The self-test and the keyboard test passed. The self-test or the keyboard test failed, and the calculator requires service. Copyright message displayed after successfully - HP 35s | HP 35s scientific calculator - User Guide - Page 352
F-6 Messages - HP 35s | HP 35s scientific calculator - User Guide - Page 353
; function names preceded by arrows (for example, DEG) are alphabetized as if the arrow clears x; clears a menu; erases last function keyed in an equation; deletes an equation; deletes a program step. Displays previous entry in catalog; moves to previous equation in equation list; moves program - HP 35s | HP 35s scientific calculator - User Guide - Page 354
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. Goes to the top line of the equation or the first line of the last label in program mode. Goes to the last line of the equation or the first line of - HP 35s | HP 35s scientific calculator - User Guide - Page 355
sum of squares of y- values. Returns population standard deviation of x-values: 12-7 1 ∑ (xi − x )2 ÷ n Returns population standard deviation of y-values: 12-7 1 ∑ (yi − y )2 ÷ n variable 8-2 Integrates the displayed equation or the program selected by FN=, using lower limit of the - HP 35s | HP 35s scientific calculator - User Guide - Page 356
Returns cosh -1 x. Activates Algebraic mode. Common exponential. Returns 10 raised to the specified power (antilogarithm). 8 Displays all significant digits. May have to scroll right (Õ) to see all of the digits 1AND) Logic operator = Replaces a complex number with its Argument "θ" Arc - HP 35s | HP 35s scientific calculator - User Guide - Page 357
Description Page Indicates a binary number Displays the base-conversion menu. 11-2 1 11-1 Selects Binary (base 2) mode. 11-1 Turns on calculator; clears x; clears messages and prompts; cancels menus; cancels catalogs; cancels equation entry; cancels program entry; halts execution of an - HP 35s | HP 35s scientific calculator - User Guide - Page 358
indicates a decimal number 11-1 1 Selects Decimal mode. 9 Selects Degrees angular mode. 11-1 4-4 Radians to degrees. Returns (360/2π) x. 4-13 1 Displays menu to set the display format, radix ( or ), thousand separator, and display format of complex number. 1-21 variable - HP 35s | HP 35s scientific calculator - User Guide - Page 359
to the specified power. Converts °C to °F. Turns on and off Fraction-display mode. 8 n Selects Fixed display with n decimal places: 0 ≤ n ≤ 11. Displays the menu to set, clear, and test flags. label Selects labeled program as the current function (used by SOLVE and ∫ FN). Fractional part - HP 35s | HP 35s scientific calculator - User Guide - Page 360
nnn of program label. Sets program pointer to PRGM TOP. 13-21 13-21 Indicates a hexadecimal number 11-1 1 Selects Hexadecimal (base 16) mode. 11-1 Displays the HYP_ prefix for 4-6 hyperbolic functions. 4-13 1 Hours to hours, minutes, seconds. Converts x from a decimal fraction - HP 35s | HP 35s scientific calculator - User Guide - Page 361
greatest integer equal to or less than given number. 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 - HP 35s | HP 35s scientific calculator - User Guide - Page 362
to miles. Displays the amount of available memory and the catalog menu. Begins catalog of programs. Page 13-3 4-1 1 4-1 1 12-4 12-7 1 4-14 1 1-28 13-22 Begins catalog of variables. 3-4 Displays menu to set ALG or RPN mode or angular modes. () Returns the number of sets of data points - HP 35s | HP 35s scientific calculator - User Guide - Page 363
, or equation, then resumes. (Used only in programs.) 13-18 13-19 Returns the 12-7 1 correlation coefficient between the x- and y-values: ∑(xi − x )(yi − y ) ∑(xi − x )2 × (yi − y )2 8 1-25 Changes the display of complex numbers. 9 4-4 Selects Radians angular mode. Degrees - HP 35s | HP 35s scientific calculator - User Guide - Page 364
x to n decimal places in FIX n 5-8 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. 9 Activates Reverse 1-9 Polish notation. Return. Marks the end of a program; the program pointer - HP 35s | HP 35s scientific calculator - User Guide - Page 365
Scientific display with n decimal places. (n = 0 through 11.) 1-22 Restarts the random- 4-15 number sequence with the seed x . n Sets flag n (n = 0 through 11). 14-12 Indicates the sign of x. 4-17 1 Shows the full mantissa (all 12 digits) of x (or the number in the current program - HP 35s | HP 35s scientific calculator - User Guide - Page 366
standard deviation of y-values: ∑ (yi − y )2 ÷ (n − 1) Tangent. Returns tan x. Hyperbolic tangent. Returns tanh x. variable Displays the labeled contents of variable without recalling the value to the stack. Evaluates the displayed equation. label Executes the program identified - HP 35s | HP 35s scientific calculator - User Guide - Page 367
y to the X-register. Displays the "x?y" comparison tests menu. If x≠y, executes next program line; if x=y, skips next program line. If x≤y, executes next program line; if x>y, skips next program line. If xy, executes - HP 35s | HP 35s scientific calculator - User Guide - Page 368
-7 If x≥0, executes next program line; if x - HP 35s | HP 35s scientific calculator - User Guide - Page 369
Name yˆ yx Keys and Description Given an x-value in the X-register, returns the y-estimate based on the regression line: yˆ = m x + b. Power. Returns y raised to the xth power. Page 12-11 1 4-2 1 Notes: 1. Function can be used in equations. Operation Index G-17 - HP 35s | HP 35s scientific calculator - User Guide - Page 370
G-18 Operation Index - HP 35s | HP 35s scientific calculator - User Guide - Page 371
annunciator 1-3, 3-2, 6-4 absolute value (real number) 4-17 addressing indirect 14-20, 14-21, 14-23 ALG 1-9 compared to equations 13-4 in programs 13-4 Algebraic mode 1-9 ALL format. See display format in equations 6-5 in programs 13-7 setting 1-23 alpha characters 1-3 angles between vectors 10 - HP 35s | HP 35s scientific calculator - User Guide - Page 372
programs 1-29, 13-23 statistics registers 12-2 variables 1-28 X-register 2-3, 2-7 clearing memory A-4, B-3 combinations 4-15 commas (in numbers) 1-23, A-1 comparison tests 14-7 complex numbers argument value 4-17 coordinate systems 9-5 entering 9-1 on stack 9-2 operations 9-2 viewing 9-2 conditional - HP 35s | HP 35s scientific calculator - User Guide - Page 373
) 1-16 E in numbers 1-15, 1-22, A-1 ENG format 1-22 See also display format entry cursor backspacing 1-4 meaning 1-17 EQN annunciator in equation list 6-4, 6-7 in Program mode 13-7 EQN LIST TOP 6-7, F-2 equality equations 6-9, 6-11, 7-1 equation list adding to 6-4 displaying 6-6 editing 6-8 EQN - HP 35s | HP 35s scientific calculator - User Guide - Page 374
F ∫ FN. See integration not programmable 5-10 toggles display mode 5-1, A-2 toggles flag 14-9 factorial function 4-15 financial calculations 17-1 FIX format 1-21 See also display format flags annunciators 14-12 clearing 14-12 default states 14-9 equation evaluation 14-11 equation prompting 14-11 - HP 35s | HP 35s scientific calculator - User Guide - Page 375
hex numbers Horner's method 13-26 humidity limits for calculator A-2 hyperbolic functions 4-6, C-6 I i 3-9, 14-20 (i) 14-20, 14-21, 14-23 imaginary part (complex numbers) 9-1, C-8 indirect addressing 14-20, 14-21, 14- 23 INPUT always prompts 14-11 entering program data 13-12 in integration programs - HP 35s | HP 35s scientific calculator - User Guide - Page 376
B-1 MEMORY CLEAR A-4, B-3, F-3 MEMORY FULL B-1, F-3 menu keys 1-6 menus example of using 1-8 general operation 1-6 leaving 1-4, 1-8 list of 1-6 messages clearing 1-4 displaying 13-16, 13-18 in equations 13-16 responding to 1-27, F-1 summary of F-1 minimum of function D-8 modes. See angular mode - HP 35s | HP 35s scientific calculator - User Guide - Page 377
13-23 clearing 13-6 duplicate 13-6 entering 13-4, 13-6 executing 13-10 indirect addressing 14-20, 14-21, 14-23 moving to 13-22 purpose 13-4 typing name 1-3 viewing 13-22 program lines. See programs program names. See program labels program pointer 13-6, 13-11, 13-19, 13-21, B-4 Program-entry mode - HP 35s | HP 35s scientific calculator - User Guide - Page 378
13-14 RCL arithmetic 3-7 real numbers operations 4-1 real part (complex numbers) 9-1 recall arithmetic 3-7 rectangular-to-polar coordinate conversion 4-10, 9-5 regression (linear) 12-7, 16-1 resetting the calculator A-4, B-2 return (program). See programs Reverse Polish Notation. See RPN Index-8 - HP 35s | HP 35s scientific calculator - User Guide - Page 379
digits 6-14 14-14 sample standard deviations 12-6 SCI format. See display format in programs 13-7 setting 1-22 scrolling binary numbers 11-8 equations 6-7, 13-7, 13-16 seed (random number) 4-15 self-test (calculator) A-5 shift keys 1-3 sign (of numbers) 1-15, 9-3, 11-6 sign conventions (finance - HP 35s | HP 35s scientific calculator - User Guide - Page 380
of 1-28, 3-4 clearing 1-28 clearing all 1-5 clearing while viewing 13-15 exchanging with X 3-8 in equations 6-3, 7-1 in programs 13-12, 15-1, 15-7 indirect addressing 14-20, 14-21 names 3-1 number storage 3-1 of integration 8-2, 15-7, C-8 polynomials 13-26 program input 13-14 program output 13-15 - HP 35s | HP 35s scientific calculator - User Guide - Page 381
conversions 4-14 weighted means 12-4 windows (binary numbers) 11-8 X evaluating equations 6-10, 6-12 running programs 13-10, 13-22 X ROOT arguments 6-17 X-register affected by prompts 6-14 arithmetic with variables 3-6 clearing 1-5, 2-3, 2-7 clearing in programs 13-7 displayed 2-3 during programs - HP 35s | HP 35s scientific calculator - User Guide - Page 382
Index-12
HP
35s scientific calculator
user's guide
H
Edition 1
HP part number
F2215AA-90001