HP 35s User manual

HP 35s scientific calculator

user's guide

H

Edition 1

HP part number F2215AA-90001

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Hewlett-Packard Company

16399 West Bernardo Drive

MS 8-600

San Diego, CA 92127-1899

USA

Printing History

Edition 1 February 2007

Contents 1

Contents

Part 1. Basic Operation

1. Getting Started............................................................1-1

Important Preliminaries............................................................. 1-1

Turning the Calculator On and Off ....................................... 1-1

Adjusting Display Contrast................................................... 1-1

Highlights of the Keyboard and Display ..................................... 1-2

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

Range of Numbers and OVERFLOW................................... 1-17

Performing Arithmetic Calculations........................................... 1-18

Single Argument or Unary Operations................................. 1-18

Two Argument or Binary Operations ................................... 1-19

Controlling the Display Format ................................................ 1-21

Periods and Commas in Numbers   .......................... 1-23

2 Contents

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 are in the Display................................2-3

Clearing the X–Register........................................................2-3

Reviewing the Stack ............................................................2-3

Exchanging the X– and Y–Registers in the Stack......................2-4

Arithmetic – How the Stack Does It.............................................2-5

How ENTER Works .............................................................2-6

How to Clear the Stack ........................................................2-7

The LAST X Register..................................................................2-8

Correcting Mistakes with LAST X ..........................................2-9

Reusing Numbers with LAST X ............................................2-10

Chain Calculations in RPN Mode.............................................2-12

Work from the Parentheses Out ..........................................2-12

Exercises..........................................................................2-14

Order of Calculation .........................................................2-14

More Exercises .................................................................2-16

3. Storing Data into Variables .........................................3-1

Storing and Recalling Numbers .................................................3-2

Viewing a Variable .................................................................3-4

Contents 3

Using the MEM Catalog ........................................................... 3-4

The VAR catalog................................................................. 3-4

Arithmetic with Stored Variables................................................ 3-6

Storage Arithmetic .............................................................. 3-6

Recall Arithmetic................................................................. 3-7

Exchanging x with Any Variable ............................................... 3-8

The Variables "I" and "J".......................................................... 3-9

4. Real–Number Functions...............................................4-1

Exponential and Logarithmic Functions ....................................... 4-1

Quotient and Remainder of Division........................................... 4-2

Power Functions ...................................................................... 4-2

Trigonometry........................................................................... 4-3

Entering π.......................................................................... 4-3

Setting the Angular Mode.................................................... 4-4

Trigonometric Functions ....................................................... 4-4

Hyperbolic Functions................................................................ 4-6

Percentage Functions ............................................................... 4-6

Physics Constants .................................................................... 4-8

Conversion Functions ............................................................. 4-10

Rectangular/Polar Conversions .......................................... 4-10

Time Conversions ............................................................. 4-13

Angle Conversions............................................................ 4-13

Unit Conversions .............................................................. 4-14

Probability Functions .............................................................. 4-15

Factorial .......................................................................... 4-15

Gamma........................................................................... 4-15

Probability ....................................................................... 4-15

Parts of Numbers................................................................... 4-16

4 Contents

5. Fractions.....................................................................5-1

Entering Fractions ....................................................................5-1

Fractions in the Display.............................................................5-2

Display Rules ......................................................................5-2

Accuracy Indicators.............................................................5-3

Changing the Fraction Display...................................................5-4

Setting the Maximum Denominator........................................5-4

Choosing a Fraction Format .................................................5-6

Examples of Fraction Displays...............................................5-8

Rounding Fractions...................................................................5-8

Fractions in Equations...............................................................5-9

Fractions in Programs .............................................................5-10

6. Entering and Evaluating Equations...............................6-1

How You Can Use Equations.....................................................6-1

Summary of Equation Operations...............................................6-3

Entering Equations into the Equation List......................................6-4

Variables in Equations .........................................................6-4

Numbers in Equations..........................................................6-5

Functions in Equations .........................................................6-5

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 for Evaluation................................................6-11

Using XEQ for Evaluation...................................................6-12

Responding to Equation Prompts .........................................6-13

The Syntax of Equations..........................................................6-14

Contents 5

Operator Precedence........................................................ 6-14

Equation Functions............................................................ 6-16

Syntax Errors.................................................................... 6-19

Verifying Equations................................................................ 6-19

7. Solving Equations........................................................7-1

Solving an Equation................................................................. 7-1

Solving built-in Equation ...................................................... 7-6

Understanding and Controlling SOLVE....................................... 7-7

Verifying the Result ............................................................. 7-7

Interrupting a SOLVE Calculation.......................................... 7-8

Choosing Initial Guesses for SOLVE ...................................... 7-8

For More Information ............................................................. 7-12

8. Integrating Equations ..................................................8-1

Integrating Equations ( ∫ FN) .................................................... 8-2

Accuracy 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.Vector Arithmetic ......................................................10-1

Vector operations .................................................................. 10-1

Absolute value of the vector ............................................... 10-3

6 Contents

Dot product ......................................................................10-4

Angle between vectors.......................................................10-5

Vectors in Equations ...............................................................10-6

Vectors in Programs................................................................... 10-7

Creating Vectors from Variables or Registers ............................10-8

11.Base Conversions and Arithmetic and Logic................11-1

Arithmetic in Bases 2, 8, and 16 .............................................11-4

The Representation of Numbers ...............................................11-6

Negative Numbers............................................................11-6

Range of Numbers ............................................................11-7

Windows for Long 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 ................................................12-6

Population Standard Deviation............................................12-7

Linear Regression ..............................................................12-7

Limitations on Precision of Data .............................................12-10

Summation Values and the Statistics Registers..........................12-11

Summation Statistics ........................................................12-11

Access to the Statistics Registers ........................................12-12

Contents 7

Part 2. Programming

13.Simple Programming.................................................13-1

Designing a Program ............................................................. 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

Testing a Program........................................................... 13-11

Entering and Displaying Data ............................................... 13-12

Using INPUT for Entering Data ......................................... 13-13

Using VIEW for Displaying Data....................................... 13-15

Using Equations to Display Messages ............................... 13-16

Displaying Information without Stopping............................ 13-18

Stopping or Interrupting a Program ....................................... 13-19

Programming a Stop or Pause (STOP, PSE) ....................... 13-19

Interrupting a Running Program ........................................ 13-19

Error Stops..................................................................... 13-19

Editing a Program ............................................................... 13-20

Program Memory ................................................................ 13-21

Viewing Program Memory ............................................... 13-21

Memory Usage .............................................................. 13-22

The Catalog of Programs (MEM)....................................... 13-22

8 Contents

Clearing One or More Programs.......................................13-23

The Checksum ................................................................13-23

Nonprogrammable Functions ................................................13-24

Programming with BASE .......................................................13-24

Selecting a Base Mode in a Program.................................13-25

Numbers Entered in Program Lines ....................................13-25

Polynomial Expressions and Horner's Method..........................13-26

14.Programming Techniques ..........................................14-1

Routines in Programs ..............................................................14-1

Calling Subroutines (XEQ, RTN) ..........................................14-1

Nested Subroutines ...........................................................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..............................14-20

The Variables "I" and "J" ................................................... 14-20

The Indirect Address, (I) and (J) .........................................14-21

Program Control with (I)/(J) ................................................ 14-23

Equations with (I)/(J) .......................................................... 14-23

Unnamed indirect variables..............................................14-23

Contents 9

15.Solving and Integrating Programs..............................15-1

Solving a Program................................................................. 15-1

Using SOLVE in a Program ..................................................... 15-6

Integrating a Program ............................................................ 15-7

Using Integration in a Program.............................................. 15-10

Restrictions on Solving and Integrating ................................... 15-11

16.Statistics Programs ....................................................16-1

Curve Fitting ......................................................................... 16-1

Normal and Inverse–Normal Distributions............................... 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 Questions ............................................ A-1

Environmental Limits................................................................. A-2

Changing the Batteries .............................................................A-3

Testing Calculator Operation .................................................... A-4

The Self–Test ........................................................................... A-5

Warranty ............................................................................... A-7

Service...................................................................................A-8

Regulatory information ........................................................... A-12

Federal Communications Commission Notice............................ A-12

10 Contents

B. User Memory and the Stack.........................................B-1

Managing Calculator Memory...................................................B-1

Resetting the Calculator ............................................................B-2

Clearing Memory.....................................................................B-3

The Status of Stack Lift ..............................................................B-4

Disabling Operations...........................................................B-5

Neutral Operations .............................................................B-5

The Status of the LAST X Register................................................B-6

Accessing Stack Register Contents ..............................................B-7

C. ALG: Summary ...........................................................C-1

About ALG ............................................................................. C-1

Doing Two argument Arithmetic in ALG ..................................... C-2

Simple Arithmetic ............................................................... C-2

Power Functions ................................................................. C-3

Percentage Calculations...................................................... C-3

Permutations and Combinations ........................................... C-4

Quotient and Remainder Of Division .................................... C-4

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 Two–Variable Data..................................... C-11

D. More about Solving.................................................... D-1

Contents 11

How SOLVE Finds a Root ......................................................... D-1

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

12 Contents

Part 1

Basic Operation

Getting Started 1-1

1

Getting Started

Important Preliminaries

Turning the Calculator On and Off

To turn the calculator on, press . ON is printed on the bottom of the key.

To turn the calculator off, press

. That is, press and release the  shift

key, then press

 (which has OFF printed in yellow above it). Since the calculator

has Continuous Memory, turning it off does not affect any information you've stored.

To conserve energy, the calculator turns itself off after 10 minutes of inactivity. If you

see the low–power indicator (  ) in the display, replace the batteries as soon as

possible. See appendix A for instructions.

Adjusting Display Contrast

Display contrast depends on lighting, viewing angle, and the contrast setting. To

increase or decrease the contrast, hold down the

 key and press or .

Watch for this symbol in the 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.

v

1-2 Getting Started

Highlights of the Keyboard and Display

Shifted Keys

Each key has three functions: one printed on its face, a left–shifted function

(yellow), and 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 press .

Getting Started 1-3

Pressing  or  turns on the corresponding or  annunciator symbol at

the top of the display. The annunciator remains on until you press the next key. To

cancel a shift key (and turn off its annunciator), press the same shift key again.

Alpha Keys

Most keysdisplay 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 the alpha keys are

“active”.

Variables are covered in chapter 3; labels are covered in chapter 13.

Cursor Keys

Each of the four cursor direction keys is marked with an arrow. In this text we will

use the graphics

Õ,Ö,× and Ø to refer to these keys.

Left-shifted

function

Right-shifted

function

Letter for alphabetic

key

1-4 Getting Started

Backspacing and Clearing

Among the first things you need to know are how to clear an entry, correct a

number, and clear the entire display to start over.

Keys for Clearing

Key Description



Backspace.

If an expression is in the process of being entered,

 erases the

character to the left of the entry cursor ( _ ). Otherwise, with a

completed expression or the result of a calculation in line 2,



replaces that result with a zero.

 also clears error messages

and exits menus.

 behaves similarly when the calculator is in

program-entry and equation-entry modes, as discussed below:

 Equation–entry mode:

If an equation is in the process of being entered or edited,

 erases the character immediately to the left of the insert

cursor; otherwise, if the equation has been entered (no insert

cursor present),

 deletes 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 cancels the current

situation (such as a menu, a message, a prompt, a catalog, or

Equation–entry or Program–entry mode).

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