HP 50G Manuel utilisateur

HP 50g graphing calculator

user’s manual

Edition 1

HP part number F2229AA-90001

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Hewlett-Packard Company

4995 Murphy Canyon Rd,

Suite 301

San Diego,CA 92123

Printing History

Edition 1 April 2006

FrontPageQS49_E.backup.fm Page 2 Friday, February 24, 2006 4:54 PM

Preface

You have in your hands a compact symbolic and numerical computer that

will facilitate calculation and mathematical analysis of problems in a

variety of disciplines, from elementary mathematics to advanced

engineering and science subjects.

This manual contains examples that illustrate the use of the basic calculator

functions and operations. The chapters in this user’s manual are organized

by subject in order of difficulty: from the setting of calculator modes, to real

and complex number calculations, operations with lists, vectors, and

matrices, graphics, calculus applications, vector analysis, differential

equations, probability and statistics.

For symbolic operations the calculator includes a powerful Computer

Algebraic System (CAS), which lets you select different modes of operation,

e.g., complex numbers vs. real numbers, or exact (symbolic) vs.

approximate (numerical) mode. The display can be adjusted to provide

textbook-type expressions, which can be useful when working with

matrices, vectors, fractions, summations, derivatives, and integrals. The

high-speed graphics of the calculator are very convenient for producing

complex figures in very little time.

Thanks to the infrared port, the USB port, and the RS232 port and cable

provided with your calculator, you can connect your calculator with other

calculators or computers. This allows for fast and efficient exchange of

programs and data with other calculators and computers.

We hope your calculator will become a faithful companion for your school

and professional applications.

SG49A.book Page 1 Friday, September 16, 2005 1:31 PM

Page TOC-1

Table of Contents

Chapter 1 - Getting started

Basic Operations, 1-1

Batteries, 1-1

Turning the calculator on and off, 1-2

Adjusting the display contrast, 1-2

Contents of the calculator’s display, 1-3

Menus, 1-3

The TOOL menu, 1-3

Setting time and date, 1-4

Introducing the calculator’s keyboard, 1-4

Selecting calculator modes, 1-6

Operating Mode, 1-7

Number Format and decimal dot or comma, 1-10

Standard format, 1-10

Fixed format with decimals, 1-10

Scientific format, 1-11

Engineering format, 1-12

Decimal comma vs. decimal point, 1-13

Angle Measure, 1-14

Coordinate System, 1-14

Selecting CAS settings, 1-15

Explanation of CAS settings, 1-16

Selecting Display modes, 1-17

Selecting the display font, 1-18

Selecting properties of the line editor, 1-18

Selecting properties of the Stack, 1-19

Selecting properties of the equation writer (EQW), 1-20

References, 1-20

Chapter 2 - Introducing the calculator

Calculator objects, 2-1

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Page TOC-2

Editing expressions in the stack, 2-1

Creating arithmetic expressions, 2-1

Creating algebraic expressions, 2-4

Using the Equation Writer (EQW) to create expressions, 2-5

Creating arithmetic expressions, 2-5

Creating algebraic expressions, 2-7

Organizing data in the calculator, 2-8

The HOME directory, 2-8

Subdirectories, 2-9

Variables, 2-9

Typing variable names , 2-9

Creating variables, 2-10

Algebraic mode, 2-10

RPN mode, 2-11

Checking variables contents, 2-13

Algebraic mode, 2-13

RPN mode, 2-13

Using the right-shift key followed by soft menu key labels, 2-13

Listing the contents of all variables in the screen, 2-14

Deleting variables, 2-14

Using function PURGE in the stack in Algebraic mode, 2-14

Using function PURGE in the stack in RPN mode, 2-15

UNDO and CMD functions, 2-16

CHOOSE boxes vs. Soft MENU, 2-16

References, 2-18

Chapter 3 - Calculations with real numbers

Examples of real number calculations, 3-1

Using powers of 10 in entering data, 3-3

Real number functions in the MTH menu, 3-5

Using calculator menus, 3-5

Hyperbolic functions and their inverses, 3-5

Operations with units, 3-7

The UNITS menu, 3-7

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Page TOC-3

Available units, 3-9

Attaching units to numbers, 3-9

Unit prefixes, 3-10

Operations with units, 3-11

Unit conversions, 3-12

Physical constants in the calculator, 3-13

Defining and using functions, 3-15

Reference, 3-16

Chapter 4 - Calculations with complex numbers

Definitions, 4-1

Setting the calculator to COMPLEX mode, 4-1

Entering complex numbers, 4-2

Polar representation of a complex number, 4-3

Simple operations with complex numbers, 4-4

The CMPLX menus, 4-4

CMPLX menu through the MTH menu, 4-4

CMPLX menu in keyboard, 4-6

Functions applied to complex numbers, 4-6

Function DROITE: equation of a straight line, 4-7

Reference, 4-7

Chapter 5 - Algebraic and arithmetic operations

Entering algebraic objects, 5-1

Simple operations with algebraic objects, 5-2

Functions in the ALG menu , 5-3

Operations with transcendental functions, 5-5

Expansion and factoring using log-exp functions, 5-5

Expansion and factoring using trigonometric functions, 5-6

Functions in the ARITHMETIC menu, 5-7

Polynomials, 5-8

The HORNER function, 5-8

The variable VX, 5-8

The PCOEF function, 5-8

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Page TOC-4

The PROOT function, 5-9

The QUOT and REMAINDER functions, 5-9

The PEVAL function , 5-9

Fractions, 5-9

The SIMP2 function, 5-10

The PROPFRAC function, 5-10

The PARTFRAC function, 5-10

The FCOEF function, 5-10

The FROOTS function, 5-11

Step-by-step operations with polynomials and fractions, 5-11

Reference, 5-12

Chapter 6 - Solution to equations

Symbolic solution of algebraic equations, 6-1

Function ISOL, 6-1

Function SOLVE, 6-2

Function SOLVEVX, 6-4

Function ZEROS, 6-4

Numerical solver menu, 6-5

Polynomial Equations, 6-6

Finding the solutions to a polynomial equation, 6-6

Generating polynomial coefficients given the polynomial's roots,

6-7

Generating an algebraic expression for the polynomial, 6-8

Financial calculations, 6-8

Solving equations with one unknown through NUM.SLV, 6-9

Function STEQ, 6-9

Solution to simultaneous equations with MSLV, 6-10

Reference, 6-11

Chapter 7 - Operations with lists

Creating and storing lists, 7-1

Operations with lists of numbers, 7-1

Changing sign , 7-1

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Page TOC-5

Addition, subtraction, multiplication, division, 7-2

Functions applied to lists, 7-4

Lists of complex numbers, 7-4

Lists of algebraic objects, 7-5

The MTH/LIST menu, 7-5

The SEQ function, 7-7

The MAP function, 7-7

Reference, 7-7

Chapter 8 - Vectors

Entering vectors , 8-1

Typing vectors in the stack, 8-1

Storing vectors into variables in the stack, 8-2

Using the Matrix Writer (MTRW) to enter vectors, 8-3

Simple operations with vectors, 8-5

Changing sign, 8-5

Addition, subtraction, 8-5

Multiplication by a scalar, and division by a scalar, 8-6

Absolute value function, 8-6

The MTH/VECTOR menu, 8-6

Magnitude, 8-7

Dot product , 8-7

Cross product, 8-7

Reference, 8-8

Chapter 9 - Matrices and linear algebra

Entering matrices in the stack, 9-1

Using the Matrix Writer, 9-1

Typing in the matrix directly into the stack, 9-2

Operations with matrices, 9-3

Addition and subtraction, 9-4

Multiplication, 9-4

Multiplication by a scalar, 9-4

Matrix-vector multiplication, 9-5

SG49A.book Page 5 Friday, September 16, 2005 1:31 PM

Page TOC-6

Matrix multiplication, 9-5

Term-by-term multiplication, 9-6

Raising a matrix to a real power, 9-6

The identity matrix, 9-7

The inverse matrix, 9-7

Characterizing a matrix (The matrix NORM menu), 9-8

Function DET, 9-8

Function TRACE, 9-8

Solution of linear systems, 9-9

Using the numerical solver for linear systems, 9-9

Solution with the inverse matrix, 9-11

Solution by “division” of matrices, 9-11

References, 9-12

Chapter 10 - Graphics

Graphs options in the calculator, 10-1

Plotting an expression of the form y = f(x), 10-2

Generating a table of values for a function, 10-4

Fast 3D plots, 10-5

Reference, 10-7

Chapter 11 - Calculus Applications

The CALC (Calculus) menu, 11-1

Limits and derivatives, 11-1

Function lim, 11-1

Functions DERIV and DERVX, 11-3

Anti-derivatives and integrals, 11-3

Functions INT, INTVX, RISCH, SIGMA and SIGMAVX, 11-3

Definite integrals, 11-4

Infinite series, 11-5

Functions TAYLR, TAYLR0, and SERIES, 11-5

Reference, 11-6

SG49A.book Page 6 Friday, September 16, 2005 1:31 PM

Page TOC-7

Chapter 12 - Multi-variate Calculus Applications

Partial derivatives, 12-1

Multiple integrals, 12-2

Reference, 12-2

Chapter 13 - Vector Analysis Applications

The del operator, 13-1

Gradient, 13-1

Divergence, 13-2

Curl, 13-2

Reference, 13-2

Chapter 14 - Differential Equations

The CALC/DIFF menu, 14-1

Solution to linear and non-linear equations, 14-1

Function LDEC, 14-1

Function DESOLVE, 14-3

The variable ODETYPE, 14-3

Laplace Transforms, 14-4

Laplace transform and inverses in the calculator, 14-4

Fourier series, 14-5

Function FOURIER, 14-5

Fourier series for a quadratic function, 14-6

Reference, 14-7

Chapter 15 - Probability Distributions

The MTH/PROBABILITY.. sub-menu - part 1, 15-1

Factorials, combinations, and permutations, 15-1

Random numbers, 15-2

The MTH/PROB menu - part 2, 15-3

The Normal distribution, 15-3

The Student-t distribution, 15-3

The Chi-square distribution, 15-4

The F distribution, 15-4

SG49A.book Page Friday, September 16, 2005 1:31 PM

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