REDUCE for Physicists: 1st Edition (Hardback) book cover

REDUCE for Physicists

1st Edition

By N MacDonald

CRC Press

168 pages

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Hardback: 9780750302777
pub: 1994-01-01
$86.95
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Description

The use of computer algebra systems in science and engineering has grown rapidly as more people realize their potential to solve tedious and extensive mathematical problems. REDUCE for Physicists provides a comprehensive introduction to one of the most widely available and simple to use computer algebra systems, focusing primarily on the needs of physicists. As a means of performing symbolic computation, REDUCE reduces tedious manual algebraic calculations and the dangers of casual errors. Each chapter introduces some aspects of REDUCE and illustrates them with applications from various branches of physics including mechanics, dynamics, dimensional analysis, quantum mechanics, and plasma physics. Emphasizing hands-on work with REDUCE to tackle real physical problems, the book includes exercises to test understanding throughout. Students and researchers in the physical sciences and engineering using REDUCE for the first time will find this book an invaluable aid to learning.

Table of Contents

A FIRST LOOK

Hands-on calculation, assignments and values

Looking back and making mistakes

A hands-on calculation: constant of motion

A programmed calculation: constant of motion

Changing the form of the output

Changes of variable

Getting values locally and globally

Summary of chapter 1

SOME BASIC TASKS

Integer and decimal arithmetic

Complex and modular arithmetic

Elementary transcendental functions

Integration

LINEAR ALGEBRAIC EQUATIONS

The solve command and lists

Dimensional analysis

Summary of chapter 3

REPETITIVE PROCESSES

Loops and procedures

A program to calculate Lagrangian equations

A program to calculate Poisson brackets

More on procedures: scalar and vector products

DETERMINANTS, POLYNOMIALS AND CONDITIONAL STATEMENTS

Stability, polynomials and determinants

An extension of the Lorenz model

Conditional statements

Summary of chapter 5

NONCOMMUTING OPERATORS

Operators

Commutators for conserved vectors

Perturbation theory for a 1-dimensional oscillator

Summary of chapter 6

HARMONIC BALANCE

The harmonic balance method for nonlinear oscillators

Chebyshev polynomial method: arrays

Trigonometric expansion and contraction

Interference of for all . . let . . commands

Harmonic balance with elliptic functions

An example to illustrate the use of parts

Numerical aspects of harmonic balance

Summary of chapter 7

THE REDUCE-FORTRAN INTERFACE

Transferring results to a numerical program

The GENTRAN package

APPENDICES

REDUCE 3.4

An application to plasma waves

References

Index

Subject Categories

BISAC Subject Codes/Headings:
SCI040000
SCIENCE / Mathematical Physics
SCI055000
SCIENCE / Physics