a0005 introduction to mathematics with mapl morebook vn 1992

Published by World Scientific Publishing Co.. 5 Toh Tuck Link, Singapore 596224 USA ofice: Suite 202, 1060 Main Street, River Edge, NJ 07661 UK ofice: 57 Shelton Street, Covent Garden, L

IflTRODUCTIOII TO

MATtlFMATIC5 WITH

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InTRODUCTlOn TO

M A T t l f MAT10

N E W JERSEY * L O N O O N - SINGAPORE * B E l J l N G S H A N G H A I * HONG KONG TAIPEI * C H E N N A I

Published by

World Scientific Publishing Co Pte Ltd

5 Toh Tuck Link, Singapore 596224

USA ofice: Suite 202, 1060 Main Street, River Edge, NJ 07661

UK ofice: 57 Shelton Street, Covent Garden, London WCZH 9HE

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INTRODUCTION TO MATHEMATICS WITH MAPLE

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ISBN 98 1-238-93 1-8

ISBN 98 1-256-009-2 (pbk)

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522 Introduction to Mathematics with Maple

commands, 513

integration, 443

Using

convert 0 , 17

collect 0, 24

diffo, 360

Digitso, 15

expando, 21

factor0, 22

int 0 , 443

normal 0 , 23

simplify(), 22

sort(), 24

Maclaurin, 400

max, 76

maximum

mean

local, 375

arithmetic, 158

geometric, 157

min, 76

minimum

Moivre, 201

multiple commands, 7

local, 375

N, the set of natural numbers,

No, the set of non-negative

Newton, 498

43

integers, 43

binomial theorem, 150

Leibniz formula, 457

nops, 502

Oresme, 309

IF', the set of positive real

Peano, 477

numbers, 43

axiomatic approach, 166

axioms, 121, 127

remainder, 397

Peano, Giuseppe, 114

Perron.0, 500

pi, 12

Polya, G, 134

polynomial, 167, 170

polynomials

unending, 169 multiplication, 170, 173 ring of, 170

previous results, 8 proc, 501

products

in Maple, 143

Q , the set of rational numbers,

quitting Map'le, 8

43

Raabe radius

range, 63 reducible, 185 relation, 63 inverse, 91 reflexive, 66 symmetric, 66 transitive, 66 integrable, 438 sum, 432

test, 304

of convergence, 301

Ri emann

Riemann, Bernard, 306

ring

isomorphic, 171

of polynomials, 170 multiple, 217

primitive of unity, 204 rational, 214

Ruffini Paulo, 220 Russell, Bertrand, 53

root

scheme

Horner, 180 semicolons, 6 sequence, 145 decreasing, 257

Index 523

Fibonacci, 148

increasing, 257

formal power, 169

countable, 232

Cartesian product, 43

countable, 232

difference, 36

enumerable, 232

intersection, 35

union, 35

series

set

sets

sgn, 74

signum, 74

sin, 76

singleton, 53

sinh, 430

spaces, 7

sqrt, 11, 76

starting Maple, 4

statement if, 502

step function, 450

stopping Maple, 8

Stusm, 218

sums

in Maple, 141

tagged division, 431

&fine, 342, 437

tan, 76

Tarski, Alfred, 55

Taylor, 400

polynomial, 180

Taylor expansion, 181

Taylor polynomial, 181

Taylor theorem, 477

test

D’Alembert, 297

D’Alembert limit, 298

Leibniz, 292

Raabe, 304

root, 299

binomial, 150

Bolzano-Cauchy, 271, 291, 354

theorem

Bolzano-Weierstrass, 273

dominated convergence, 497

greatest lower bound, 117 least upper bound, 124

monotone convergence, 495

square root, 198 Taylor, 477

The Intermediate Value Weierstrass, 344, 347

Theorem, 340

Vieta, 214 von Neumann, John, 96 Wallis, 470

formula, 471 What is Maple?, 4

Z, the set of integers, 43

zero polynomial, 171