IflTRODUCTIOII TO MATtlFMATIC5 WITH This page intentionally left blank 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 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 British Library Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library INTRODUCTION TO MATHEMATICS WITH MAPLE Copyright 2004 by World Scientific Publishing Co Pte Ltd All rights reserved This book, or parts thereoJ may not be reproduced in any form or by any means, electronic or mechanical, includingphotocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA In this case permission to photocopy is not required from the publisher ISBN 98 1-238-931-8 ISBN 98 1-256-009-2 (pbk) Printed by FuIsland Offset Printing (S) Pte Ltd, Singapore Introduction to Mathematics with Maple 522 commands, 513 integration, 443 Using convert0 , 17 collect0,24 diffo, 360 Digitso, 15 expando, 21 factor0, 22 int , 443 normal , 23 simplify(), 22 sort(), 24 Maclaurin, 400 max, 76 maximum local, 375 mean arithmetic, 158 geometric, 157 min, 76 minimum local, 375 Moivre, 201 multiple commands, N, the set of natural numbers, 43 No, the set of non-negative integers, 43 Newton, 498 binomial theorem, 150 Leibniz formula, 457 nops, 502 Oresme, 309 IF', the set of positive real numbers, 43 Peano, 477 axiomatic approach, 166 axioms, 121, 127 remainder, 397 Peano, Giuseppe, 114 Perron.0, 500 pi, 12 Polya, G, 134 polynomial, 167, 170 unending, 169 polynomials multiplication, 170, 173 ring of, 170 previous results, proc, 501 products in Maple, 143 Q , the set of rational numbers, 43 quitting Map'le, R , the set of real numbers, 43 Raabe test, 304 radius of convergence, 301 range, 63 reducible, 185 relation, 63 inverse, 91 reflexive, 66 symmetric, 66 transitive, 66 Riemann integrable, 438 sum, 432 Riemann, Bernard, 306 ring isomorphic, 171 of polynomials, 170 root multiple, 217 primitive of unity, 204 rational, 214 Ruffini Paulo, 220 Russell, Bertrand, 53 scheme Horner, 180 semicolons, sequence, 145 decreasing, 257 Index Fibonacci, 148 increasing, 257 series formal power, 169 set countable, 232 sets Cartesian product, 43 countable, 232 difference, 36 enumerable, 232 intersection, 35 union, 35 sgn, 74 signum, 74 sin, 76 singleton, 53 sinh, 430 spaces, sqrt, 11, 76 starting Maple, statement if, 502 step function, 450 stopping Maple, 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 theorem binomial, 150 Bolzano-Cauchy, 271, 291, 354 523 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 Theorem, 340 Weierstrass, 344, 347 Vieta, 214 von Neumann, John, 96 Wallis, 470 formula, 471 What is Maple?, Z, the set of integers, 43 zero polynomial, 171 ... permission to photocopy is not required from the publisher ISBN 98 1-238-931-8 ISBN 98 1-256-009-2 (pbk) Printed by FuIsland Offset Printing (S) Pte Ltd, Singapore Introduction to Mathematics with Maple... mechanical, includingphotocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher For photocopying of material... Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library INTRODUCTION TO MATHEMATICS WITH MAPLE Copyright 2004 by World Scientific Publishing Co Pte Ltd All rights reserved