a0005 introduction to mathematics with mapl morebook vn 1992

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


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INTRODUCTION TO MATHEMATICS WITH MAPLE
Copyright 0 2004 by World Scientific Publishing Co. Pte. Ltd.

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Introduction to Mathematics with Maple

522

commands, 513
integration, 443
Using
convert0 , 17
collect0,24

diffo, 360
Digitso, 15
expando, 21
factor0, 22
int 0 , 443
normal 0 , 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, 7

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, 8
proc, 501
products
in Maple, 143

Q , the set of rational numbers,
43

quitting Map'le, 8

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, 6

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, 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
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?, 4
Z, the set of integers, 43
zero polynomial, 171