Introduction to Analysis / Edition 3

Introduction to Analysis / Edition 3

by William R. Wade
     
 

ISBN-10: 0131453335

ISBN-13: 9780131453333

Pub. Date: 07/28/2004

Publisher: Prentice Hall

User-friendly--yet rigorous--in approach, this introduction to analysis meets readers where they are by providing extra support for those who like a slower, less detailed approach, but not getting in the way of those who want a quicker pace and deeper focus. It uses analogy and geometry to motivate and explain the theory, and precedes…  See more details below

Overview

User-friendly--yet rigorous--in approach, this introduction to analysis meets readers where they are by providing extra support for those who like a slower, less detailed approach, but not getting in the way of those who want a quicker pace and deeper focus. It uses analogy and geometry to motivate and explain the theory, and precedes many complicated proofs with a "Strategy" which motivates the proof, shows why it was chosen, and why it should work. Examples follow many theorems, showing why each hypothesis is needed, allowing readers to remember the hypotheses by recalling the examples. Proofs are presented in complete detail, with each step carefully documented, and proofs are linked together in a way that teaches readers to think ahead. Physical interpretations are used to examine some concepts from a second or third point of view. Includes over 200 worked examples and over 600 exercises. Provides extensive coverage of multidimensional analysis.

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Product Details

ISBN-13:
9780131453333
Publisher:
Prentice Hall
Publication date:
07/28/2004
Edition description:
REV
Pages:
648
Product dimensions:
7.30(w) x 9.42(h) x 1.08(d)

Table of Contents

Pt. IOne-dimensional theory
1The real number system1
2Sequences in R35
3Continuity on R58
4Differentiability on R85
5Integrability on R107
6Infinite series of real numbers154
7Infinite series of functions184
Pt. IIMultidimensional theory
8Euclidean spaces225
9Convergence in R[superscript n]256
10Metric spaces290
11Differentiability on R[superscript n]321
12Integration on R[superscript n]381
13Fundamental theorems of vector calculus449
14Fourier series506
15Differentiable manifolds538
App. AAlgebraic laws570
App. BTrigonometry573
App. CMatrices and determinants577
App. DQuadric surfaces583
App. EVector calculus and physics587
App. FEquivalence relations590

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