Rent 9780131453333 | Introduction to Analysis | Wade, William R. @knetbooks.com

Summary Table of Contents

For one- or two-semester junior or senior level courses in Advanced Calculus, Analysis I, or Real Analysis.This text is designed to challenge advanced students while encouraging and helping weaker students. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint.

Offering readability, practicality and flexibility, Wade presents Fundamental Theorems from a practical viewpoint.Introduces central ideas of analysis in a one-dimensional setting, then co... MORE

Preface

Part I. ONE-DIMENSIONAL THEORY

1 The Real Number System

(34)

1.1 Ordered field axioms

... MORE

1.2 Well-Ordering Principle

(5)

1.3 Completeness Axiom

(6)

1.4 Functions, countability, and the algebra of sets

(11)

2 Sequences in R

(23)

2.1 Limits of sequences

(4)

2.2 Limit theorems

(6)

2.3 Bolzano-Weierstrass Theorem

(4)

2.4 Cauchy sequences

(3)

2.5 Limits supremum and infimum

(6)

3 Continuity on R

(27)

3.1 Two-sided limits

(8)

3.2 One-sided limits and limits at infinity

(5)

3.3 Continuity

(8)

3.4 Uniform continuity

(6)

4 Differentiability on R

(22)

4.1 The derivative

(7)

4.2 Differentiability theorems

(2)

4.3 Mean Value Theorem

(8)

4.4 Monotone functions and Inverse Function Theorem

102

(5)

5 Integrability on R

107

(47)

5.1 Riemann integral

107

(10)

5.2 Riemann sums

117

(10)

5.3 Fundamental Theorem of Calculus

127

(9)

5.4 Improper Riemann integration

136

(6)

5.5 Functions of bounded variation

142

(5)

5.6 Convex functions

147

(7)

6 Infinite Series of Real Numbers

154

(30)

6.1 Introduction

154

(6)

6.2 Series with nonnegative terms

160

(5)

6.3 Absolute convergence

165

(8)

6.4 Alternating series

173

(4)

6.5 Estimation of series

177

(4)

6.6 Additional tests

181

(3)

7 Infinite Series of Functions

184

(41)

7.1 Uniform convergence of sequences

184

(8)

7.2 Uniform convergence of series

192

(5)

7.3 Power series

197

(10)

7.4 Analytic functions

207

(12)

7.5 Applications

219

(6)

Part II. MULTIDIMENSIONAL THEORY

8 Euclidean Spaces

225

(31)

8.1 Algebraic structure

225

(9)

8.2 Planes and linear transformations

234

(8)

8.3 Topology of Rn

242

(7)

8.4 Interior, closure and boundary

249

(7)

9 Convergence in Rn

256

(34)

9.1 Limits of sequences

256

(7)

9.2 Limits of functions

263

(7)

9.3 Continuous functions

270

(7)

9.4 Compact sets

277

(3)

9.5 Applications

280

(10)

10 Metric Spaces

290

(31)

10.1 Introduction

290

(6)

10.2 Limits of functions

296

(5)

10.3 Interior, closure and boundary

301

(5)

10.4 Compact sets

306

(6)

10.5 Connected sets

312

(4)

10.6 Continuous functions

316

(5)

11 Differentiability on Rn

321

(60)

11.1 Partial derivatives and partial integrals

321

(11)

11.2 Definition of differentiability

332

(7)

11.3 Derivatives, differentials, and tangent planes

339

(9)

11.4 Chain Rule

348

(4)

11.5 Mean Value Theorem and Taylor's Formula

352

(6)

11.6 Inverse Function Theorem

358

(11)

11.7 Optimization

369

(12)

12 Integration on Rn

381

(68)

12.1 Jordan regions

381

(13)

12.2 Riemann integration on Jordan regions

394

(13)

12.3 Iterated integrals

407

(13)

12.4 Change of variables

420

(12)

12.5 Partitions of unity

432

(9)

12.6 Gamma function and volume

441

(8)

13 Fundamental Theorems of Vector Calculus

449

(57)

13.1 Curves

449

(12)

13.2 Oriented curves

461

(7)

13.3 Surfaces

468

(11)

13.4 Oriented surfaces

479

(9)

13.5 Theorems of Green and Gauss

488

(8)

13.6 Stokes's Theorem

496

(10)

14 Fourier Series

506

(32)

14.1 Introduction

506

(6)

14.2 Summability of Fourier series

512

(7)

14.3 Growth of Fourier coefficients

519

(7)

14.4 Convergence of Fourier series

526

(6)

14.5 Uniqueness

532

(6)

15 Differentiable Manifolds

538

(32)

15.1 Differential forms on Rn

538

(12)

15.2 Differentiable manifolds

550

(11)

15.3 Stokes's Theorem on manifolds

561

Appendices

A. Algebraic laws

570

(3)

B. Trigonometry

573

(4)

C. Matrices and determinants

577

(6)

D. Quadric surfaces

583

(4)

E. Vector calculus and physics

587

(3)

F. Equivalence relations

590

(2)

References

592

(1)

Answers and Hints to Exercises

593

(18)

Subject Index

611

(13)

Notation Index

624

RENT TEXTBOOKS

Introduction to Analysis

Why Rent from Knetbooks?

Top 5 reasons to order all your textbooks from Knetbooks:

Related Products