**Pure and Applied Undergraduate Texts**

Volume: 1;
1998;
240 pp;
Hardcover

MSC: Primary 26;

Print ISBN: 978-0-8218-4787-9

Product Code: AMSTEXT/1

List Price: $66.00

AMS Member Price: $52.80

MAA Member Price: $59.40

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**Electronic ISBN: 978-1-4704-1114-5
Product Code: AMSTEXT/1.E**

List Price: $66.00

AMS Member Price: $52.80

MAA Member Price: $59.40

# Introduction to Analysis: Fifth Edition

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*Edward D. Gaughan*

Introduction to Analysis is designed to bridge the gap between
the intuitive calculus usually offered at the undergraduate level and the
sophisticated analysis courses the student encounters at the graduate
level. In this book the student is given the vocabulary and facts
necessary for further study in analysis. The course for which it is
designed is usually offered at the junior level, and it is assumed that
the student has little or no previous experience with proofs in analysis.
A considerable amount of time is spent motivating the theorems and proofs
and developing the reader's intuition. Of course, that intuition must be
tempered with the realization that rigorous proofs are required for
theorems. The topics are quite standard: convergence of sequences, limits
of functions, continuity, differentiation, the Riemann integral, infinite
series, power series, and convergence of sequences of functions. Many
examples are given to illustrate the theory, and exercises at the end of
each chapter are keyed to each section. Also, at the end of each section,
one finds several Projects. The purpose of a Project is to give the reader
a substantial mathematical problem and the necessary guidance to solve
that problem. A Project is distinguished from an exercise in that the
solution of a Project is a multi-step process requiring assistance for the
beginner student.

An instructor's manual for this title is available electronically. Please
send email to textbooks@ams.org for more
information.

#### Readership

Undergraduate students interested in learning analysis.

#### Table of Contents

# Table of Contents

## Introduction to Analysis: Fifth Edition

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Preface v6 free
- Contents ix10 free
- Chapter 0 Preliminaries 114 free
- Chapter 1 Sequences 3346
- Chapter 2 Limits of Functions 6376
- Chapter 3 Continuity 8396
- Chapter 4 Differentiation 111124
- Chapter 5 The Riemann Integral 137150
- 5.1 THE RIEMANN INTEGRAL 138151
- 5.2 CLASSES OF INTEGRABLE FUNCTIONS 146159
- 5.3 RIEMANN SUMS 148161
- 5.4 THE FUNDAMENTAL THEOREM OF INTEGRAL CALCULUS 154167
- 5.5 ALGEBRA OF INTEGRABLE FUNCTIONS 155168
- 5.6 DERIVATIVES OF INTEGRALS 160173
- 5.7 MEAN-VALUE AND CHANGE-OF-VARIABLE THEOREMS 162175
- EXERCISES 165178
- PROJECTS 169182

- Chapter 6 Infinite Series 173186
- Chapter 7 Sequences and Series of Functions 215228
- Index 237250
- Back Cover Back Cover1254