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Introduction to Analysis: Fifth Edition

Edward D. Gaughan New Mexico State University, Las Cruces, NM
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Hardcover ISBN: 978-0-8218-4787-9
Product Code: AMSTEXT/1
List Price: $70.00 MAA Member Price:$63.00
AMS Member Price: $56.00 Electronic ISBN: 978-1-4704-1114-5 Product Code: AMSTEXT/1.E List Price:$66.00
MAA Member Price: $59.40 AMS Member Price:$52.80
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List Price: $105.00 MAA Member Price:$94.50
AMS Member Price: $84.00 Click above image for expanded view Introduction to Analysis: Fifth Edition Edward D. Gaughan New Mexico State University, Las Cruces, NM Available Formats:  Hardcover ISBN: 978-0-8218-4787-9 Product Code: AMSTEXT/1  List Price:$70.00 MAA Member Price: $63.00 AMS Member Price:$56.00
 Electronic ISBN: 978-1-4704-1114-5 Product Code: AMSTEXT/1.E
 List Price: $66.00 MAA Member Price:$59.40 AMS Member Price: $52.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$105.00 MAA Member Price: $94.50 AMS Member Price:$84.00
• Book Details

Volume: 11998; 240 pp
MSC: Primary 26;

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.

Undergraduate students interested in learning analysis.

• Cover
• Title page
• Preface
• Contents
• Chapter 0. Preliminaries
• Chapter 1. Sequences
• Chapter 2. Limits of functions
• Chapter 3. Continuity
• Chapter 4. Differentiation
• Chapter 5. The Riemann integral
• Chapter 6. Infinite series
• Chapter 7. Sequences and series of functions
• Index
• Back Cover

• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 11998; 240 pp
MSC: Primary 26;

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.

Undergraduate students interested in learning analysis.

• Cover
• Title page
• Preface
• Contents
• Chapter 0. Preliminaries
• Chapter 1. Sequences
• Chapter 2. Limits of functions
• Chapter 3. Continuity
• Chapter 4. Differentiation
• Chapter 5. The Riemann integral
• Chapter 6. Infinite series
• Chapter 7. Sequences and series of functions
• Index
• Back Cover
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.