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Introduction to Analysis: Fifth Edition
 
Edward D. Gaughan New Mexico State University, Las Cruces, NM
Front Cover for Introduction to Analysis
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
Sale Price: $45.50
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
Sale Price: $42.90
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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
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AMS Member Price: $84.00
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Front Cover for Introduction to Analysis
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  • Front Cover for Introduction to Analysis
  • Back Cover for Introduction to Analysis
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
Sale Price: $45.50
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
Sale Price: $42.90
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
Sale Price: $68.25
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    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.

    Readership

    Undergraduate students interested in learning analysis.

  • Table of Contents
     
     
    • Cover
    • Title page
    • Copyright
    • 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
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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.

Readership

Undergraduate students interested in learning analysis.

  • Cover
  • Title page
  • Copyright
  • 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
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