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Real Analysis

Frank Morgan Williams College, Williamstown, MA
Available Formats:
Hardcover ISBN: 978-0-8218-3670-5
Product Code: REAL
List Price: $49.00 MAA Member Price:$44.10
AMS Member Price: $39.20 Electronic ISBN: 978-1-4704-1213-5 Product Code: REAL.E List Price:$46.00
MAA Member Price: $41.40 AMS Member Price:$36.80
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List Price: $73.50 MAA Member Price:$66.15
AMS Member Price: $58.80 Click above image for expanded view Real Analysis Frank Morgan Williams College, Williamstown, MA Available Formats:  Hardcover ISBN: 978-0-8218-3670-5 Product Code: REAL  List Price:$49.00 MAA Member Price: $44.10 AMS Member Price:$39.20
 Electronic ISBN: 978-1-4704-1213-5 Product Code: REAL.E
 List Price: $46.00 MAA Member Price:$41.40 AMS Member Price: $36.80 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:$73.50 MAA Member Price: $66.15 AMS Member Price:$58.80
• Book Details

2005; 151 pp
MSC: Primary 26;

This book is written by award-winning author, Frank Morgan. It offers a simple and sophisticated point of view, reflecting Morgan's insightful teaching, lecturing, and writing style.

Intended for undergraduates studying real analysis, this book builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbb{R}^n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It gives the three characterizations of compactness: as "closed and bounded," via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem.

This concise text not only provides efficient proofs, but also shows students how to derive them. The excellent exercises are accompanied by select solutions. Ideally suited as an undergraduate textbook, this complete book on real analysis will fit comfortably into one semester.

Frank Morgan received the first Haimo Award for distinguished college teaching from the Mathematical Association of America. He has also garnered top teaching awards from Rice University (Houston, TX) and MIT (Cambridge, MA).

Undergraduate students interested in real analysis.

• Cover
• Title
• Contents
• Preface
• Part I. Real Numbers and Limits
• Chapter 1. Numbers and Logic
• Chapter 2. Infinity
• Chapter 3. Sequences
• Chapter 4. Functions and Limits
• Part II. Topology
• Chapter 5. Open and Closed Sets
• Chapter 6. Continuous Functions
• Chapter 7. Composition of Functions
• Chapter 8. Subsequences
• Chapter 9. Compactness
• Chapter 10. Existence of Maximum
• Chapter 11. Uniform Continuity
• Chapter 12. Connected Sets and the Intermediate Value Theorem
• Chapter 13. The Cantor Set and Fractals
• Part III. Calculus
• Chapter 14. The Derivative and the Mean Value Theorem
• Chapter 15. The Riemann Integral
• Chapter 16. The Fundamental Theorem of Calculus
• Chapter 17. Sequences of Functions
• Chapter 18. The Lebesgue Theory
• Chapter 19. Infinite Series ∑a[sub(n)]
• Chapter 20. Absolute Convergence
• Chapter 21. Power Series
• Chapter 22. Fourier Series
• Chapter 23. Strings and Springs
• Chapter 24. Convergence of Fourier Series
• Chapter 25. The Exponential Function
• Chapter 26. Volumes of n-Balls and the Gamma Function
• Part IV. Metric Spaces
• Chapter 27. Metric Spaces
• Chapter 28. Analysis on Metric Spaces
• Chapter 29. Compactness in Metric Spaces
• Chapter 30. Ascoli's Theorem
• Partial Solutions to Exercises
• Greek Letters
• Index
• A
• B
• C
• D
• E
• F
• G
• H
• I
• J
• L
• M
• N
• O
• P
• R
• S
• T
• U
• V
• W
• Back Cover

• Reviews

• Reading your book is a refreshingly delightful change from the usual emphasis on series, rather than topology, as a foundation of analysis.

Robert Jones, University of Dusseldorf
• 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
2005; 151 pp
MSC: Primary 26;

This book is written by award-winning author, Frank Morgan. It offers a simple and sophisticated point of view, reflecting Morgan's insightful teaching, lecturing, and writing style.

Intended for undergraduates studying real analysis, this book builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbb{R}^n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It gives the three characterizations of compactness: as "closed and bounded," via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem.

This concise text not only provides efficient proofs, but also shows students how to derive them. The excellent exercises are accompanied by select solutions. Ideally suited as an undergraduate textbook, this complete book on real analysis will fit comfortably into one semester.

Frank Morgan received the first Haimo Award for distinguished college teaching from the Mathematical Association of America. He has also garnered top teaching awards from Rice University (Houston, TX) and MIT (Cambridge, MA).

Undergraduate students interested in real analysis.

• Cover
• Title
• Contents
• Preface
• Part I. Real Numbers and Limits
• Chapter 1. Numbers and Logic
• Chapter 2. Infinity
• Chapter 3. Sequences
• Chapter 4. Functions and Limits
• Part II. Topology
• Chapter 5. Open and Closed Sets
• Chapter 6. Continuous Functions
• Chapter 7. Composition of Functions
• Chapter 8. Subsequences
• Chapter 9. Compactness
• Chapter 10. Existence of Maximum
• Chapter 11. Uniform Continuity
• Chapter 12. Connected Sets and the Intermediate Value Theorem
• Chapter 13. The Cantor Set and Fractals
• Part III. Calculus
• Chapter 14. The Derivative and the Mean Value Theorem
• Chapter 15. The Riemann Integral
• Chapter 16. The Fundamental Theorem of Calculus
• Chapter 17. Sequences of Functions
• Chapter 18. The Lebesgue Theory
• Chapter 19. Infinite Series ∑a[sub(n)]
• Chapter 20. Absolute Convergence
• Chapter 21. Power Series
• Chapter 22. Fourier Series
• Chapter 23. Strings and Springs
• Chapter 24. Convergence of Fourier Series
• Chapter 25. The Exponential Function
• Chapter 26. Volumes of n-Balls and the Gamma Function
• Part IV. Metric Spaces
• Chapter 27. Metric Spaces
• Chapter 28. Analysis on Metric Spaces
• Chapter 29. Compactness in Metric Spaces
• Chapter 30. Ascoli's Theorem
• Partial Solutions to Exercises
• Greek Letters
• Index
• A
• B
• C
• D
• E
• F
• G
• H
• I
• J
• L
• M
• N
• O
• P
• R
• S
• T
• U
• V
• W
• Back Cover
• Reading your book is a refreshingly delightful change from the usual emphasis on series, rather than topology, as a foundation of analysis.

Robert Jones, University of Dusseldorf
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
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