Overview

Real Analysis 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. The text not only provides efficient proofs, but also shows the student how to come up with them. The excellent exercises come with select solutions in the back. Here is a real analysis text that is short enough for the student to read and understand and complete enough to be the primary text for a serious undergraduate course. Frank Morgan is the author of five books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this book, Morgan has finally brought his famous direct style to an undergraduate real analysis text.

Full Product Details

Author:   Frank Morgan
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.151kg
ISBN:  

9781470484774

ISBN 10:   1470484773
Pages:   151
Publication Date:   15 March 2005
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of 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

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

Author Information

Frank Morgan, Williams College, Williamstown, MA

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