Real Analysis
American Mathematical Society (Publisher)
Will be published approx. on 15. March 2005
Book
Paperback/Softback
151 pages
978-1-4704-8477-4 (ISBN)
Description
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.
Reviews / Votes
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 DusseldorfMore details
Other editions
Previous edition
Frank Morgan
Real Analysis
Book
07/2005
American Mathematical Society
€78.19
Article not available at the moment
Person
Content
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
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