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Book Summary of Real and Complex Analysis,Rudin
This is an advanced text for the one- or two-semester course
in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level.
The basic techniques and theorems of analysis are presented
in such a way that the intimate connections between its
various branches are strongly emphasized. The traditionally
separate subjects of 'real analysis' and 'complex analysis' are
thus united in one volume. Some of the basic ideas from
functional analysis are also included. This is the only book
to take this unique approach. The third edition includes a
new chapter on differentiation. Proofs of theorems presented
in the book are concise and complete and many challenging
exercises appear at the end of each chapter. The book is
arranged so that each chapter builds upon the other, giving
students a gradual understanding of the subject.
Table Of Contents
Preface Prologue: The Exponential Function
Chapter 1: Abstract Integration
Chapter 2: Positive Borel Measures
Chapter 3: Lp-Spaces
Chapter 4: Elementary Hilbert Space Theory
Chapter 5: Examples of Banach Space Techniques
Chapter 6: Complex Measures
Chapter 7: Differentiation
Chapter 8: Integration on Product Spaces
Chapter 9: Fourier Transforms
Chapter 10: Elementary Properties of Holomorphic Functions
Chapter 11: Harmonic Functions
Chapter 12: The Maximum Modulus Principle
Chapter 13: Approximation by Rational Functions
Chapter 14: Conformal Mapping
Chapter 15: Zeros of Holomorphic Functions
Chapter 16: Analytic Continuation
Chapter 17: Hp-Spaces
Chapter 18: Elementary Theory of Banach Algebras
Chapter 19: Holomorphic Fourier Transforms
Chapter 20: Uniform Approximation by Polynomials
Appendix: Hausdorff's Maximality Theorem
Notes and Comments
Bibliography
List of Special Symbols
Index
Table Of Contents
Preface Prologue: The Exponential Function
Chapter 1: Abstract Integration
Chapter 2: Positive Borel Measures
Chapter 3: Lp-Spaces
Chapter 4: Elementary Hilbert Space Theory
Chapter 5: Examples of Banach Space Techniques
Chapter 6: Complex Measures
Chapter 7: Differentiation
Chapter 8: Integration on Product Spaces
Chapter 9: Fourier Transforms
Chapter 10: Elementary Properties of Holomorphic Functions
Chapter 11: Harmonic Functions
Chapter 12: The Maximum Modulus Principle
Chapter 13: Approximation by Rational Functions
Chapter 14: Conformal Mapping
Chapter 15: Zeros of Holomorphic Functions
Chapter 16: Analytic Continuation
Chapter 17: Hp-Spaces
Chapter 18: Elementary Theory of Banach Algebras
Chapter 19: Holomorphic Fourier Transforms
Chapter 20: Uniform Approximation by Polynomials
Appendix: Hausdorff's Maximality Theorem
Notes and Comments
Bibliography
List of Special Symbols
Index
Details of Book: Real and Complex Analysis,Rudin
| Book: | Real and Complex Analysis,Rudin |
| Author: | Rudin Walter |
| ISBN: | 0070619875 |
| ISBN-13: | 9780070619876,978-0070619876 |
| Binding: | Paperback |
| Publishing Date: | 2007 |
| Publisher: | Tata Mcgraw Hill Education Private Limited |
| Edition: | 3rd |
| Number of Pages: | 483 |
| Language: | English |
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