A Complete Solution Guide to Real and Complex Analysis I

✍ Scribed by Kit-Wing Yu

• Publisher: 978-988-78797-9-4
• Year: 2019
• Tongue: English
• Leaves: 330
• Category: Library

✦ Synopsis

This is a complete solution guide to all exercises from Chapters 1 to 9 in Rudin's Real and Complex Analysis. The features of this book are as follows:

1. It covers all the 176 exercises from Chapters 1 to 9 with detailed and complete solutions. As a matter of fact, my solutions show every detail, every step and every theorem that I applied.
2. There are 11 illustrations for explaining the mathematical concepts or ideas used behind the questions or theorems.
3. Sections in each chapter are added so as to increase the readability of the exercises.
4. Different colors are used frequently in order to highlight or explain problems, lemmas, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only)
5. Necessary lemmas with proofs are provided because some questions require additional mathematical concepts which are not covered by Rudin.
6. Many useful or relevant references are provided to some questions for your future research.

✦ Table of Contents

Title page
About the author
Preface
List of Figures
Contents
Chapter 1 Abstract Integration
Chapter 2 Positive Borel Measure
Chapter 3 L^p-Spaces
Chapter 4 Elementary Hilbert Space Theory
Chapter 5 Examples on Banach Space Techniques
Chapter 6 Complex Measures
Chapter 7 Differentiation
Chapter 8 Integration on Product Spaces
Chapter 9 Fourier Transforms
Index
Bibliography