Problems and Solutions for Undergraduate Complex Analysis

Yu, Kit-Wing

ISBN 10: 9887607428 / ISBN 13: 9789887607427

Published by 978-988-76074-2-7, 2022

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Bibliographic Details

• Title: Problems and Solutions for Undergraduate Complex Analysis
• Publisher: 978-988-76074-2-7
• Publication Date: 2022
• Language: English
• ISBN 10: 9887607428
• ISBN 13: 9789887607427
• Binding: hardcover
• Condition: New
• Book Type: book

About this title

Synopsis

The present book Problems and Solutions for Undergraduate Complex Analysis is the combined
volume of author’s two books Problems and Solutions for Undergraduate Complex Analysis I and II. By offering 453 exercises with different levels of difficulty, this book gives a brief exposition of the foundations of first-year undergraduate complex analysis. Furthermore, we believe that students and instructors may find that the book can also
be served as a source for some advanced courses or as a reference.
The wide variety of problems, which are of varying difficulty, include the following topics:

• Complex Numbers
• Geometry of Complex Numbers
• nth Roots of a Complex Number
• Complex Functions and the Analyticity
• Power Series
• Elementary Theory of Complex Integration
• Properties of Analytic and Entire Functions
• Further Properties of Analytic Functions
• Isolated Singularities of Analytic Functions
• The Residue Theorem and its Consequences
• Applications of the Residue Theorem to Integrals and Sums
• Sequences and Series of Analytic Functions
• Conformal Mappings and the Riemann Mapping Theorem
• Introduction to Harmonic Functions
• Entire Functions as Infinite Products
• Zeros of Entire Functions.

Furthermore, the main features of this book are listed as follows:

1. The book contains 453 problems which cover the topics mentioned above. The solutions are detailed and complete in the sense that every step and every theorem that I applied will be presented.
2. Each chapter starts with a brief and concise note of introducing the notations, terminologies, basic mathematical concepts or important/famous/frequently used theorems (without proofs) relevant to the topic.
3. Three levels of difficulty have been assigned to problems so that you can sharpen your mathematics step-by-step.
4. There are 65 illustrations for explaining the mathematical concepts or ideas used behind the questions or theorems.
5. Different colors are used in appropriate places so as to highlight or explain problems, examples, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only)
6. Different authors may have different setup for the theory of complex integration. To reduce confusions and save your time of cross-checking, an appendix is made for recording some terminologies of some common complex analysis textbooks, such as Ahlfors, Asmar and Grafakos, Bak and Newmann, Conway, Gamelin, Rudin as well as Stein and Shakarchi.