An introduction to complex analysis and the Laplace transform
著者
書誌事項
An introduction to complex analysis and the Laplace transform
（Textbooks in mathematics）（A Chapman & Hall book）
CRC Press, 2022
- : hbk
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注記
Includes bibliographical references (p. 379) and index
内容説明・目次
内容説明
The aim of this comparatively short textbook is a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications. Several important applications in physics and engineering are considered in the book.
This thorough presentation includes all theorems (with a few exceptions) presented with proofs. No previous exposure to complex numbers is assumed. The textbook can be used in one-semester or two-semester courses.
In one respect this book is larger than usual, namely in the number of detailed solutions of typical problems. This, together with various problems, makes the book useful both for self- study and for the instructor as well.
A specific point of the book is the inclusion of the Laplace transform. These two topics are closely related. Concepts in complex analysis are needed to formulate and prove basic theorems in Laplace transforms, such as the inverse Laplace transform formula. Methods of complex analysis provide solutions for problems involving Laplace transforms.
Complex numbers lend clarity and completion to some areas of classical analysis. These numbers found important applications not only in the mathematical theory, but in the mathematical descriptions of processes in physics and engineering.
目次
Preface
Introduction
Chapter 1. Complex Numbers and Their Arithmetic
Chapter 2. Functions of a Complex Variable
Chapter 3. Differentiation of Functions of a Complex Variable
Chapter 4. Conformal Mappings
Chapter 5. Integration
Chapter 6. Series
Chapter 7. Residue Theory
Chapter 8. Applications
Chapter 9. The Laplace Transform
Solutions, hints, and answers to selected problems
Appendix
Bibliography
Index
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