An Introduction to Complex Analysis and the Laplace Transform 1st Edition by Vladimir Eiderman 9781000511123 100051112X

An Introduction to Complex Analysis and the Laplace Transform 1st Edition Vladimir Eiderman – Ebook Instant Download/Delivery ISBN(s): 9780367409784,036740978X, 9781000511123, 100051112X

Product details:

• ISBN 10: 100051112X
• ISBN 13: 9781000511123
• Author:  Vladimir Eiderman

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.

Table contents:

1 Complex Numbers and Their Arithmetic

2 Functions of a Complex Variable

3 Differentiation of Functions of a Complex Variable

4 Conformal Mappings

5 Integration

6 Series

7 Residue Theory

8 Applications

9 The Laplace Transform

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