An Introduction to Complex Analysis and the Laplace Transform

Vladimir Eiderman (Indiana University, IN, USA.)

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Hardback

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English

Chapman & Hall/CRC
21 December 2021

Series: Textbooks in Mathematics

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.

By: Vladimir Eiderman (Indiana University IN USA.)
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 453g
ISBN: 9780367409784
ISBN 10: 036740978X
Series: Textbooks in Mathematics
Pages: 384
Publication Date: 21 December 2021
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

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

Vladimir Eiderman holds a Ph.D. from Mathematical Institute of Academy of Sciences, Armenian SSR. He is Rothrock Lecturer of Indiana University. He has been Professor, Moscow State University of Civil Engineering, Visiting Professor of University of Kentucky, University of Wisconsin-Madison, and Indiana University. Dr. Eiderman has more than 30 research publications.