An Introduction to Complex Analysis and the Laplace Transform
An Introduction to Complex Analysis and the Laplace Transform by Vladimir Eiderman is a comprehensive textbook published by CRC Press on December 21, 2021. This 384-page edition is written in English and aims to provide a thorough understanding of the fundamentals of complex variable theory, preparing students for various applications in fields such as physics and engineering.
Readers will find a detailed exposition of theorems, complete with proofs, making it suitable for both one-semester and two-semester courses. The book includes numerous solutions to typical problems, enhancing its utility for self-study and instructional purposes. A notable feature is the inclusion of the Laplace transform, which is closely related to complex analysis, allowing for the formulation and proof of essential theorems. The text emphasizes the importance of complex numbers in classical analysis and their applications in mathematical descriptions of physical processes.
Official synopsis Publisher
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.
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