Complex Variables and the Laplace Transform for Engineers

By Wilbur R. LePage and Wilbur R Le Page

Book Overview

"An excellent text; the best I have found on the subject." -- J. B. Sevart, Department of Mechanical Engineering, University of Wichita
"An extremely useful textbook for both formal classes and for self-study." -- Society for Industrial and Applied Mathematics
Engineers often do not have time to take a course in complex variable theory as undergraduates, yet is is one of the most important and useful branches of mathematics, with many applications in engineering. This text is designed to remedy that need by supplying graduate engineering students (especially electrical engineering) with a course in the basic theory of complex variables, which in turn is essential to the understanding of transform theory. Presupposing a good knowledge of calculus, the book deals lucidly and rigorously with important mathematical concepts, striking an ideal balance between purely mathematical treatments that are too general for the engineer, and books of applied engineering which may fail to stress significant mathematical ideas.
The text is divided into two basic parts: The first part (Chapters 1-7) is devoted to the theory of complex variables and begins with an outline of the structure of system analysis and an explanation of basic mathematical and engineering terms. Chapter 2 treats the foundation of the theory of a complex variable, centered around the Cauchy-Riemann equations. The next three chapters -- conformal mapping, complex integration, and infinite series -- lead up to a particularly important chapter on multivalued functions, explaining the concepts of stability, branch points, and riemann surfaces. Numerous diagrams illustrate the physical applications of the mathematical concepts involved.
The second part (Chapters 8-16) covers Fourier and Laplace transform theory and some of its applications in engineering, beginning with a chapter on real integrals. Three important chapters follow on the Fourier integral, the Laplace integral (one-sided and two-sided) and convolution integrals. After a chapter on additional properties of the Laplace integral, the book ends with four chapters (13-16) on the application of transform theory to the solution of ordinary linear integrodifferential equations with constant coefficients, impulse functions, periodic functions, and the increasingly important Z transform.
Dr. LePage's book is unique in its coverage of an unusually broad range of topics difficult to find in a single volume, while at the same time stressing fundamental concepts, careful attention to details and correct use of terminology. An extensive selection of interesting and valuable problems follows each chapter, and an excellent bibliography recommends further reading. Ideal for home study or as the nucleus of a graduate course, this useful, practical, and popular (8 printings in its hardcover edition) text offers students, engineers, and researchers a careful, thorough grounding in the math essential to many areas of engineering. "An outstanding job." -- American Mathematical Monthly

• Format: Paperback
• Language: English
• ISBN: 0486639266
• ISBN13: 9780486639260
• Release Date: July 2010
• Publisher: Dover Publications
• Length: 512 Pages
• Weight: 1.15 lbs.
• Dimensions: 0.9" x 5.6" x 8.2"

Customer Reviews

You'll learn it well from this gem of a book

In 1962 I had a course which was supposed to teach me this mathematics. I passed, but it failed. I really didn't understand these topics well enough to apply them. Two years later, in my first year of graduate school in electrical engineering, I had a mandatory course that used this textbook. That time I really understood what this math was about, how to use it, and how to build on it. Part of that was due to good teaching, but a major part was due directly to this book. This textbook is a gem, a brilliantly and clearly written text on an area of mathematics that is highly important to more than a few areas of engineering. My office mate of many years ago liked it so much that he took my copy and never returned it. I'm about to buy it again (in paperback this time) because I've forgotten some topics that I need to restudy. I know LePage will teach me well once again.

Excellent and practical text for complex analysis and transform theory

This is one of my all time favorite math books. Transform theory is covered as rigorously as can be done without introducing measure theory. The level of detail used makes application of the subject much easier since the restrictions about where and how the mathematics can be applied are clear. While providing some of the fundamentals and details that one wouldn't necessarily have time to cover in an engineering course, this text is still very accessible. With only self study from this text I learned complex variables, Fourier transform theory, and Laplace transform theory using this book (in between first and second year engineering terms). Later when we covered this in school I repeatedly referred to this text instead of my course text (despite that one also being excellent).

Good material for a self-study, ok as a reference

This book makes an excellent guide for self-study on the subject. It is very detailed, deliberate and self-contained. Even though Laplace transform is in the title, he doesn't get to that until chapter 10, since there is a great deal of background material he covers to get there. The book may be better titled "Everything you need to know to use Laplace transforms", since it is more background than actual material about Laplace transforms. He doesn't provide much in the way of look-up tables of Laplace transforms, which I thought was kind of strange. He states that you can compute them yourself once you have learned all the material in the book... true, but I would still have liked tables. If you are a grad student doing anything with Laplace transforms, and you are not in mathematics, this is a good, cheap book to get. It explains many of the essential proofs and theorems in ways non-mathematicians can understand (or at least it did for me). He has lots of figures, which I like (why do math books never have figures?)