Complex Variables and the Laplace Transform for Engineers (Dover Books on Electrical Engineering) by Wilbur R. LePage (PDF)

Description

“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 MathematicsEngineers 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

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐Complex variables and the Laplace Transform…. Well awesome! All the ideas written in this book are essential to any Graduate student in Electrical Engineering and many Graduate Math students. Warning this book is intended for a mature audience (graduate students). I’m currently a double major in Math and Computer engineering and I use the Laplace Transform extensively. Both inside and outside the classroom. The issue is this book has so much theory and it’s not easy to pick up. I’ve taken Calculus 1-3, Linear Algebra, Differential Equations 1 and more math classes that have matured me in the computational side of mathematics. The issue of the book isn’t that its hard to read, its just not possible to take some of the integrals with the integrating techniques learned at the early undergraduate level. This book is great if your a grad student and want to increase your knowledge of the Laplace Transform (very useful and many applications) or if you do research, but will be most likely hard to pick up if your still an undergraduate.

⭐There were a couple pages of the basics, but then completely switched gears (like an editor decided to cut a couple chapters). Just once, I’d like to pick up a math text that delivers the basics up-to and including the point of the book. This “engineer-level” book requires prior knowledge and didn’t work for me as a self-teach/refresher.

⭐What a well written book for the engineer of the interesting development of the mathematics of the Laplace transform.

⭐This is the best book b far on the topic.

⭐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).

⭐I enjoyed reading this little book. The explanations are clear and the illustrations ample. Perfect for self-study or as an occassional reference for understanding 2D conformal mapping techniques used to solve problems in inviscid (i.e. potential) flow, magnetostatics, and elasticity (the Laplace equation). Also useful for solutions of differential equations and fourier transform methods. The Dover paperback edition is a very good buy..”

⭐Me compré este libro para seguir una asignatura de una carrera de ingeniería a pesar de que no estaba en la bibliografía. Está bien para estudiar variable compleja por tu cuenta y la transformada de laplace. Quizás falten más ejemplos resueltos y se echa en falta una tabla con las TL.Excellent reference.

⭐ラプラス変換を使いこなせる人にとっては退屈かもしれません。斗にかく説明が詳しい。

⭐

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