Fundamentals of Complex Analysis with Applications to Engineering and Science

by Edward B. Saff, Arthur David Snider

This book provides a comprehensive introduction to complex variable theory and its applications to current engineering problems and is designed to make the fundamentals of the subject more easily accessible to readers who have little inclination to wade through the rigors of the axiomatic approach. Modeled after standard calculus books--both in level of exposition and layout--it incorporates physical applications "throughout, " so that the mathematical methodology appears less sterile to engineers. It makes frequent use of analogies from elementary calculus or algebra to introduce complex concepts, includes fully worked examples, and provides a dual heuristic/analytic discussion of all topics. A downloadable MATLAB toolbox--a state-of-the-art computer aid--is available. Complex Numbers. Analytic Functions. Elementary Functions. Complex Integration. Series Representations for Analytic Functions. Residue Theory. Conformal Mapping. The Transforms of Applied Mathematics. MATLAB ToolBox for Visualization of Conformal Maps. Numerical Construction of Conformal Maps. Table of Conformal Mappings. Features coverage of Julia Sets; modern exposition of the use of complex numbers in linear analysis (e.g., AC circuits, kinematics, signal processing); applications of complex algebra in celestial mechanics and gear kinematics; and an introduction to Cauchy integrals and the Sokhotskyi-Plemeij formulas. For mathematicians and engineers interested in Complex Analysis and Mathematical Physics.

Genres: Mathematics, Textbooks, Reference, Engineering, Nonfiction

563 pages, Hardcover

First published December 1, 1999

About the author

Edward Barry Saff

Reviews

[Logan · Rating 1 out of 5]

This is a great textbook for someone who doesn’t want to learn anything about complex analysis. The proofs are nonexistent, mathematical rigor is entirely ignored, and many topics are either just left out, or discussed in minute detail. To paraphrase a passage from section 6.7, “you will prove in advanced calculus texts the Balzano-Weierstrass theorem.” The Balzano-Weierstrass theorem is not that difficult to prove if the text would introduce even the most basic notions of set theory. Other proofs are completely ignored, and the book fails to mention anything about elliptic and modular functions, which Richard Borcherds, a fields medal winner, has claimed is a necessary topic for a good complex analysis textbook. Some will claim that since it is geared towards engineers, it should be less mathematically rigorous. I would argue that not understanding the why behind a concept in mathematics presents a significant detriment to one’s education. This textbook should not be used in any formal setting to teach students if they actually want to learn anything about complex analysis.

[Othello Gomes · Rating 3 out of 5]

PTSD.

[Samu]

Good book

[Alex · Rating 4 out of 5]

Great introduction for undergrads.

[aruushi · Rating 4 out of 5]

7/10

A helpful addition to a complex analysis course I was taking, but it did not add any additional information or nuance that I believe could not have already been included or better explained in the course itself. That said, it did help me in my course when all required knowledge was not always taught in class.

[James Millikan · Rating 4 out of 5]

This was a fine text for my Complex Analysis course. Reading the book after lectures helped to clarify concepts and explore additional applications. Nevertheless, with so much good complex variables content on Youtube, I didn't use it as much as I anticipated. If your prof requires this text, I would recommend reading the relevant chapter before starting a new unit, but then look elsewhere for more interactive content (videos, Desmos graphs, etc) to help complete the problem sets.