Topics in Complex Analysis

by Joel L Schiff

Complex analysis is found in many areas of applied mathematics, from fluid mechanics, thermodynamics, signal processing, control theory, mechanical and electrical engineering to quantum mechanics, among others. And of course, it is a fundamental branch of pure mathematics. The coverage in this text includes advanced topics that are not always considered in more elementary texts. These topics include, a detailed treatment of univalent functions, harmonic functions, subharmonic and superharmonic functions, Nevanlinna theory, normal families, hyperbolic geometry, iteration of rational functions, and analytic number theory. As well, the text includes in depth discussions of the Dirichlet Problem, Green’s function, Riemann Hypothesis, and the Laplace transform. Some beautiful color illustrations supplement the text of this most elegant subject.

292 pages, Hardcover

Published October 24, 2022

Reviews

[Ashlee · Rating 4 out of 5]

An outstanding text that combines rigorous theory with practical examples. This book has deepened my understanding of complex analysis in ways I didn’t expect.

Gershwyn,
Moderator: Goodreads Librarians Group.

[Jeri · Rating 4 out of 5]

The discussion on analytic continuation was very interesting. I wonder if the author plans to explore more modern applications of this topic in a future edition?

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[Angelique · Rating 4 out of 5]

The structure of this book is remarkable. Every chapter builds seamlessly on the previous, making even challenging topics approachable and insightful.

Moderator: Angelique.

[Patti and Deborah · Rating 4 out of 5]

I’m fascinated by the treatment of conformal mappings in Chapter 3. Could the author provide more examples of real-world applications?

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[Lily · Rating 5 out of 5]

Well-written and logically organized. I especially appreciated the exercises at the end of each chapter that reinforce the concepts.

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[Jenn G · Rating 4 out of 5]

Informative but sometimes dense. Certain proofs could benefit from more detailed explanations to aid understanding.

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[Alyana · Rating 5 out of 5]

A decent resource for complex analysis, though it may require supplementary material for beginners to fully grasp some concepts.

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