Name: Visual Complex Functions
ISBN: 9783034801799

Visual Complex Functions

This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains. Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes. In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions. Visual Complex Functions may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits.

What Hacker News says

bmitcAug 2024

A good book is Visual Complex Functions: An Introduction with Phase Portraits: https://www.amazon.com/Visual-Complex-Functions-Introduction...

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simonmysunAug 2024

It reminds me that each year Freiberg University of Mining and Technology publishes a calendar of Complex Beauties[1], of which I buy several copies as gifts every year.

It includes 12 visualizations of selected complex functions and their background and related mathematicians. I would highly recommend reading them. Prof. Dr. Elias Wegert, the author who actively contributes to this calendar, also wrote Visual Complex Functions: An Introduction with Phase Portraits which is mentioned by another comment here.

[1]: https://blogs.hrz.tu-freiberg.de/mathekalender/english/

Edit: Navigate to the german page if you want to buy it

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thisrodJun 2017

What, because all the good ones were written before scientists could afford books with pictures? :-p

Check this out:

https://www.amazon.com/Visual-Complex-Functions-Introduction...

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jacobolusMar 2017

First, note that Needham’s book Visual Complex Analysis is not interactive. It’s just a book with slightly more pictures and more geometrically motivated explanations than most books have.

Personally I don’t think it’s ideal to use as an only book for a complex analysis course, but I found it very helpful for crystalizing my intuition/thinking about the subject. I would recommend every university math student try reading it, especially after going through a traditional course. (Also recommended is Wegert’s book Visual Complex Functions, but definitely not as a primary text.)

Finally, I suspect switching primary books is only going to work well if the professor makes a commitment to teaching using the same explanations. If the book goes about the subject in a completely different way than the lectures, I can well imagine students working homework sets on a short deadline may get confused.

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simonmysunAug 2024

For the past 14 years, Freiberg University of Mining and Technology has been publishing calendars of Complex Beauties, which include 12 stunning visualizations of complex functions each year, along with the background information and the related mathematicians. I would highly recommend reading the stories behind these complex functions. I have bought several copies as gifts in recent years and feel sad to learn that the 2024 version is the last one. I guess this is because Prof. Wegert may have retired.

Prof. Elias Wegert, the author who actively contributes to these calendars, also wrote Visual Complex Functions: An Introduction with Phase Portraits[1].

[1]: https://doi.org/10.1007/978-3-0348-0180-5

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omershapiraJan 2023

Donald Sarason's "Complex Function Theory". There are bigger more complete books on complex analysis. There are even ones that are more appealing, like "Visual Complex Functions" by Elias Wegert.

Sarason's book is only 160 pages long, with legible text and clear examples. It covers the length of an undergraduate university class, and explains Holomorphic functions perfectly. The proofs are crystal clear, and so are the motivations. I haven't seen a better introduction.

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