Visual Complex Functions
by Elias Wegert · first published 2012
80% recommend20% neutral
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
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…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…
on “Immersive Linear Algebra – textbook with fully interactive figures (2015)” ↗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...
on “The future of education is plain text” ↗A good book is Visual Complex Functions: An Introduction with Phase Portraits: https://www.amazon.com/Visual-Complex-Functions-Introduction...
on “Visualizing Complex Functions” ↗…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
on “Visualizing Complex Functions” ↗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.…
on “Ask HN: Math books that made you significantly better at math?” ↗…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
on “Complex Beauties: Calendars with visualizations of complex functions” ↗…shewing its age. Mathematicians have invented things such as Algebraic Geometry; despite their best efforts, some of those things might be useful. And computers enable the printing of books such as Visual Complex Functions: An Introduction with Phase Portraits. The book Calculus on Manifolds helped readers such as physicists and engineers to think about vector calculus in the way that mathematicians did. Is there an equivalent…
on “Does Whittaker and Watson have a modern equivalent?” ↗