We know complex analysis is one of the most important branches of mathematics connecting myriad areas. It is replete with profound results and theorems and theorems. However, a good number of the theorems both in elementary and advanced complex analysis are of existential sort. As a prime example take the Riemann open mapping theorem. I would be highly obliged if somebody could kindly recommend me some books that takes a computational and algorithmic approach to the subject combined with a geometric approach. Books that illustrate examples with coding examples, if any such books are there, are also requested. Thanking you in advance
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4$\begingroup$ The obvious reference here is Peter Henrici's three volume set Applied and Computational Complex Analysis. $\endgroup$– Christian ClasonCommented Jun 1, 2022 at 8:18
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$\begingroup$ that is too old,are there any recent books $\endgroup$– AgnostMysticCommented Jun 1, 2022 at 8:48
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3$\begingroup$ What is it about being “old” that makes it a bad suggestion? I would have agreed Henrici’s books are the obvious reference. $\endgroup$– KConradCommented Jun 1, 2022 at 14:08
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1$\begingroup$ No way a bad suggestion...I thoght a recent book might include explicit implementable algorithms or code examples. And i was just wondering why nobody has written a book after that book on such a fascinating subject Anyways ,lots of thanks for the recommendation $\endgroup$– AgnostMysticCommented Jun 1, 2022 at 14:19
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2 Answers
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Peter Henrici, Applied and computational complex analysis, in 3 volumes, Willey and Sons, NY, 1988.
This is a kind of encyclopedic book, addressing all aspects of complex analysis. Also, if you read other languages,
W. Koppenfels, F. Stallmann, Praxis der Konformen Abbildung, Springer, 1959
М. А. Лаврентьев, Б. В. Шабат, Методы теории функций комплексного переменного, Москва, Наука, 1973.
answered Jun 1, 2022 at 11:16
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This edited volume is specific to Riemann surfaces but might be of interest:
Computational Approach to Riemann Surfaces, Bobenko & Klein (eds), Springer 2011