I have completely finished some of calculus, such as Limits, Derivatives, Sequence and series, Indefinite and Definite Integration and many more. And have solved humongous amount questions on these topics. I am also good with basics. So to expand my knowledge more, I wanna self study Complex analysis and Contour Integration as I did for previous topics. Can you please suggest some good books for them? Starting from stratch so that it's easy for me to self study? It don't have to be one book, can be series of books too. Any help would be greatly appreciated, thank you. :)
2026-03-30 08:41:23.1774860083
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Good books to learn Complex Analysis and Contour Integration?
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Starting from scratch and completely rigorous (way more rigorous than a few suggestions on this page, no hand-waving whatsoever) is "Theory of Functions of a Complex Variable" by Markushevich. If you have the freedom to invest a good time in it, it is the book to go.
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I too am starting to learn contour integration and some things what I have found useful so far I detail for you.
At this site down in the comments some book suggestions can be found.
At the same site is many interesting examples for contour integration and the author might respond if something is not clear. In any case it's free.
If it's learning with math software then, though old, William T. Shaw - Complex Analysis with MATHEMATICA is quite good.
Also Lars Ahlfors - Complex Analysis has some useful examples.
In any case borrow them before buying - many a time what works for one person might not for another.
I would recommend Complex Analysis (Princeton Lectures in Analysis, Volume II) written by Elias M. Stein (Ph.D advisor of the famous Professor Terrence Tao) and Rami Shakarchi. This is the second analysis book in the serious of books and the authors aim to sacrifice the depth of presented topics in exchange for the demonstration of various connections of the materials to other branch of mathematics, which in my mind will help you to hunt for next interested topics in your mind along the journey.