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PostPosted: Mon Jul 30, 2018 9:53 pm 

Joined: Wed Nov 15, 2017 12:37 pm
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What are some of your book recommendations on Complex Analysis? I've been told that Jerold Marsden's "Basic Complex Analysis" is a must-read one, but after going through it, it seemed like a tough way to be introduced to these new concepts. What about "Complex Variables and Applications" by J.W. Brown and R.V. Churchill? I'm really starting to dig into it. Thanks!


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PostPosted: Tue Jul 31, 2018 11:51 pm 
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I would suggest that you read the following books on Complex Analysis:

  • J. Marsden, M. Hoffman - Basic Complex Analysis : Although it is developed in a rather slow manner, the exposition is in my opinion very nice, and the book contains lots of examples as well as exercises that help one acquire a good understanding of the theory.
  • E. Stein, R. Shakarchi - Complex Analysis : In contrast to the above book, this one introduces the reader to the basic concepts of complex analysis in a much quicker way and also contains some rather advanced topics (not necessarily treated in the previous book). The exposition is also very nice.
  • L. Ahlfors - Complex Analysis : A classical one, but may be considered rather hard as an introductory text.
  • W. Fischer, I. Lieb - A Course in Complex Analysis : This book is not only an introduction to the theory of (holomorphic) functions of one complex variable, but also to the theory of holomorphic functions of several variables.

Depending on your goals or needs, you could choose to focus on a particular one, but you could also consult all of the above books if, for example, you would like to read about more special topics or about several complex variables. Maybe the second and the fourth book cover in a rather quick (but transparent) way what is typically required in an undergraduate course on complex analysis.


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