Suggested Textbooks for Complex Analysis w/Proofs & Accessible w/o Real Analysis

In summary, The conversation is about a person asking for suggestions on a textbook on complex analysis that has proofs and is accessible without a formal real analysis course. One person recommends "Complex Analysis" by Freitag and Busam, which requires a lot of calculus but is still manageable without formal real analysis. Another person suggests "Visual complex analysis" by Needham, which may not require as much real analysis but may not be as rigorous.
  • #1
Skrew
131
0
I don't think this is the right area to post this question so to the mods: please be kind and move it to a better section if one exists.

I'm looking for a textbook on complex analysis which gives proofs but is accessible without a formal real analysis course.

I would appreciate suggestions on books.
 
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  • #2
I would recommend "Complex Analysis" by Freitag and Busam. It requires a lot of calculus (integrals, power series, sequences, compactness,...). But if you haven't seen any formal real analysis, then I think you could get away with it.

Give it a try!
 
  • #3
micromass said:
I would recommend "Complex Analysis" by Freitag and Busam. It requires a lot of calculus (integrals, power series, sequences, compactness,...). But if you haven't seen any formal real analysis, then I think you could get away with it.

Give it a try!

I don't know what compactness is, not that I couldn't look it up but I want the book to be more or less self contained.
 
  • #4
Well, compactness is explained in the book. So the book is quite self-contained. (only some proofs of theorems in the first chapter are not given).

But the more calculus and real analysis you've seen, the better. And this is true for every complex analysis book...
 
  • #5
Well, a book that doesn't have many requisites is "Visual complex analysis" by Needham. I don't think you'll need much real analysis for it. But it comes with a price. It might not be as rigorous as you would like... Still, it's a recommended read for everyone...
 

1. What is the best textbook for learning Complex Analysis with proofs?

There are many great textbooks available for learning Complex Analysis with proofs, but some of the most highly recommended options include "Complex Analysis" by Joseph Bak and Donald J. Newman, "Complex Analysis: A First Course with Applications" by Dennis G. Zill and Patrick D. Shanahan, and "Introduction to Complex Analysis" by H. A. Priestley.

2. Do I need to have knowledge of Real Analysis before studying Complex Analysis?

While having a background in Real Analysis can be helpful, it is not always necessary for studying Complex Analysis. Some textbooks may assume prior knowledge of Real Analysis, but there are also many accessible options that do not require this background.

3. Are there any textbooks that provide both proofs and accessible explanations of Complex Analysis?

Yes, there are several textbooks that strike a balance between rigorous proofs and accessible explanations. Some recommended options include "Complex Variables and Applications" by James Ward Brown and Ruel V. Churchill, "Complex Analysis: The Geometric Viewpoint" by Steven G. Krantz, and "Visual Complex Analysis" by Tristan Needham.

4. Which textbook is best for self-study of Complex Analysis?

The best textbook for self-study will depend on your individual learning style and goals. Some popular options for self-study include "A First Course in Complex Analysis with Applications" by Dennis G. Zill and Patrick D. Shanahan, "Introductory Complex Analysis" by Richard A. Silverman, and "Complex Analysis: A Modern First Course in Function Theory" by Jerry R. Muir Jr. and Michael J. Cloud.

5. Are there any online resources that can supplement my textbook study of Complex Analysis?

Yes, there are many online resources that can enhance your learning experience when studying Complex Analysis. Some popular options include video lectures on platforms like YouTube and Coursera, online problem sets and practice quizzes, and discussion forums for asking questions and getting help from others studying the subject.

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