Complex Bootcamp Exercises: Basics of Holomorphic Functions
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Welcome to the complex analysis bootcamp. In this first set of problems we focus on basic properties of holomorphic functions and work up to branches of functions.
Complex Prelim Resources
Several problems and the order of presentation follows Ahlfors Complex Analysis. I recommend you read from this book or one of Conway, Palka, or Rudin.Other resources are available in the bookcase in the grad lounge and on Ken's website.
2022
Complex Bootcamp Exercises: Conformal Maps
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This set of problems focuses on conformal mappings.
Complex Bootcamp Exercises: Integration I
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This set of problems focuses on some fundamental theorems relating to integration (Cauchy’s theorem, integral formula, zeros, singularities, and the maximum principle.)
Complex Bootcamp Exercises: Integration II
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This set of problems focuses on the residue theorem, argument principle, and existence of branches. Some more problems on topics from the last post are also included.
Complex Bootcamp Exercises: Products and Series
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This set of problems focuses on series and product representations of holomorphic and meromorphic functions.
Complex Bootcamp Exercises: Normal Families
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This set of problems focuses on normal families (precompact sets of functions,) Picard’s theorem, Jensen’s formula, and other topics.