Complex Analysis through Examples and Exercises

1. Front Matter

   Pages i-x

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2. The Complex Numbers

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   Pages 1-35

3. Sequences and series

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   Pages 37-52

4. Complex functions

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   Pages 53-72

5. Conformal mappings

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   Pages 73-102

6. The Integral

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   Pages 103-127

7. The Analytic functions

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   Pages 129-170

8. Isolated Singularities

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   Pages 171-190

9. Residues

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   Pages 191-226

10. Analytic continuation

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    Pages 227-254

11. Integral transforms

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    Pages 255-311

12. Miscellaneous Examples

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    Pages 313-332

13. Back Matter

    Pages 333-337

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The book Complex Analysis through Examples and Exercises has come out from the lectures and exercises that the author held mostly for mathematician and physists . The book is an attempt to present the rat her involved subject of complex analysis through an active approach by the reader. Thus this book is a complex combination of theory and examples. Complex analysis is involved in all branches of mathematics. It often happens that the complex analysis is the shortest path for solving a problem in real circum­ stances. We are using the (Cauchy) integral approach and the (Weierstrass) power se ries approach . In the theory of complex analysis, on the hand one has an interplay of several mathematical disciplines, while on the other various methods, tools, and approaches. In view of that, the exposition of new notions and methods in our book is taken step by step. A minimal amount of expository theory is included at the beinning of each section, the Preliminaries, with maximum effort placed on weil selected examples and exercises capturing the essence of the material. Actually, I have divided the problems into two classes called Examples and Exercises (some of them often also contain proofs of the statements from the Preliminaries). The examples contain complete solutions and serve as a model for solving similar problems given in the exercises. The readers are left to find the solution in the exercisesj the answers, and, occasionally, some hints, are still given.

• Complex analysis
• DEX
• Turing
• Volume
• complex number
• conformal map
• function
• functions
• integral transform
• knowledge
• mapping
• mathematics
• maximum
• residue
• set

• Institute of Mathematics, University of Novi Sad, Novi Sad, Yugoslavia

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