# Complex Analysis through Examples and Exercises

• Endre Pap

Part of the Kluwer Text in the Mathematical Sciences book series (TMS, volume 21)

1. Front Matter
Pages i-x
2. Endre Pap
Pages 1-35
3. Endre Pap
Pages 37-52
4. Endre Pap
Pages 53-72
5. Endre Pap
Pages 73-102
6. Endre Pap
Pages 103-127
7. Endre Pap
Pages 129-170
8. Endre Pap
Pages 171-190
9. Endre Pap
Pages 191-226
10. Endre Pap
Pages 227-254
11. Endre Pap
Pages 255-311
12. Endre Pap
Pages 313-332
13. Back Matter
Pages 333-337

### Introduction

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.

### Keywords

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

• Endre Pap
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