Ebook: Complex Analysis through Examples and Exercises

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.

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This volume on complex analysis offers an exposition of the theory of complex analysis via a comprehensive set of examples and exercises. The book is self-contained and the exposition of new notions and methods is introduced step by step. A minimal amount of expository theory is included at the beginning of each section in the Preliminaries, with maximum effort placed on well-selected examples and exercises capturing the essence of the material. 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 exercises; the answers, and occasionally, some hints, are given. Special sections contain so-called Composite Examples which consist of combinations of different types of examples explaining some problems completely and giving the reader an opportunity to check all his previously accepted knowledge.
Audience: This volume is intended for undergraduate and graduate students in mathematics, physics, technology and economics interested in complex analysis.

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This volume on complex analysis offers an exposition of the theory of complex analysis via a comprehensive set of examples and exercises. The book is self-contained and the exposition of new notions and methods is introduced step by step. A minimal amount of expository theory is included at the beginning of each section in the Preliminaries, with maximum effort placed on well-selected examples and exercises capturing the essence of the material. 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 exercises; the answers, and occasionally, some hints, are given. Special sections contain so-called Composite Examples which consist of combinations of different types of examples explaining some problems completely and giving the reader an opportunity to check all his previously accepted knowledge.
Audience: This volume is intended for undergraduate and graduate students in mathematics, physics, technology and economics interested in complex analysis.
Content:
Front Matter....Pages i-x
The Complex Numbers....Pages 1-35
Sequences and series....Pages 37-52
Complex functions....Pages 53-72
Conformal mappings....Pages 73-102
The Integral....Pages 103-127
The Analytic functions....Pages 129-170
Isolated Singularities....Pages 171-190
Residues....Pages 191-226
Analytic continuation....Pages 227-254
Integral transforms....Pages 255-311
Miscellaneous Examples....Pages 313-332
Back Matter....Pages 333-337

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This volume on complex analysis offers an exposition of the theory of complex analysis via a comprehensive set of examples and exercises. The book is self-contained and the exposition of new notions and methods is introduced step by step. A minimal amount of expository theory is included at the beginning of each section in the Preliminaries, with maximum effort placed on well-selected examples and exercises capturing the essence of the material. 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 exercises; the answers, and occasionally, some hints, are given. Special sections contain so-called Composite Examples which consist of combinations of different types of examples explaining some problems completely and giving the reader an opportunity to check all his previously accepted knowledge.
Audience: This volume is intended for undergraduate and graduate students in mathematics, physics, technology and economics interested in complex analysis.
Content:
Front Matter....Pages i-x
The Complex Numbers....Pages 1-35
Sequences and series....Pages 37-52
Complex functions....Pages 53-72
Conformal mappings....Pages 73-102
The Integral....Pages 103-127
The Analytic functions....Pages 129-170
Isolated Singularities....Pages 171-190
Residues....Pages 191-226
Analytic continuation....Pages 227-254
Integral transforms....Pages 255-311
Miscellaneous Examples....Pages 313-332
Back Matter....Pages 333-337
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