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.
Author(s): Endre Pap
Series: Kluer Texts in the Mathematical Sciences 21
Edition: Reprint
Publisher: Springer
Year: 1999,2010
Language: English
Pages: C, X, 337, B
Tags: Mathematical Analysis Mathematics Science Math Functional Pure Algebra Trigonometry Calculus Geometry Statistics New Used Rental Textbooks Specialty Boutique
Preface
Chapter 1 The Complex Numbers
1.1 Algebraic Properties
1.1.1 Preliminaries
1.1.2 Examples and Exercises
1.2 The Topology of the Complex Plane
1.2.1 Preliminaries
1.2.2 Examples and Exercises
Chapter 2 Sequences and series
2.1 Sequences
2.1.1 Preliminaries
2.1.2 Examples and Exercises
2.2 Series
2.2.1 Preliminaries
2.2.2 Examples and Exercises
Chapter 3 Complex functions
3.1 General Properties
3.1.1 Preliminaries
3.1.2 Examples and Exercises
3.2 Special Functions
3.2.1 Preliminaries
3.2.2 Examples and Exercises
3.3 Multi-valued functions
3.3.1 Preliminaries
3.3.2 Examples and Exercises
Chapter 4 Conformal mappings
4.1 Basics
4.1.1 Preliminaries
4.1.2 Examples and Exercises
4.2 Special mappings
4.2.1 Preliminaries
4.2.2 Examples and Exercises
Chapter 5 The Integral
5.1 Basics
5.1.1 Preliminaries
5.1.2 Examples and Exercises
Chapter 6 The Analytic functions
6.1 The Power Series Representation
6.1.1 Preliminaries
6.1.2 Examples and Exercises
6.2 Composite Examples
Chapter 7 Isolated Singularities
7.1 Singularities
7.1.1 Preliminarie
7.1.2 Examples and Exercises
7.2 Laurent series
7.2.1 Preliminaries
7.2.2 Examples and Exercises
Chapter 8 Residues
8.1 Residue Theorem
8.1.1 Preliminaries
8.1.2 Examples and Exercises
8.2 Composite Examples
Chapter 9 Analytic continuation
9.1 Continuation
9.1.1 Preliminaries
9.1.2 Examples and Exercises
9.2 Composite Examples
Chapter 10 Integral transfornns
10.1 Analytic Functions Defined by Integrals
10.1.1 Preliminaries
10.1.2 Examples and Exercises
10.2 Composite Examples
Chapter 11 Miscellaneous Examples
Bibliography
List of Symbols
Index
