# Complex Analysis Through Examples And Exercises (texts In The Mathematical Sciences)

by Endre Pap /
2010 / English / PDF

10.6 MB Download

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.

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.