Complex Analysis

This book provides a logical development of the subject from its elementary root. The book is meant for the undergraduate students of Mathematics, Physics and Engineering. Complex Analysis is a subject developed from an imaginary number but it is beautifully applied in many Engineering disciplines. The book is an introductory treatise.

However, it does not suffer from lack of rigour. Our aim is to provide the reader an elementary, thorough and systematic introduction of the subject. In doing so, a stress is made on important basic ideas.

For example, the idea of the complex infinity is brought out through the Stereo graphic Projection and also through the mapping w = 1 / z in a lucid manner. This presentation enhances the understanding of the physical meaning of the complex infinity and its neighbourhood.

1. Complex Number System 1–7

2. Complex Plane 8–26

3. Sets Of Complex Points 27–32

4. Analytic Functions 33–60

5. Sequences And Series 61–70

6. Power Series And Elementary Functions 71–101

7. Elementary And Con formal Mappings 102–137

8. Complex Integration 138–188

9. Taylor’S And Laurent’S Series 189–233

10. Residues 234–278

11. Meromorphic Functions 279–288