Complex Functions Examples c-2

This is the second book containing examples from the Theory of Complex Functions. The first topic will be examples of the necessary general topological concepts. Then follow some examples of complex functions, complex limits and complex line integrals. Finally, we reach the subject itself, namely the analytic functions in general. The more specific properties of these analytic functions will be given in the books to follow.

Even if I have tried to be careful about this text, it is impossible to avoid errors, in particular in the first edition. It is my hope that the reader will show some understanding of my situation.

Leif Mejlbro

30th May 2008

• Introduction

1. Some necessary theoretical results
2. Topological concepts
3. Complex Functions
4. Limits
5. Line integrals
6. Differentiable and analytic functions; Cauchy-Riemann’s equations
7. The polar Cauchy-Riemann’s equations
8. Cauchy’s Integral Theorem
9. Cauchy’s Integral Formula
10. Simple applications in Hydrodynamics