Complex Functions Examples c-6 - Calculus of Residues

This is the sixth textbook you can download containing examples from the Theory of Complex Functions. In this volume we shall consider the rules of calculations or residues, both in finite singularities and in ∞. The theory heavily relies on the Laurent series from the fifth book in this series. The applications of the calculus of residues are given in the seventh book.

This is the sixth book containing examples from the Theory of Complex Functions. In this volume we shall consider the rules of calculations or residues, both in finite singularities and in ∞. The theory heavily relies on the Laurent series from the fifth book in this series. The applications of the calculus of residues are given in the seventh book.

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

15th June 2008

Introduction

1. Rules of computation of residues

2. Residues in nite singularities

3. Line integrals computed by means of residues

4. The residuum at ∞