Cauchy’s Theorem

Introduction

In this Section we introduce Cauchy’s theorem which allows us to simplify the calculation of certain contour integrals. A second result, known as Cauchy’s integral formula, allows us to evaluate some integrals of the form ${&oint;}_{C} \frac{f (z)}{z - z_{0}} d z$ where $z_{0}$ lies inside $C$ .

Prerequisites

be familiar with the basic ideas of functions of a complex variable
be familiar with line integrals

Learning Outcomes

state and use Cauchy’s theorem
state and use Cauchy’s integral formula

1 Cauchy’s theorem

1.1 Simply-connected regions

2 Cauchy’s integral formula

2.1 The derivative of an analytic function

Cauchy’s Theorem

Introduction

Prerequisites

Learning Outcomes

Contents

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