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 ${\oint }_C\frac{f\left(z\right)}{z-z_0}dz$ 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