Introduction

Complex variable techniques have been used in a wide variety of areas of engineering. This has been particularly true in areas such as electromagnetic field theory, fluid dynamics, aerodynamics and elasticity. With the rapid developments in computer technology and the consequential use of sophisticated algorithms for analysis and design in engineering there has been, in recent years, less emphasis on the use of complex variable techniques and a shift towards numerical techniques applied directly to the underlying full partial differential equations which model the situation. However it is useful to have an analytical solution, possibly for an idealized model in order to develop a better understanding of the solution and to develop confidence in numerical estimates for the solution of more sophisticated models.

The design of aerofoil sections for aircraft is an area where the theory was developed using complex variable techniques. Throughout engineering, transforms defined as complex integrals in one form or another play a major role in analysis and design. The use of complex variable techniques allows us to develop criteria for the stability of systems.

Prerequisites

• be able to carry out integration of simple real-valued functions
• be familiar with the basic ideas of functions of a complex variable
• be familiar with line integrals

Learning Outcomes

• understand the concept of complex integrals