Introduction

We have seen how changing the variable of integration of a single integral or changing the

coordinate system for multiple integrals can make integrals easier to evaluate. In this Section we introduce the Jacobian. The Jacobian gives a general method for transforming the coordinates of any multiple integral.

Prerequisites

• have a thorough understanding of the various techniques of integration
• be familiar with the concept of a function of several variables
• be able to evaluate the determinant of a matrix

Learning Outcomes

• decide which coordinate transformation simplifies an integral
• determine the Jacobian for a coordinate transformation
• evaluate multiple integrals using a transformation of coordinates