### Introduction

The derivatives div, grad and curl from Section 28.2 can be carried out using coordinate systems other than the rectangular Cartesian coordinates. This Section shows how to calculate these derivatives in other coordinate systems. Two coordinate systems - cylindrical polar coordinates and spherical polar coordinates - will be illustrated.

#### Prerequisites

- be able to find the gradient, divergence and curl of a field in Cartesian coordinates
- be familiar with polar coordinates

#### Learning Outcomes

- find the divergence, gradient or curl of a vector or scalar field expressed in terms of orthogonal curvilinear coordinates

#### Contents

1 Orthogonal curvilinear coordinates1.1 Cylindrical polar coordinates

1.2 Spherical polar coordinates

2 Vector derivatives in orthogonal coordinates

3 Cylindrical polar coordinates

4 Engineering Example 2

4.1 Divergence of a magnetic field

5 Spherical polar coordinates

6 Engineering Example 3

6.1 Electric potential