### Introduction

A vector field or a scalar field can be differentiated with respect to position in three ways to produce another vector field or scalar field. This Section studies the three derivatives, that is: (i) the gradient of a scalar field (ii) the divergence of a vector field and (iii) the curl of a vector field.

#### Prerequisites

- be familiar with the concept of a function of two variables
- be familiar with the concept of partial differentiation
- be familiar with scalar and vector fields

#### Learning Outcomes

- find the divergence, gradient or curl of a vector or scalar field

#### Contents

1 The gradient of a scalar field2 The divergence of a vector field

3 The curl of a vector field

4 Engineering Example 1

4.1 Current associated with a magnetic field

5 The Laplacian

6 Examples involving grad, div, curl and the Laplacian

7 Identities involving grad, div and curl