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