Upon completion of this course the student will be able to:
- use the concepts of vector fields, rotation, divergence and gradient, conservative fields,
- integrate vector fields along a line, over a 2D surface, 3D volume and over surfaces in space,
- use the theorems of Green, Gauss and Stokes to calculate integrals of vector fields.
This section focuses on the calculation of vector fields. The concepts of rotation, divergence and gradient are introduced, and special attention is given to conservative vector fields. In addition, integrals of vector fields along a line, a surface and 3D volume are treated, using the theorems of Green, Stokes and Gauss to establish relationships between these different types of integrals. This provides more insight into the meaning of integrals of vector fields and important theoretical relationships, but can also often be used to calculate these integrals more easily. These mathematical techniques are used directly in the module Electricity and Magnetism.|
The following topics are covered.
- vector fields, gradient, divergence, rotation, and conservative fields,
- integrals of vector fields over lines, surfaces, and also three-dimensional spaces and volumes,
- theorems by Green, Gauss and Stokes.