This module will show intuitive geometric and physical concepts such as length, area, volume, mass, circulation and flux can be translated into mathematical formulae. Its focus is the practical calculation of these formulae and their application to geometric problems in 2D and 3D.
We will study parametric curves and surfaces using the tools of vector calculus. The bulk of the course content relies on the use of partial differentiation and multiple integrals.
On successful completion of this module students should be able to:
- Parametrise simple curves and surfaces in Cartesian and other coordinates, including polar, cylindrical and spherical coordinates
- Calculate lengths of curves in R^2 and R^3
- Understand and be able to calculate line, surface and volume integrals with respect to various coordinate systems. This includes change of variables and change of order of integration in double/triple integrals
- Understand and prove simple properties of a conservative vector field
- State the Green's, Divergence and Stokes' Theorems and use them to aid calculations
- Apply all these techniques to problems in mechanics (mass, work done, circulation and flux) and geometry (area, volume, centre of mass).
Books: See the reading list on TalisLink opens in a new window