This module builds on the calculus covered in earlier modules and introduces areas like differential equations and functions of two variables. It introduces the learner to vector calculus and line integrals. It extends the material on complex numbers to include the ability to deal with polar coordinates.
First order – separable, homogeneous, linear. Second order linear with constant coefficients. Modelling simple systems: chemical kinetics and simple and damped harmonic motion (e.g., natural and forced oscillations of mechanical and electrical systems).
Functions of two variables
Partial derivatives. Directional derivatives. Stationary points. Applications of Maxima and minima. Apply methods to physics problems.
Vector valued functions
Vector and scalar fields. Gradient, divergence and curl operators. Vector differential calculus. Line integrals. Green’s Theorem. Divergence Theorem, Stokes’ Theorem. Applications to applied physics problems.
Graphs in circular polar co-ordinates. Integration in polar co-ordinates – areas in the plane. Spherical polar co-ordinates. Applications to wave equations.
Lectures supported by tutorials and problem sheets which may be supplemented by online materials and the use of mathematical software packages.
|Module Content & Assessment