This module is the fourth in a series of four mathematical modules for students across the Faculty of Science. It covers matrix algebra and numerical methods (with applications to many multi-variable problems in science) second order partial differential equations (which govern the behaviour of diffusive, advective and wave-like systems) and solid mechanics (applications in geophysics, glaciology and material science). There is a continuing emphasis on applied examples, and the use of numerical computing software (Matlab) is extended with a dedicated programming component.