Pre-requisite: 64627
This unit is broadly divided into two interrelated strands. One strand unifies linear algebra and differential calculus into the calculus of vector functions. It develops the differential and integral calculus, establishes their properties, and shows how these properties give formula in general coordinate systems. The unit develops the application of these mathematical tools to inviscid and incompressible fluid dynamics. The other strand establishes properties of the basic partial differential equations (PDEs) that arise commonly in applications such as the heat equation, the wave equation and Laplace's equation. It develops the mathematical tools of Fourier transforms, Green's functions and special functions necessary to analyse such PDEs.