Module overview
Differential equations occupy a central role in mathematics because they allow us to describe a wide variety of real-world systems. Their study and applications range from pure and applied mathematics to physics, engineering , biology and finance, among others.
The module begins with ordinary differential equations (ODEs) discussing how to solved first and second order homogeneous and inhomogeneous ODEs. We study boundary value problems and develop Sturm-Liouville theory. We then look at how one can express a general periodic function in terms of Fourier series of sine and cosine functions.
Next, we introduce some of the basic concepts of partial differential equations (PDEs). The three important classes of second order PDE appropriate for modelling different sorts of phenomena are introduced and the appropriate boundary conditions for each of these are considered. The technique of separation of variables is used to reduce the problem to that of solving the sort of ordinary differential equations seen at the start of the module and writing the general solution using Fourier series and Sturm-Liouville theory. Throughout the module there will be a strong emphasis on problem solving and examples.
The last part of the module is an introduction to integral transforms with emphasis on Laplace transforms. We show how Laplace transforms may be used to solve ordinary and partial differential equations.
Linked modules
Prerequisites (MATH1056 or MATH1059 and MATH1060) and MATH2039 or (MATH1006 and MATH1007)