When mathematical modelling is used to describe physical, biological, chemical or other phenomena, one of the most common results is either a differential equation or a system of differential equations, which, together with appropriate boundary and/or initial conditions, describe the situation. This module explores how differential and difference equations are obtained from these models and methods for solving and analysing them. Methods for solving 2nd order (or higher) linear ordinary differential equations are developed, alongside separable solutions of partial differential equations using Fourier series.
Learning Outcomes
By the end of the module students should be able to:
Formulate models of problems in terms of systems of difference or differential equations.
Apply a range of methods to solve or analyse solutions of systems of difference or differential equations.
Be able to classify the equilibrium points of two-dimensional systems of linear ordinary differential equations.
Understand the physical derivations of the advection, diffusion and wave equations in 1-D.
Understand the theory of, and be able to solve, standard types of ordinary differential equations using a variety of methods including variation-of-parameters and series solutions.
Understand the theory of Fourier series and be able to apply it to the solution of linear ordinary and partial differential equations.
Assessment
Assessment Methods & Exceptions
Assessment:
2hr examination (80%) In-course assessment (20%) (including a variety of assessment possibly including problem sheets, class tests, online quizzes and group projects)
