This course aims to introduce aspects of the theory and methods used in mathematical modelling. Topics covered in the course include: dynamical systems and integral transforms. It is an essential course for intending honours students. The emphasis is on methods and applications.

2 x lectures per week. Fortnightly tutorials.

Mathematics 2A: Multivariable Calculus, Mathematics 2B: Linear Algebra.

  One degree examination (80%) (1 hour 30 mins); coursework (20%).

Reassessment will not be available for continuous assessment. Immediate feedback will be given to students at the assignment deadline, and it is not practical to set multiple versions of each of these exercises.

In total 80% of the assessment can be repeated for students not reaching the threshold grade.

Note that students are required to submit 75% of the assessments in order to receive a grade for the course. Accordingly, students who have a substantial period of illness and have all eAssignments and tutorial group work MV'ed, will not be in danger of failing to receive credits.

This course aims to introduce aspects of the theory and methods used in mathematical modelling. The course first aims to provide an introduction to dynamical systems associated with mathematical models. Students will learn to construct the solution of the ordinary differential equations arising in such models and qualitatively analyse these solutions. The course then aims to provide an introduction to Fourier series, Fourier and Laplace transforms, including their use in simplifying and solving differential equations.

By the end of this course, students will be able to:

■ Analyse dynamical systems consisting of a single dependent variable and which are modelled using ordinary differential equations. 

■ Analyse the stability of equilibrium points in first order autonomous ordinary differential equations and construct phase portraits for single dependent variable dynamical systems.

■ Solve linear systems of autonomous ordinary differential equations using the matrix exponential and identify phase portraits of two-dimensional systems.

■ Compute Fourier series, Fourier and Laplace transforms, including the use of their elementary properties to simplify and solve differential equations.

■ State the definitions, results and formulae presented in lectures; apply and adapt these to solve suitable problems.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.