teaching

ACM30130 Advanced Computational Science

ACM30130 is a hands-on computational module designed to teach students how to approach mathematical modelling problems using computational tools such as Python and Mathematica.

Typical module content includes

• Shooting methods for boundary value problems
• Finite difference methods for boundary value problems
• Errors and Richardson extrapolation
• Symbolic computer algebra
• Computer-aided matched asymptotic expansions

ACM30140 Numerical Methods for PDEs

ACM30140 provides an introduction to numerical analysis through the development of standard numerical methods for partial differential equations. Two lectures per week focus on theoretical aspects, and one class per week focuses on its practical implementation in Python.

Typical module content includes

• Convergence and linear stability of one-step methods for ODEs
• Introduction to higher-order timestepping methods
• Finite difference methods for evolutionary PDEs
• The solution of large linear systems
• Fourier stability analysis of numerical methods
• 2-D problems and fast Poisson solvers

ACM40690 Applied Complex Variables

ACM40690 provides an overview of advanced methods in applied mathematics, particularly focused on using complex analysis to obtain closed-form solutions.

Typical module content includes

• Contour integrals in the complex plane
• Laplace transforms
• Asymptotic analysis of integrals
• The method of steepest descent
• Green’s functions
• Conformal mapping