Introductory description

N/A

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Concepts of Mathematical Modelling, e.g. conservation and dissipation principle, dimensional analysis, non dimensionalization,
asymptotic expansion, introduction to calculus of variations, minimization, Hamiltonian dynamics, Lagrange multipliers, inverse and optimal control problems, gradient flow Numerical approximations Derivation of explicit and implicit Runge Kutta and multistep methods, Butcher tableau, Newton’s method, polynomial interpolation and quadrature, stability, consistency, and convergence analysis.

This module focuses on fundamental concepts of mathematical modelling involving ordinary differential equations and their numerical solution. Modelling concepts such as conservation and dissipation principles, calculus of variations, and non dimensionalisation will be covered using typical examples from physics, biology, and other areas of science and engineering. Basic numerical approximation methods will be presented for solving the resulting systems of differential equations like Runge-Kutta and multistep methods. Concepts like stability, consistency, and convergence will be covered in this module, with the aim of introducing the approximation techniques used in tackling mathematical problems which do not yield to closed form analytic formulae.

Learning outcomes

By the end of the module, students should be able to:

• - Implement and test numerical methods using a scripting language
• - Understand the central concepts of mathematical modelling
• - Be able to derive and analyse fundamental numerical methods

Indicative reading list

D. F. F. Griffiths and D. J. Higham, Numerical Methods for Ordinary Differential Equations: Initial Value
Problems, Springer (2010)
T. Witlski, M.Brown, Methods of Mathematical Modelling: Continuous System and Differential Equations,
Springer (2015)
R. L. Burden and J. D Faires, Numerical Analysis, 8th edition, Brooks-Cole Publishing (2004).

Subject specific skills

You should understand the principles used to derive mathematical models of time dependent and stationary problems arising in scientific areas such as physics, chemistry and biology but also in economics, finance and social sciences. Also you should be able to solve the resulting systems of ordinary differential equation using different approximations methods and have a good understanding of the different properties of these methods. This module will provide you with the foundations required for a wide range of topics in applied and computational mathematics including mathematical modelling.

Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.