MAT7201 Mathematical Modelling and Simulations

Mathematical modelling is a set of principles, methods and processes for using mathematical tools to understand systems or solve real world problems. In this course, students study the problem-solving process. Students learn how to identify a problem, construct or select an appropriate model, determine what data needs to be collected, test the validity of the model, calculate solutions and implement the model. Emphasis lies on model construction in order to promote student creativity and demonstrate the link between theoretical mathematics and real-world applications.

Course Objective
The overall objective of this course is to provide an introduction to the principles and processes of mathematical modelling while giving students an opportunity to develop and construct appropriate models for various problem situations, analyze given models to uncover underlying assumptions, and investigate the problems to find out what has already been done toward developing solutions.

Learning Outcomes
After completing the course the student is expected to

• formulate various problems starting from simple physical principles and derive the corresponding Euler-Lagrange equation such that you can derive basic equations for continuous equilibrium problems in one, two, and three space dimensions;
• model (spatially discrete) time-dependent systems by ordinary differential equations;
• investigate the stability of autonomous systems and explore geometrically the phase space of 2D dynamical systems using analytical and numerical tools;
• derive asymptotic expansions for certain simple singular perturbation problems;
• analyze and select iterative methods for large linear systems.