Mathematical Modelling

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Abstract

This subject develops students' practical skills by using computer software to solve mathematical applications. The two main applications considered are the numerical solutions of differential equations (ordinary and partial); and fitting data to a model using least-squares regression (linear and non-linear).

Syllabus

The subject will cover the following topics: Introduction to mathematical modelling.Programming with Maple.Linear regression: simple and multiple; forward selection and backwards elimination methods.Numerical solution of ordinary differential equations for both initial and boundary value problems; Euler's method, Runge-Kutta method, shooting method and finite difference methods.Fourier series.Partial differential equations (parabolic, hyperbolic … For more content click the Read More button below.

The subject will cover the following topics:

Introduction to mathematical modelling.
Programming with Maple.
Linear regression: simple and multiple; forward selection and backwards elimination methods.
Numerical solution of ordinary differential equations for both initial and boundary value problems; Euler's method, Runge-Kutta method, shooting method and finite difference methods.
Fourier series.
Partial differential equations (parabolic, hyperbolic and elliptic): separation of variables, numerical solution using finite difference methods; stability of finite difference methods and method of characteristics.
Non-linear regression: various numerical methods: grid, gradient, Gauss-Newton and mixed.

Learning outcomes

Upon successful completion of this subject, students should:

be able to write computer programs to solve real-life problems;

be able to numerically calculate the solutions of ordinary differential equations using various methods;

be able to adapt existing code to produce numerical solutions for differential equations;

be able to generate suitable finite difference equations from differential equations;

be able to determine the stability of a finite difference equation;

be able to calculate the solutions of partial differential equations using various methods;

be able to fit data to a model using linear and non-linear regression techniques; and

be able to interpret mathematical models and communicate their output to non-mathematical audiences.

Enrolment restrictions

Only available to post graduate students

Pre-requisite

Incompatible