University of Galway

Course Module Information

Course Modules

Semester 2 | Credits: 5

This is a mathematical methods course, and amongst the topics considered are the heat equation, Laplace's equation, Sturm-Liouville theory, the Fourier transform, and the numerical solution of partial differential equations using finite difference techniques.
(Language of instruction: English)

Learning Outcomes
  1. Solve the 1-dimensional heat equation subject to different boundary conditions and initial conditions
  2. Prove orthogonality of eigensolutions and reality of eigenvalues of a Sturm-Liouville system
  3. Calculate eigenvalues and construct corresponding eigenfunctions for some simple Sturm-Liouville problems
  4. Solve the 2-dimensional Laplace equation subject to different boundary conditions in a rectangular or a rotationally symmetric region
  5. Solve the 1-dimensional heat equation on an infinite region by use of the Fourier transform
  6. Solve the 1-d heat equation numerically by use of the finite difference method
Assessments
  • Written Assessment (70%)
  • Continuous Assessment (30%)
Teachers
Reading List
  1. "Advanced engineering mathematics" by Erwin Kreyszig
    ISBN: 978-047045836.
    Publisher: Wiley
  2. "Mathematical methods for physics and engineering" by K. F. Riley, M. P. Hobson, S. J. Bence
    ISBN: 978-052167971.
    Publisher: Cambridge University Press
  3. "Mathematical Methods in the Physical Sciences" by Mary L. Boas
    ISBN: 978-047119826.
    Publisher: John Wiley and Sons
The above information outlines module MP554: "Advanced Applied Mathematics for Engineers 2" and is valid from 2016 onwards.
Note: Module offerings and details may be subject to change.