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 n/a
    ISBN: 9780471507284.
    Publisher: New York, Wiley [1972]
  2. "Mathematical methods for physics and engineering (2nd ed)" by n/a
    ISBN: 9780521683395.
    Publisher: CUP
  3. "Mathematical Methods in the Physical Sciences" by Mary L. Boas
    ISBN: 9788126508105.
    Publisher: Wiley
The above information outlines module MP346: "Mathematical Methods II" and is valid from 2018 onwards.
Note: Module offerings and details may be subject to change.