University of Galway

Course Module Information

Course Modules

Semester 1 | Credits: 5

This course introduces some advanced methods of mathematical physics for solving ordinary differential equations, using analytical, series approximation and numerical methods.
(Language of instruction: English)

Learning Outcomes
  1. Find the general solution to a second-order linear differential equation with constant coefficients when it is homogeneous, and a particular solution when it is inhomogeneous;
  2. Find a second, linearly independent, solution to a second-order differential equation when one is known;
  3. Compute the first few terms of a power series or Frobenius series solution to a second-order linear equation with variable coefficients, when it exists;
  4. Derive orthogonality relations for trigonometric, Legendre and Bessel functions;
  5. Compute real integrals using the theorems of complex contour integration.
  6. Approximate the solution to a second-order ordinary differential equation using finite differences
Assessments
  • Written Assessment (70%)
  • Continuous Assessment (30%)
Teachers
Reading List
  1. "Advanced Engineering Mathematics" by E. Kreyszig
The above information outlines module MP345: "Mathematical Methods I" and is valid from 2018 onwards.
Note: Module offerings and details may be subject to change.