University of Galway

Course Module Information

Course Modules

Semester 1 | Credits: 5

This module is a first course on the mathematical analysis of numerical methods for solving important computational problems. Topics covered include: Solving nonlinear equations; Technques for computing solutions to initial value problems; Matrix factorisation methods for solving linear systems; The estimation and applications of eigenvalues.

Learning Outcomes
  1. Derive Newton's (and related) methods for solving nonlinear equations;
  2. Give a mathematical analysis of the convergence properties of iterative methods for nonlinear equations;
  3. Provide a derivation and analysis of Euler's method based on Taylor's series;
  4. Motivate and apply Runge-Kutta methods for solving initial value problems;
  5. Construct a matrix factorisation method for solving systems of linear equations;
  6. Analyse the stability of linear solvers based on condition numbers;
  7. Implement the numerical algorithms described above in Matlab.
Assessments
  • Written Assessment (70%)
  • Continuous Assessment (30%)
Teachers
Reading List
  1. "An Introduction to Numerical Analysis" by Suli and Mayers
  2. "Afternotes on Numerical Analysis" by G. W. Stewart
  3. "Numerical Computing with Matlab" by Cleve B. Moler
The above information outlines module MA530: "Numerical Analysis I" and is valid from 2015 onwards.
Note: Module offerings and details may be subject to change.