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Course Module Information
Course Modules
MA530: Numerical Analysis I
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
- Derive Newton's (and related) methods for solving nonlinear equations;
- Give a mathematical analysis of the convergence properties of iterative methods for nonlinear equations;
- Provide a derivation and analysis of Euler's method based on Taylor's series;
- Motivate and apply Runge-Kutta methods for solving initial value problems;
- Construct a matrix factorisation method for solving systems of linear equations;
- Analyse the stability of linear solvers based on condition numbers;
- Implement the numerical algorithms described above in Matlab.
Assessments
- Written Assessment (70%)
- Continuous Assessment (30%)
Teachers
- NOELLE GANNON:
Research Profile |
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- MARY KELLY:
Research Profile |
Email
- NIALL MADDEN:
Research Profile |
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- COLLETTE MCLOUGHLIN:
Research Profile |
Email
Reading List
- "An Introduction to Numerical Analysis" by Suli and Mayers
- "Afternotes on Numerical Analysis" by G. W. Stewart
- "Numerical Computing with Matlab" by Cleve B. Moler
Note: Module offerings and details may be subject to change.