Mathematics
MA385: Numerical Analysis I (5 ECTS)
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.
Taught in Semester(s) 1. Examined in Semester(s) 1.
Workload: 100 hours (24 Lecture hours, 8 Tutorial hours, 10 Lab hours, 58 Self study hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- 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;
- Estimate the eigenvalues of large symmetric matrices;
- Implement the numerical algorithms described above in Matlab.
Indicative Content
Most mathematical problems arising in engineering and the physical sciences are expressed as nonlinear equations, differential equations, or systems of linear equations. This module provides the mathematical understanding of the methods that can be applied to solve these problems, and the knoweldge of how to determine which algorithm is most appropriate in which setting. In addition, the students learns how to program these methods in Matlab - the industry standard software tool for numerical prototyping.
Module Resources
- Suli and Mayers, An Introduction to Numerical Analysis.
- G. W. Stewart, Afternotes on Numerical Analysis
- Cleve B. Moler, Numerical Computing with Matlab.
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