Fundamentals of Scientific Computing module (MA32005)

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Credits

Module code

MA32005

About the module

Matrix algebra is a fundamental and widely used resource for modelling a wide variety of problems in science, technology, industry and commerce. The aim of this course is to use computers to implement algorithms and to solve a number of problems that can be stated in terms of matrix-related equations, and to understand the relevant matrix theory that underpins these algorithms. This module is mandatory for students taking the BSc or MMath in Mathematics and may optionally be taken in combination with other modules by students on any of the Mathematics combined degrees. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module must have achieved a pass mark in each of the modules MA21001 and MA22001, or equivalents.

Indicative Content

Direct Methods for Solving Linear Systems of Equations
Basic properties of matrices, Gaussian elimination, partial pivoting. LU-factorization. Tridiagonal systems.
Iterative Methods
A general iterative method and convergence, Jacobi method, Gauss-Seidel method, SOR (successive over-relaxation).
Iterative Methods for Solving Eigenvalue Problems
Review of eigenvalue problems, QR factorizations
Using MATLAB to solve problems in linear algebra
Introduction to MATLAB, Application of MATLAB to algorithms for LU factorization, iterative methods and QR factorizations.

Delivery and Assessment

The module is delivered in the form of lectures and workshops/tutorials and computer labs, and assessed via an exam (70%) and computer homeworks (30%).