Fundamentals of Scientific Computing module (MA32005)

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Credits

15

Module code

MA32005

Matrix algebra is a fundamental and widely used resource for modelling various problems in science, technology, industry, and commerce. In the module, you will learn to use mathematical software to implement algorithms and solve several problems that can be stated in matrix-related equations. You will also learn about the relevant matrix algebra theory that underpins these algorithms, including the concepts of numerical error, condition number and convergence.

You will learn to programme using MATLAB and gain practical experience using numerical methods to solve various mathematical problems, including root-finding, numerical integration, and matrix-iterative methods.

Topics include:

  • Direct methods for solving linear systems of equations - basic properties of matrices, Gaussian elimination, partial pivoting. LU factorisation.
  • Iterative methods - recursive formulae, Jacobi method, Gauss-Seidel method, SOR (successive over-relaxation), QR factorisation, theorems for convergence.
  • Errors and stability - finite precision arithmetic, machine epsilon, absolute and relative error, numerical stability, condition number of a matrix.
  • Using MATLAB to solve problems in mathematics - introduction to MATLAB, applications of MATLAB to algorithms for root finding, numerical integration, LU factorisation, iterative methods and QR factorisations.

Courses

This module is available on following courses: