This module presents a range of numerical techniques for solving the types of problems that occur in science and mathematics. The aim of this module is to extend on the techniques covered in m MATH 2806 and to introduce the learner to more advanced numerical techniques. The module is suitable for stage 3 learners of the TU873/TU874 course or equivalent.
Approximation Theory
Orthogonal polynomials and the least square’s approximation, Chebyshev polynomials and economisation of power series, Padé approximations.
Numerical Differentiation
Central differences, forward and backward differences, Richardson’s extrapolation, error estimates.
Numerical Integration
Newton-Cotes formulas, composite numerical integration, error estimates.
Solution of ordinary differential equations
Euler’s method and higher order Taylor series methods, Runge-Kutta methods, predictor-corrector methods, systems of differential equations.
Eigenvalues and Eigenvectors
Gerschgorin’s circle theorem. the Power method, Householder’s method and the QR algorithm.
Lectures are primarily used to impart module content to the learner. Problem solving sessions are designed to encourage learners to work both individually and in groups.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |