Numerical Methods - MAST5009

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Module delivery information

Location Term Level1 Credits (ECTS)2 Current Convenor3 2023 to 2024
Canterbury
Spring Term 5 15 (7.5) Ana F. Loureiro

Overview

This module is an introduction to the methods, tools and ideas of numerical computation. In mathematics, one often encounters standard problems for which there are no easily obtainable explicit solutions, given by a closed formula. Examples might be the task of determining the value of a particular integral, finding the roots of a certain non-linear equation or approximating the solution of a given differential equation. Different methods are presented for solving such problems on a modern computer, together with their applicability and error analysis. A significant part of the module is devoted to programming these methods and running them in MATLAB.

Introduction: Importance of numerical methods; short description of flops, round-off error, conditioning

Solution of linear and non-linear equations: bisection, Newton-Raphson, fixed point iteration

Interpolation and polynomial approximation: Taylor polynomials, Lagrange interpolation, divided differences, splines

Numerical integration: Newton-Cotes rules, Gaussian rules

Numerical differentiation: finite differences

Introduction to initial value problems for ODEs: Euler methods, trapezoidal method, Runge-Kutta methods.

Details

Contact hours

Total contact hours: 42
Private study hours: 108
Total study hours: 150

Method of assessment

Assessment 1 Exercises, requiring on average between 10 and 15 hours to complete 20%
Assessment 2 Exercises, requiring on average between 10 and 15 hours to complete 20%
Examination 2 Hours 60%
The coursework mark alone will not be sufficient to demonstrate the student's level of achievement on the module.

Indicative reading

R. L. Burden, J. D. Faires, A. M. Burden. Numerical Analysis. 2016.
J. H. Matthews, K. D. Fink. Numerical methods using MATLAB. Pearson, 2004.
W. Gautschi. Numerical Analysis. Birkhäuser Boston, 2012 (ebook available from the Library)

See the library reading list for this module (Canterbury)

Learning outcomes

The intended subject specific learning outcomes. On successfully completing the module students will be able to:

1 demonstrate knowledge and critical understanding of the well-established principles within a wide range of basic numerical methods, including iterative methods,
interpolation, quadrature, finite difference approximation of initial-value problems for ordinary differential equations (ODEs);
2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the
following areas: root finding, interpolation, numerical quadrature, finite differences, initial-value problems for ODEs;
3 apply the concepts and principles in basic numerical approximation in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate
critically the appropriateness of different tools and techniques;
4 make appropriate use of MATLAB commands to implement numerical methods.

Notes

1. Credit level 5. Intermediate level module usually taken in Stage 2 of an undergraduate degree.
2. ECTS credits are recognised throughout the EU and allow you to transfer credit easily from one university to another.
3. The named convenor is the convenor for the current academic session.
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