Module Identifier MA25110  
Academic Year 2003/2004  
Co-ordinator Professor Tim Phillips  
Semester Semester 2  
Pre-Requisite MA11110  
Mutually Exclusive MX35110  
Course delivery Lecture   19 x 1 hour lectures  
  Seminars / Tutorials   3 x 1 hour example classes  
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  100%
Supplementary Assessment2 Hours (written examination)  100%

Learning outcomes

On completion of this module, students should be able to:

Brief description

It is often impossible to find the exact solution of a mathematical problem using standard techniques. In these situations one has to resort to numerical techniques. Numerical analysis is concerned with the development and analysis of methods for the numerical solution of practical problems. This course will provide an introduction to the subject.


To introduce students to the techniques for the numerical approximation of mathematical problems, and to the analysis of these techniques.


1. POLYNOMIAL INTERPOLATION: Lagrange's formula. Newton's formula and divided differences. The forward difference formula. Interpolation error. Cubic spline interpolation.
2. NUMERICAL INTEGRATION: Trapezoidal rule, Simpson's rule. Composite integration rules. Quadrature errors. Romberg integration. Orthogonal polynomials and Gaussian quadrature rules.
3. SOLUTION OF NONLINEAR EQUATION IN A SINGLE VARIABLE: Bisection method. Fixed point methods and contraction mappings. Newton's method. Order of convergence.
4. INITIAL VALUE PROBLEMS: Existence and uniqueness of solutions. Euler's method. Local truncation error.
Consistency. Convergence. Stability. General one-step methods. Trapezoidal method. Predictor-corrector methods.

Reading Lists

** Supplementary Text
C F Gerald and P O Wheatley (1999) Applied Numerical Analysis 6th Ed. Addison-Wesley 0201474352
J F Epperson (2001) An Introduction to Numerical Methods and Analysis Wiley 0471316474
A S Wood (1999) Introduction to Numerical Analysis Addison Wesley 020134291X


This module is at CQFW Level 5