Module Identifier MA25110  
Academic Year 2000/2001  
Co-ordinator Professor T N Phillips  
Semester Semester 2  
Pre-Requisite MA11110  
Mutually Exclusive MX35110  
Course delivery Lecture   19 x 1hour lectures  
  Seminars / Tutorials   3 x 1hour example classes  
Assessment Exam   2 Hours (written examination)   100%  
  Resit assessment   2 Hours (written examination)   100%  

General 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 mehtods 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.

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

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. (1994) Applied Numerical Analysis. 5th edition. Addison-Wesley
I B Jacques and C Judd. (1987) Numerical Analysis. Chapman and Hall