620-381 Computational Mathematics

Credit Points

Coordinator

Prerequisites

Any of 620-112, 620-122, 620-200, 620-211, together with one of 620-130, 620-132; and either Computer Science 433-142 or 620-131 or other evidence of competence in a procedural programming language such as Basic, Fortran, Pascal, Java or C. Engineering Faculty students with [98]620-172 and a suitable programming background will also be permitted to enrol. Engineering Faculty students with [98]620-182 should consult the coordinator regarding their background.

Semester

Contact

Subject Description

This subject introduces the underlying basis for numerical techniques to solve a variety of problems; the role of various kinds of numerical error and how algorithms are designed to minimise this error; and develops basic algorithms in the areas of root-finding, linear systems, interpolation, quadrature and solution of differential equations. Students should acquire skills in implementing the above algorithms in well-constructed computer programs and interpreting the results obtained from the programs. This subject demonstrates the difficulties and possible pitfalls in numerical computation. It also shows where to find sources of reliable numerical software.

Errors: roundoff, truncation error, stability. Root-finding: iteration, bisection, Newton's method, secant method. Linear systems: Gauss elimination, pivoting, LU factorisation, tridiagonal systems, condition number. Interpolation: polynomial, spline. Data fitting: least squares methods. Quadrature: Newton-Cotes, Gaussian quadrature, adaptive quadrature, improper integrals. Differential equations: initial value problems: Euler, Runge-Kutta, predictor-corrector, stiff problems.

Assessment

A 1.5 hour end-of-semester written examination and project work as required.