620-381 Computational Mathematics

Credit Points

HECS Band

Coordinator

Prerequisites

Any one of 620-112, 620-122, 620-142, [99]620-200, 620-211, together with one of 620-113, 620-123, 620-143, [98]620-130, [98]620-132 and one of computer science 433-171 or 433-142 or 620-131 or other evidence of competence in C, Cplusplus, Fortran, Pascal, or similar languages.

Note: [98]620-142 is not sufficient to enrol in this subject.

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.

Topics include 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; and differential equations, initial value problems: Euler, Runge-Kutta, predictor-corrector, stiff problems.

Assessment

A 2-hour end-of-semester written examination and project work as required.