620-381 Computational Mathematics

Note

Students may only gain credit for one of 620-381, 618-381 (1997 Handbook), 618-242 (1996 Handbook).

Credit Points

Coordinator

Prerequisites

Any of 620-112, 620-122, 620-200, 620-211 (1997 Handbook 618-112, 122, 200, 211), together with one of 620-130, 620-132 (1997 Handbook 618-130, 132), and either Computer Science 433-142 or 620-131 (1997 Handbook 617-141) or other evidence of competence in a procedural programming language such as Basic, Fortran, Pascal or C. Engineering Faculty students with 620-172 (1997 Handbook 618-172) and a suitable programming background will also be permitted to enrol. Engineering Faculty students with 620-182 (1997 Handbook 618-182) should consult the coordinator regarding their background.

Semester

Contact

Subject Description

Students completing this subject should comprehend

• 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;
• basic algorithms in the areas of root-finding, linear systems, interpolation, quadrature and solution of differential equations;

have developed

• skills in implementing the above algorithms in well-constructed computer programs and interpreting the results obtained from the programs;

and appreciate

• the difficulties and possible pitfalls in numerical computation;
• 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, Romberg integration, adaptive quadrature. Differential equations: initial value problems: Euler, Runge-Kutta, predictor-corrector.

Assessment

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