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Handbook 1997 : Faculty of Science : Mathematics

618-381 Computational Mathematics

Note:

Students may not gain credit for both 618-381 and 618-242 (1996 Handbook).

Credit Points:

15.0

Coordinator:

Dr S L Carnie

Prerequisite/s:

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

Timetable:

Semester 1

Contact:

2 lectures and 1 practical class per week and 56 hours project work

Objectives:

On completion of this subject, students 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.

Appreciate:

  • the difficulties and possible pitfalls in numerical computation;

  • where to find sources of reliable numerical software.

Content:

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; boundary value problems: shooting, finite differences.

Assessment:

A 1.5 hour end-of-semester written examination and project work as required.
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Handbook 1997 : Faculty of Science : Mathematics 
Status:                   OFFICIAL 1997
Last Modified:            Wednesday March 12 3:36 pm
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Email Enquiries:          Course_Information@registrar.unimelb.edu.au
Copyright © University of Melbourne 1997.