MAT2077

Numerical methods

Dr David Wilson

4 points - Second semester - 2 hours of lectures and one 1-hour tutorial per week - Gippsland and distance - Prerequisites: MAT1085 - Prohibitions: GAS2622, MAA2032, MAT2072

Objectives The objectives of this subject are for students to be able to employ any of a suite of numerical approximation techniques to solve a nonlinear equation in a single variable; find an interpolating polynomial, using limited data; solve a system of linear equations; estimate the eigenvalue (of greatest magnitude) for a square matrix; estimate the value of a definite integral; solve a nonlinear differential equation; find a 'best fit' representation of a function; have a good idea of the likely numerical imprecision inherent in the results, and know (in some instances) ways to reduce such inaccuracies.

Synopsis This subject is intended to introduce some of the methods commonly used in numerical computations; to develop the theoretical bases of the algorithms, as well as assessing their likely accuracy and any possible difficulties. Areas covered include numerical methods for solving nonlinear equations; solving systems of linear equations; numerical differentiation and integration; interpolation, least squares fitting, orthogonal polynomials; numerical solution of ordinary differential equations with initial and/or boundary conditions; comparison of methods by operations count, order of convergence, error bounds, and empirical error estimates; introduction to the use of computer packages for numerical analysis. For distance students, four two-hour expository and discussion classes are available over the semester, to supplement full notes and the textbook.

Assessment Class tests and assignments: 30% - Examination: 70%

Prescribed texts

Gerald C F and Wheatley P O Applied numerical analysis 5th edn, Addison-Wesley, 1994
Mathews J H Numerical methods for mathematics, science and engineering 2nd edn, Prentice-Hall, 1992

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