Numerical Methods

Course aim

To introduce students to a selection of basic numerical techniques, and to give some insight into numerical analysis theory, practice and application.

Course content

Non-linear equations: fixed point iteration, Newton’s method and variants, accelerating convergence.
Interpolation: Lagrange polynomials, divided differences. Polynomial least squares. Numerical differentiation. Root-finding without derivatives. Numerical integration: Newton-Cotes formulae, Romberg integration. Direct solution of systems of linear equations. Ordinary differential equations: initial value problems by Taylor and Runge-Kutta methods, higher order systems, linear boundary value problems by linear shooting. Optimisation: one dimensional minimisation by golden ratio, parabolic, gradient descent, Nelder-Mead; Brent’s and Newton’s methods, and cubic interpolation.

Textbook(s)

Nil

Prerequisite(s)

Common to all relevant programs
Subject Area & Catalogue Number	Course Name
MATH 1056	Linear Algebra
MATH 1055	Calculus 2

Corequisite(s)

Nil

Teaching method

Component	Duration
INTERNAL, MAWSON LAKES
Seminar	2 hours x Weekly
Tutorial	1 hour x Weekly
Computer Practical	1 hour x Weekly

Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Assessment

Examination, Problem solving exercise, Test/Quiz

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 1)
To determine the fee for this course as part of a Commonwealth Supported program, go to:
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Fee-paying program for domestic and international students
International students and students undertaking this course as part of a postgraduate fee paying program must refer to the relevant program home page to determine the cost for undertaking this course.

Non-award enrolment
Non-award tuition fees are set by the university. To determine the cost of this course, go to:
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Not all courses are available on all of the above bases, and students must check to ensure that they are permitted to enrol in a particular course.

* Equivalent Full Time Study Load. Please note: all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation.