Numerical Methods

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Description

To explore complex systems, physicists, engineers, financiers and mathematicians require computational methods since mathematical models are only rarely solvable algebraically. Numerical methods, based upon sound computational mathematics, are the basic algorithms underpinning computer predictions in modern systems science. Such methods include techniques for simple optimisation, interpolation from the known to the unknown, linear algebra underlying systems of equations, ordinary differential equations to simulate systems, and stochastic simulation under unknown influences.

Objective

Throughout science and engineering, problems are modelled in the form of either algebraic or ordinary dierential equations. This course develops the mathematical and computational foundations of the numerical approximation and solution of equations on modern high performance workstations and using advanced software.

Content

Topics covered are: the mathematical and computational foundations of the numerical approximation and solution of scientific problems; simple optimisation; vectorisation; clustering; polynomial and spline interpolation; pattern recognition; integration and differentiation; solution of large scale systems of linear and nonlinear equations; modelling and solution with sparse equations; explicit schemes to solve ordinary differential equations; random numbers; stochastic system simulation

Trent Mattner Lecturer for this course

Delivery

42 hours of lectures and tutorials

Assessment

Ongoing assessment 30%, exam 70%.

Graduate attributes

• Applying mathematical knowledge (1)
• Interpreting data and drawing conclusions (2)
• Formulating mathematical problems (3)
• Problem solving skills (4)
• Flexibility in working environment (5)
• Team participation and leadership (7)

Linkage past

Prerequisites: MATHS 1012 Mathematics IB. Assumed knowledge: MATHS 2102 Dierential Equations (or equivalent); computer programming equivalent to APP MTH 1000.

Linkage present

The subject empowers Mathematics, Science and Engineering students to use computers for scientic problem solving.

Linkage future

Any of the Level III Applied Mathematics and many science and engineering courses may use the techniques and concepts developed in this course.

Restrictions

None.

Recommended text

E. Kreyszig, Advanced engineering mathematics, 9th edi- tion, 2006, Wiley. Especially Chapters 19{21.D. P. O'Leary, Scientic computing with case studies, 2008, SIAM.D. M. Etter, Engineering problem solving with matlab, 1993, Prentice{Hall.W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical recipes in . . . , 2nd edition, [http://www.nrbook.com/nr3/]. Note: These Second Edition versions of Numerical Recipes in C, Fortran 77, and Fortran 90 are no longer supported, but are made available for users with legacy code."