Overview

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Academic contacts

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Offerings

MURDOCH-S1-INT-2018-ONGOING
MURDOCH-S2-INT-2018-ONGOING

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Enrolment rules

Enrolment in Honours in Mathematics and Statistics.

Other learning activities

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Learning activities

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Learning outcomes

1.
Use and analyse direct methods, with error analysis, for systems of linear equations
2.
Use and analyse iterative methods, with convergence analysis, for systems of linear equations
3.
Use and analyse iterative and factorization methods for matrix eigenvalue problems
4.
Use and analyse methods for non-linear equations
5.
Use and analyse polynomial and spline interpolation
6.
Use and analyse methods for numerical integration
7.
Use and analyse methods for ordinary and partial differential equations
8.
Use the software MATLAB to implement various numerical methods

Assessments

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Additional information

Unit content:Topics covered in this unit include: • Gaussian elimination and factorization methods for systems of linear equations • Iterative methods, including Jacobi and Gauss-Seidel, for systems of linear equations • Operation counts, conditioning and error analysis for matrix problems • Power method and inverse power method for eigenvalue problems • QR factorization, Hessenberg form and QR algorithm • Fixed point methods and Newtons’s method for a single or system of non-linear equations • Lagrange and Newton forms of the interpolating polynomial • Spline interpolation • Interpolatory quadrature rules, trapezoidal and Simpsons’s rules, and adaptive quadrature • Romberg integration and Gaussian quadrature • Euler, Taylor and Runge-Kutta methods for initial value problems • Multistep methods and stability of methods • Shooting method and finite difference method for boundary value problems for ordinary differential equations • Finite difference methods for elliptic partial differential equations