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Enrolment in Honours in Mathematics and Statistics.

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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