Approximation theory: norms, weighted least-squares approximation, polynomial minimax approximation, Chebyshev polynomials and Chebyshev expansions, rational Pade approximation, rational minimax approximation, piecewise polynomial approximation, Lagrange and Newton interpolation and splines.
Matrix eigenvalues/eigenvector analysis: vector and matrix norms, matrix algorithms, Givens' and Householder zeroising transformations, Power Method and inverse iteration, Jacobi method, Householder reduction to tridiagonal form, QR method.
Numerical integration: review of basic techniques, interpolatory quadrature, Gaussian quadrature, applications of orthogonal polynomials and the Christoffel-Darboux identity to Gaussian quadrature, errors, integration over infinite intervals.
Practials: three practical assigments, to implement in MATLAB Chebyshev series and the minimax approximation, the Pade approximation, and the Power Method.