Requirements/prerequisites: None

Duration: 24 Weeks

Number of lectures per week: 3

Assessment: Examination and Homework assignments

End-of-year Examination: One 3-hour examination; counts 90%; homework counts 10%

Description:

Numerical Linear Algebra: Gaussian elimination and Gauss-Jordan elimination; LU decomposition; Condition number of a matrix; SVD and sparse matrix methods; Stability and error analysis; Iterative solutions and convergence including Krylov subspace techniques.

Numerical Integration: Integration of functions, ODEs and PDEs; Introduction to path integrals.

Integral Equations and Inverse Theory: Fredholm and Volterra equations; Integral equations and singular kernals; Inverse problems and a priori information.

Evaluation of Functions: Series and convergence; Polynomial and rational functions; Chebyshev and Padé approximations.

Interpolation and Extrapolation: Polynomial and rational interpolation and extrapolation; Cubic spline interpolation; Interpolating in more than two dimensions. The point-wise error in Lagrange interpolation.

Statistical description and Modeling of Data: Moments of a distribution - mean, variance etc; Comparing two distributions; Correlations in datasets; Fitting data to a straight line; Fitting data with errors in x and y coordinates; Bootstrapping and Monte Carlo Methods.

Oct 12, 2000