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%
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