**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

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On 12 Oct 2000, 10:29.