January 2017 CSE218: Numerical Methods

CSE 218 Numerical Methods

4 hours in a week, 2.00 credits

Introduction; Solution of Non-linear Equations: Fixed Point Iteration, Bi-Section method, False Position method, Newton-Raphson method, Bairstow's Method; Solution of Linear equations: Triangular systems and back substitution, Gauss-Jordan elimination method, Pivoting, LU-factorization, Cholesky's method, Dolittle and Crout factoriza-tion; Interpolation and Approximation: Taylor's Series, Lagrangian interpolation, Divided differences formula, Newton's forward and backward interpolation, Spline interpolation; Differentiation: Numerical differentiation, Richardson's extrapolation; Integration: Newton's-Cote integration, Trapezoidal rule, Simpson's rule, Romberg's integration; Ordinary Differential Equations: Euler's method, Picard's method, Milne's method, Taylor's series method, Runge-Kutta method; Curve Fitting:

Least squares lines, Least square polynomials, Non-linear curve fitting; Numerical Optimization: Golden Ratio search, Newton's search, Powell's method, Gradient search.

Reference Tools: Matlab. Codes are to be written as well in Matlab.