Math 254: Numerical Methods

Numerical Methods for Solving Nonlinear Equations: Bisection method, fixed point method, Newton’s method, secant method, multiple roots, modified Newton’s method, rate of convergence (error analysis), Newton's method for solving nonlinear systems. Solving Systems of Linear Equations: Gaussian elimination, Gaussian elimination with partial pivoting, LU-decomposition, Jacobi method, Gauss-Seidel method. Interpolation and Polynomial Approximations Lagrange interpolation formula, Newton's interpolation formula, interpolation using linear splines. Numerical Differentiation and Integration: Trapezoidal, and Simpson's rules.  Numerical solutions of Ordinary Differential equations; Taylor methods and Runge-Kutta method of order two, details in LMS.