Course information

Introduction to Fortran, Matlab and Mathematica. An Introduction to Rounding Errors: Numbers Arithmetic Representation, Basic Rounding Errors. Linear Systems: Gauss Elimination Method, LUandCholeski Factorization Methods. Norms (Vector, Matrix, Function).Stability of Linear Systems.Fixed Point Iteration Schemes.Jacobi, Gauss‐Seidel and Relaxation Methods.Least Squares Methods and Applications.Numerical Computation of Eigenvalues/Eigenvectors.Nonlinear Equations: Bisection Method. Fixed Point Iteration Methods, Newton-Raphson (for Equations and Systems).Interpolation and Approximation: Lagrange Interpolation.Newton Polynomial.Hermite Interpolation.Cubic Splines.Best Approximation via Least Squares. Orthogonal Polynomials.Numerical Integration: Newton‐CotesRules (Trapezoidal, Simpson, 3/8). Gauss Integration.Introduction to ODEs: Euler, Taylor and Runge-Kutta Methods.