Course Contents

QR method, Singular value decomposition (SVD), Jordan canonical form, Generalized inverses, Perturbation theory for linear systems of equations, Numerical solution of systems of non-linear equations. Stationary iterative method, Gauss-Seidel, Jacobi and SOR,Convergence of stationary Iterative method, Steepest descent and conjugate gradient methods,Convergence of conjugate gradient methods and preconditioning, Ordinary differential equations: variable stepsize schemes, Two-point boundary value problems.

Course Learning Outcomes

Understand and apply basic numerical methods and the theory behind them, related to interpolation and approximation, numerical integration, and solving first order ordinary differential equations, Implementation and analysis of efficient and reliable numerical algorithms for solving several classes of mathematical problems. can use Matlab or other high-level computational language to write programs for the algorithms to have hands-on experience to implement the methods. Choose appropriate algorithms to solve various computational problems from science and engineering and interpret the results.