System of Linear Systems & Linear Least-Squares: Special types of matrices: Symmetric, Positive definite, Banded,
Dense and Sparse matrices; Diagonal dominance, Matrix and vector norms, Condition numbers; Matrix Decomposition
Methods: LU decomposition, QR factorisation, Singular value decompositions; Basic iterative methods for linear
systems: Jacobi, Gauss-Seidel and successive over relaxation methods; Projection Methods - Steepest descent, Minimal
residual iteration, Residual Norm Steepest descent.
System of Nonlinear Equations: Newton Method, Broyden’s method (secant type).
Numerical Differentiation: Finite differences, Richardson extrapolation, Automatic differentiation; Numerical
Integration: Gauss quadrature methods, Multiple integrals, Monte-Carlo integration methods.
Methods for Ordinary Differential Equations: Initial value problems: Euler and backward Euler methods, Runge-Kutta
methods, Applications to Stiff differential equations, Linear multi-step methods /predictor-corrector methods; Boundary
value problems: Shooting method, Finite difference methods, Finite element method - Galerkin method.