ENGG(SERC) 1-4703: Computational Methods (L-T-P-C) : 3-0-0-3

Faculty: Dr. A. Rama Mohan Rao, Dr. J. Rajasankar

Approximations: Accuracy and precision, definitions of round off and truncation errors, error propagation; Algebraic equations: Formulation and solution of linear algebraic equations, Gauss elimination, LU decomposition, iteration methods (Gauss-Seidal), convergence of iteration methods, norms and errors, condition numbers, Conjugate Gradient methods, Pre conditioning, PCG methods, eigenvalues and eigenvectors; computer implementation, Interpolation methods: Newton’s divided difference, interpolation polynomials, Lagrange interpolation polynomials; Differentiation and Integration: Numerical Integration; finite differences, Newton cotes rules, trapezoidal rule, Simpson’s rule, extrapolation, Gaussian quadrature; Numerical solution of ordinary differential equations; Explicit and implicit formulations, single and multi-step methods, predictor-corrector methods, accuracy, convergence, stability; Solution of nonlinear equations: Open methods, closed methods, Newton-Raphson method, convergence, Variants of Newton Raphson method, Secant method, computer implementation, Numerical solution of Partial Differential equations: solution to elliptical, parabolic and hyperbolic equations; computer implementation Regression methods: Linear and non-linear regression, multiple linear regression, general linear least squares; Introduction to optimization methods