Computational Techniques

Contents:
Introduction : Motivation and applications.

Computation and Error Analysis : Accuracy and precision; Truncation and round-off errors; Binary Number System; Error propagation.

Linear Systems and Equations : Matrix representation; Cramer’s rule; Gauss Elimination; Matrix Inversion; LU Decomposition; Iterative Methods; Relaxation Methods; Eigen Values.

Algebraic Equations : Bracketing methods: Bisection, Reguli-Falsi; Open methods: Secant, Fixed point iteration, Newton-Raphson; Multivariate Newton’s method.

Regression and Curve Fitting : Linear regression; Least squares; Total Least Squares; Interpolation; Newton’s Difference Formulae; Cubic Splines.

Numerical Differentiation : Numerical differentiation; higher order formulae.
Integration and Integral Equations : Trapezoidal rules; Simpson’s rules; Quadrature.

ODEs: Initial Value Problems : Euler’s methods; Runge-Kutta methods; Predictor-corrector methods; Adaptive step size; Stiff ODEs.

ODEs: Boundary Value Problems : Shooting method; Finite differences; Over/Under Relaxation (SOR).
PDEs : Introduction to Partial Differential Equations.