Computational Techniques

COURSE LAYOUT

Week-1: Introduction & Approximations

Motivation and Applications

Accuracy and precision; Truncation and round-off errors; Binary Number System; Error propagation

Week-2: Linear Systems and Equations

Matrix representation; Cramers rule; Gauss Elimination; Matrix Inversion; LU Decomposition;

Week-3: Linear Systems and Equations

Iterative Methods; Relaxation Methods; Eigen Values

Week-4: Algebraic Equations: Bracketing Methods

Introduction to Algebraic Equations

Bracketing methods: Bisection, Reguli-Falsi;

Week-5: Algebraic Equations: Open Methods

Secant; Fixed point iteration; Newton-Raphson; Multivariate Newtons method

Week-6: Numerical Differentiation

Numerical differentiation; error analysis; higher order formulae

Week-7: Integration and Integral Equations

Trapezoidal rules; Simpsons rules; Quadrature

Week-8: Regression

Linear regression; Least squares; Total Least Squares;

Week-9: Interpolation and Curve Fitting

Interpolation; Newtons Difference Formulae; Cubic Splines

Week-10: ODEs: Initial Value Problems

Introduction to ODE-IVP

Eulers methods; Runge-Kutta methods; Predictor-corrector methods;

Week-11: ODE-IVP (Part-2)

Extension to multi-variable systems; Adaptive step size; Stiff ODEs

Week-12: ODEs: Boundary Value Problems

Shooting method; Finite differences; Over/Under Relaxation (SOR)