Numerical Methods for Engineers

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; Cramer’s 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 Newton’s method

Week-6: Numerical Differentiation Numerical differentiation; error analysis; higher order formulae

Week-7: Integration and Integral Equations Trapezoidal rules; Simpson’s rules; Quadrature

Week-8: Regression Linear regression; Least squares; Total Least Squares;

Week-9: Interpolation and Curve Fitting Interpolation; Newton’s Difference Formulae; Cubic Splines

Week-10: ODEs: Initial Value Problems Introduction to ODE-IVP Euler’s 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)