The development of fast, efficient and inexpensive computers has significantly increased the range of engineering problems that can be solved reliably. Numerical Methods use computers to solve problems by step-wise, repeated and iterative solution methods, which would otherwise be tedious or unsolvable by hand-calculations. This course is designed to give an overview of numerical methods of interest to scientists and engineers. However, the focus being on the techniques themselves, rather than specific applications, the contents should be relevant to varied fields such as engineering, management, economics, etc. INTENDED AUDIENCE: First/Second Year UG students in any branch of engineering (or science) PREREQUISITES: 12th standard Math background
Overview
Syllabus
]]>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)
Taught by
Prof. Niket Kaisare
