Computational Techniques

IIT Madras, , Prof. Niket Kaisare

Updated On 02 Feb, 19

Overview

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

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Lecture 1: Mod-01 Lec-01 Introduction

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Lecture Details

Computational Techniques by Dr. Niket Kaisare, Department of Chemical Engineering, IIT Madras. For more details on NPTEL visit httpnptel.iitm.ac.in

Course Details

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)