Computational Techniques

IIT Madras Course , Prof. Niket Kaisare

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 http://nptel.iitm.ac.in

Course Description :

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 Newtons method.

Regression and Curve Fitting : Linear regression; Least squares; Total Least Squares; Interpolation; Newtons 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.

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