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Computational Techniques

IIT Madras, , Prof. Niket Kaisare

Updated On 02 Feb, 19

Overview

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.

Includes

Lecture 1: Mod-01 Lec-01 Introduction

4.1 ( 11 )


Lecture Details

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

Ratings

2.6


12 Ratings
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Comments
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Sam

Excellent course helped me understand topic that i couldn't while attendinfg my college.

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Dembe

Great course. Thank you very much.

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