# Computational Techniques

IIT Madras, , Prof. Niket Kaisare

Updated On 02 Feb, 19

IIT Madras, , Prof. Niket Kaisare

Updated On 02 Feb, 19

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

- 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)

Sam

Sep 12, 2018

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

Dembe

March 29, 2019

Great course. Thank you very much.