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Course Co-ordinated by IIT Madras
Coordinators
 
Dr. Niket S.Kaisare
IIT Madras

 

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Objectives:

The development of fast, efficient and inexpensive computers has significantly increased the range of engineering problems that can be solved reliably.

Computational techniques 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 computational techniques of interest to process engineer. Understanding of computational techniques will be enhanced using several solved examples, which will be done using MS Excel. Since the focus is on the techniques themselves, rather than specific applications, the contents should be relevant to varied fields such as engineering, management, economics, etc.

 

 

 

S.No

Topics

No. of Hours

1

Introduction

Motivation and applications.

1

2

Computation and Error Analysis

Accuracy and precision; Truncation and round-off errors; Binary Number System; Error propagation.

2

3

Linear Systems and Equations

Matrix representation; Cramer's rule; Gauss Elimination; Matrix Inversion; LU Decomposition; Iterative Methods; Relaxation Methods; Eigen Values.

6

4

Algebraic Equations

Bracketing methods: Bisection, Reguli-Falsi; Open methods: Secant, Fixed point iteration, Newton-Raphson; Multivariate Newton’s method.

5

5

Regression and Curve Fitting

Linear regression; Least squares; Total Least Squares; Interpolation; Newton’s Difference Formulae; Cubic Splines.

5

6

Numerical Differentiation

Numerical differentiation; higher order formulae.

3

7

Integration and Integral Equations

Trapezoidal rules; Simpson's rules; Quadrature.

4

8

ODEs: Initial Value Problems

Euler's methods; Runge-Kutta methods; Predictor-corrector methods; Adaptive step size; Stiff ODEs.

8

9

ODEs: Boundary Value Problems

Shooting method; Finite differences; Over/Under Relaxation (SOR).

3

10

PDEs

Introduction to Partial Differential Equations.

4

 

Total

41

 

  1. Gupta S.K. (1995) Numerical Methods for Engineers, New Age International.

  2. Chapra S.C. and Canale R.P. (2006) Numerical Methods for Engineers, 5th Ed; McGraw Hill.


Numerical Recipes in Fortran and C:

www.nr.com



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