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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