Introduction & Error analysis: Introduction to Numerical methods and its significance in chemical engineering, Classification of errors, significant digits and numerical stability

(5 hrs)

Linear Algebraic Equations:Cramer's rule, Gauss Elimination and LU Decomposition, Gauss-Jordan elimination, Gauss-Seidel and Relaxation Methods.

(7 hrs)

Non Linear Algebraic Equations:Single variable successive substitutions (Fixed Point Method), Multivariable successive substitutions, single variable Newton-Raphson Technique, Multivariable Newton-Raphson Technique

(10 hrs)

Eigen values and Eigen vectors of Matrices:Faddeev-Leverrier's Method, Power Method.

(6 hrs)

Function Evaluation:Least squares curve-fit (Linear Regression), Newton's interpolation formulae (equal intervals), Newton's Divided Difference Interpolation Polynomial, Lagrangian Interpolation Unequal intervals). Numerical Differentiation, Numerical Integration or Quadratures (Trapezoidal, Simpson's 1/3 and 3/8 rules).

(12 hrs)

Ordinary Differential Equations (ODE-IVPs) and partial differential Equations:The Finite difference Technique, Runge-Kutta method

(8 hrs)

BOOKS RECOMMENDED:

1. Gupta S.K., Numerical Methods for Engineers, 2nd Ed., New Age International Publishers, 2009 

2. Jain M.K., Iyengar SRK and Jain R.K., Numerical Methods for Scientific and Engineering Computation, New Age International.

3. Finlayson, B.A. Nonlinear Analysis in Chemical Engineering, MCGraw Hill, New York, 1980

4. Villadsen J, and Michelsen, M.L. Solution of Differential Equation Models by Polynomial Approximation, Prentice Hall, N.J., 1978.

5. Rice R. G., Do Duong D., Applied Mathematics and Modelling for Chemical Engineers, John Wiley & Sons, Inc, 1995.