Course Code: MAT

Course Code: MAT 205Title: Applied Numerical MethodsL T P C 3 1 0 4

Version No. 1.1

Course Prerequisites MAT 201 Complex Variables and Partial Differential Equations

Objectives This course attempts to cover certain basic, important computer oriented numerical methods for analyzing problems that arise in engineering and physical sciences. The students are expected to use MATLAB as the primary computer language to obtain solutions to a few assigned problems.

Expected Outcome By the end of the course, students should be able to appreciate the power of numerical methods and use them to analyze the problems connected with data analysis, and solution of ordinary and partial differential equations that arise in their respective engineering courses.

Unit Nos. Unit Title Number of hours (per Unit)

Introduction / ReviewMATLAB fundamentals, MATLAB graphics, simple matlab demonstration programs. Numerical errors: Round off error, Truncation error, Propagated error.( No question should be set from review portions)2 hours

Unit 1 Algebra and Transcendental System of Equations

9 +3 hours

General iterative method- secant method- Newton Raphson method - non-linear equations- solution of system of equations- generalized Newtons method(roots of equation-solution of system of equations), - rate of convergence- Gauss Seidel method for system of linear equations convergence criterion- positive definiteness of a matrix- spectral radius of a matrix-tridiagonal system of equations Thomas algorithm.

Unit 2 Numerical Differentiation and Integration 9 +3 hours

Interpolation- finite differences- Newtons formulae for interpolation- Langrage interpolation, interpolation with cubic splines, - numerical differentiation- maxima minima for tabulated values-numerical integration: Trapezoidal rule, Simpsons 1/3 rd and 3/8th rules. Rombergs method.

Unit 3 Ordinary Differential Equations9+ 3 Hours

(Review: Taylor series method-Euler and modified Eulers methods). Runge Kutta methods -

fourth order R.K method systems of equations and higher order equations.-multi step methods: Adams-Bashforth method- boundary value problems- the shooting method, eigen value problems- finite difference method.

Unit 4 Partial Differential Equations9+3 Hours

Elliptic equation-Laplace equation- Liebmanns method Jacobis method- Gauss- Seidal method- parabolic equations - hyperbolic equations -explicit methods Crank Nicholson implicit method -Von Neumann stability condition-CFL(CourantFriedrichsLewy) stability condition.

Unit 5 Calculus of Variation9 +3 hours

Functionals- - Euler- Lagrange equation- extremals- isoperimetric problems - The Rayleigh Ritz method- Galerkins method.

Text Books1. M. K. Jain, S. R. K. Iyengar and R. K. Jain, Numerical methods for scientific and Engineering, New Age International Ltd., 5th Edition (2010).The topics in the chapters 2,3,4,5,6,72. C. F. Gerald and P.V. Wheatley. Applied Numerical analysis, Addition-wesley, 7th Edition(2004).

Reference Books 1. S.S.Sastry, Introductory Methods of Numerical Analysis, PHI Pvt Ltd ,New Delhi(2003)

2. W.Y. Yang, W. Cao, T.S. Chung and J. Morris, Applied Numerical

Methods Using MATLAB Wiley India Edt(2007)

3. Steren C. Chapra and Ra P. Canale, Numerical methods for Engineers with programming and software applications, 3rd Edition, Tata McGraw Hill(2001) .

Mode of Evaluation

Recommended by the Board of Studies on 12-05-2012

Date of approval by the Academic Council