MAT205 Applied Numerical Methods L T P C 

3 1 0 4  Version No.  1.1  Course Prerequisites   MAT201      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. Introduction / Review                    2 hours MATLAB fundamentals, MATLAB graphics, simple matlab demonstration programs. Numerical errors: Round – off error, Truncation error, Propagated error. (No question should be set from review portions) 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 Newton’s 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- Newton’s 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 3/8 th rules. –Romberg’s method. Unit 3  Ordinary Differential Equations  9+ 3 hours (Review: Taylor series method-Euler and modified Euler’s 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 Equations 9+3 hoursElliptic equation-Laplace equation- Liebmann’s method –Jacobi’s method- Gauss- Seidal method- parabolic equations - hyperbolic equations –-explicit methods – Crank – Nicholson implicit method -Von Neumann stability condition-CFL(Courant–Friedrichs–Lewy) stability condition.

822

Proceedings of the 26th Academic Council held on 18.5.2012

Unit 5  Calculus of Variation  9 +3 hours Functionals- - Euler- Lagrange equation- extremals- isoperimetric problems - The Rayleigh – Ritz method- Galerkin’s method. Text Books 1. 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 2,3,4,5,6,7 2. 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 12­05­2012

Date of approval by the Academic Council    

823

Proceedings of the 26th Academic Council held on 18.5.2012