AMAT 22025

>< Type/ Status : Core
>< Title : Numerical Methods
>< Pre-requisites : PMAT 12035
>< Objectives :
At the end of this course, the student will be able to use different numerical schemes to solve problems. They will also be familiar with the process of numerical analysis.
>< Course Content :

Introduction:

Floating point number system, Error in numerical computation, Notion of algorithm.

Solution of equations with one variable:

Numerical solution of nonlinear equations, Solutions of polynomial equations.

Interpolation:

Polynomial interpolation, Spline interpolation.

Approximation of functions:

Least square method, Best fit.

Solution of System of Linear Equations (Direct and Iterative Methods):

Gaussian eliminations with partial pivoting, Ill conditioning, Operation counts, Jacobi and Gauss-Seidel iterative methods and their convergence.

Numerical Differentiation and Integration:

Trapezoidal, Simpson quadratic formulae, Romberg integration method, Gaussian quadrature.

Numerical Solutions of Ordinary Differential Equations:

Explicit and Implicit numerical schemes, Euler’s method, Computation of error bound, Stability of methods, Predictor-Corrector methods.

>< Methodology : A combination of lectures and tutorial discussions
>< Scheme of Evaluation : Based on tutorials, tests and end of course examination
>< Recommended Reading :
1. Sastry, S. S. (2003). Introductory Methods of Numerical Analysis, Prentice Hall, India.
2. Kreyszig, E. (1983). Advanced Engineering Mathematics, John Wiley, New York.
3. Burden, R.L. & Faireu, J.D. (1993). Numerical Analysis, PWS, India.
4. Gerald,C.F. Wheatley, P.O. (1994). Applied Numerical Analysis, Addison Wesley.

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