<AMAT 41014> <AMAT 41024> <AMAT 42034> <AMAT 42044> <AMAT 41204> <AMAT 41214> <AMAT 42224> <AMAT 42234>

AMAT 42034

>< Type/ Status : Core
>< Title : Advanced Computational Mathematics
>< Pre-requisites : AMAT 41014
>< Objectives :
At the end of this course, the student will be familiar with computational solutions to Mathematical problems and be able to analyze, program and solve given mathematical problems.
>< Course Content :

Numerical Linear Algebra :

Vector Norms, Matrix Norms, General Properties of Vector Norms.

Modern Methods for Solving Linear Systems of Equations:

Relative error bound, Condition number,
Matrix Decomposition Techniques : LU Factorization, Cholesky factorization for positive definite symmetric matrices,
Relaxation Methods : Jocobi, Gauss-Siedel, Richardson,
Gradient Method : Preconditioning, Conjugate gradient method, Steepest decent method iterative method : SOR Iterative methods.

Finite Difference Method :

Consistency, Stability and convergence of finite difference schemes, Introduction to finite difference schemes for solving some parabolic and hyperbolic equations.

Finite Element Methods :

Variational formulation of problem, Reitz-Galerkin formulation, Basic functions, Error bound, Mesh generation, Triangular elements, Rectangular elements, Assembly of element matrices, Dirichlet boundary condition, Neumann boundary condition, Incorporating boundary conditions into the set of equations.

Practicals using Matlab / Mathematica

>< Methodology : A combination of lectures and tutorial discussions, computer practicals
>< Scheme of Evaluation : Based on tutorials, tests, presentations and end of course examination
>< Recommended Reading :
1. Golub, H.& Vanloan, C.F. (1996). Matrix Computations, Johns Hopkins.
2. Hanselman, D. & Littlefield, B.R. (2000). Mastering MATLAB 6, Prentice Hall, New York.
3. Becker, E.B., Carey, G.F. & Oden J.T. (1981). Finite Elements: An Introduction, Prentice Hall, New York.
4. Chandrupatla, T.R. & Belegundu, A.D. (2002). Introduction to Finite Elements in Engineering, Prentice Hall, New York.
5. Chun, T.J. (2002). Computational Fluid Dynamics, Cambridge University Press

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