AMAT 41014

>< Type/ Status : Core
>< Title : Qualitative and Quantitative Behaviour of the Solutions of Ordinary Differential Equations
>< Pre-requisites : AMAT 22025
>< Objectives :
At the end of the course, the student will acquire a knowledge of numerical solutions of Differential equations and their implementations using standard Mathematical software.
>< Course Content :

Introduction to Matlab/Mathematica:

Basic procedures in using Matlab/Mathematica, Handling numbers and matrices, Control structures in Matlab/Mathematica, Program design in Matlab/Mathematica language, Plotting. Basic Properties of the Solutions of Ordinary Differential Equations:
Stability of the solution and State-Space Analysis, Qualitative behavior of the solution of ODE’s.

Numerical Solution of Ordinary Differential Equations : Concept of consistency, Stability and convergence properties of numerical schemes, Single and multistep methods, Solving Stiff systems, Shooting method, Gear's implementation of automatic ordinary differential equation solver, Finite difference discretizations for second order boundary value problems.

Lab work using Matlab / Mathematica : Algorithms studied in AMAT 22025 and in this unit will be implemented using Matlab / Mathematica.

>< Methodology : A combination of lectures, practicals, tutorial discussions and presentations
>< Scheme of Evaluation : Based on tutorials, tests, presentations and end of course examination.
>< Recommended Reading :
1. Vanloan, C.F. (2000). Introduction to scientific computing: a matrix-vector approach using MATLAB, Prentice Hall, New York.
2. Hanselman, D. & Littlefield, B.R. (2000). Mastering MATLAB 6, Prentice Hall, New York.
3. Ferdinand, V. (2000). Nonlinear differential equations and dynamical systems, Springer Verlag.

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