ME682A - Difference Equations for Engineers
Prerequisites:
3-0-0-9
Course Contents
1. Introduction and Some Applications of Difference Equations in Engineering.
2. Preliminaries in algebra and analysis.
3. Analogies between differential and difference equations.
4. Elementary Difference Operations. The Difference and shift operators.
5. The Difference Calculus. Summation.
6. Interpolation, Extrapolation.
7. Generating functions.
8. Linear difference equations, First order equations.
9. Higher Order Difference Equations.
10. Linear difference equations with constant coefficients.
11. Linear difference equations with variable coefficients.
12. Method of undetermined coefficients and variation of parameters.
13. Limiting behavior of solutions.
14. Systems of Linear difference equations and application.
15. The transform and its applications.
16. The Sturmian theory and Fourier analysis.
17. Nonlinear difference equations and boundary value problems.
18. Asymptotic methods.
19. Stability theory and relevance to dynamical systems.
20. Partial Difference Equations.
21. Lagrangian and Hamiltonian Formalism for Difference Equations. Symmetry.
22. Difference Equations with Continuous Time, Differential difference equations.
23. Discrete Mechanics.
24. Open problems.
Topics
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