| Code |
Course Name |
Language |
Type |
| MAT 391E |
Advanced Topics in ODE |
English |
Elective |
| Local Credits |
ECTS |
Theoretical |
Tutorial |
Laboratory |
| 3 |
6 |
3 |
0 |
0 |
| Course Prerequisites and Class Restriction |
| Prerequisites |
MAT 232 MIN DD
or MAT 232E MIN DD
|
| Class Restriction |
None |
| Course Description |
| Nonlinear Differential Equations and Stability: The Phase Plane-Linear Systems, Autonomous Systems and Stability, Locally
Linear Systems, Competing Species, Predator-Prey Equations, Liapunov’s Second Method, Periodic Solutions and Limit Cycles,
Chaos and Strange Attractors: The Lorenz Equations. Two-point boundary-value problems; definition, examples, existence and
uniqueness of solutions. Linear homogeneous boundary-value problems; eigenvalues and eigenvectors. Sturm-Liouville
boundary-value problems; Lagrange identity, orthogonality of eigenfunctions, self-adjoint problems. Nonhomogeneous
boundary-value problems; non-homogeneous Sturm-Liouville problems, non-homogeneous heat conduction problems.
Singular Sturm-Liouville problems; definition, continuous spectrum, vibration of a circular elastic membrane, Series of
orthogonal functions; convergence and completeness. Techniques of Green`s function; generalised functions, Green`s
function, modified Green`s function. |
|
