MAT 391E  Advanced Topics in ODE
Course Objectives
1. Teach the basics on stability of dynamical systems.
2. To develop a basic understanding of occurrence of two point boundary value problems, their classification and related problems; such as, initial value, boundary value and initialboundary value problems in the real world.
3. To develop a basic understanding of the theory and methods of solutions for these problems.
Course Description
Nonlinear Differential Equations and Stability: The Phase PlaneLinear Systems, Autonomous Systems and Stability, Locally Linear Systems, Competing Species, PredatorPrey Equations, Liapunov’s Second Method, Periodic Solutions and Limit Cycles, Chaos and Strange Attractors: The Lorenz Equations. Twopoint boundaryvalue problems; definition, examples, existence and uniqueness of solutions. Linear homogeneous boundaryvalue problems; eigenvalues and eigenvectors. SturmLiouville boundaryvalue problems; Lagrange identity, orthogonality of eigenfunctions, selfadjoint problems. Nonhomogeneous boundaryvalue problems; nonhomogeneous SturmLiouville problems, nonhomogeneous heat conduction problems. Singular SturmLiouville 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.


Course Coordinator
Semra Ahmetolan
Course Language
English


