- English
- فارسی
Elementary Theory of Ordinary Differential Equations
- Scalar Autonomous Equations, Existence and Uniqueness, Geometry of Flows, Stability of Equilibria
- Elementary Bifurcations, Dependence on Parameters, Local perturbations Near Equilibria, Equivalence of Flows
- Planar Autonomous Systems, Examples of Planar Systems, General Properties and Geomtery, Product Systems, First Integral and Conservative Systems.
- Linear Systems, Properties of Linear systems, Reduction to Cannnical Forms, Qualitative Equivalence in Linear systems, Bifurcations in Linear Systems.
- Nonlinear systems, Asymptotic Stability and Instability from Linearization. Liapunov Equations, Lassalle Invariance Principle. Stable and Unstable manifolds, Hartman-Grobman Theorem.
Stability and Bifurcations of equilibrium points in the presence of Zero Eigenvalue using Center Manifold Theorem.
Textbooks:
- J. Hale, H Kocak, Dynamics and Bifurcations, Springer- Verlag, 1996
- M.W. Hirsch, S. Smale, R. Devaney, Differential Equations, Dynamical Systems and an Introduction to Chaos, Elsevier, 2004.
Prerequisites:
Foundations of Analysis , Linear Algebra, Elementary Differential Equation
Grading Policy:
Quiz1:5%
Quiz2:5%
Quiz3: 5%
Quiz4:5%
Midterm:30%
Final :50%
Time:
Class hour: Staurday-Monday 10-12
Office hour: Sunday-Tuesday 11-12
Files:
Term:
Fall 2015
Grade:
Undergraduate