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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

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