Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 716: Ordinary Differential Equations

The course is a self contained introduction to ordinary differential equations at the graduate level. 
Topics selected from:

  • Existence, uniqueness, and continuous dependence of solutions on parameters.  
  • Implicit Function Theorem in Banach spaces
  • Linear theory of differential equations.  
  • Stability, Lyapunov functions, invariant manifolds, local hyperbolic theory.
  • Periodic orbits, Poincaré maps
  • Bifurcations of fixed points
  • Hopf bifurcations
  • Normal forms, averaging method. Applications to bifurcations.
  • Homoclinic orbits, Melnikov method, chaotic solutions.

Offered in spring 2021:  Course website for 2021

3 (N-A)
Linear Algebra and Real Analysis (Math 521 and 522) and basic knowledge of Ordinary Differential Equations (Math 319 or 320).

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, WI  53706

(608) 263-3054

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