Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 519: Ordinary Differential Equations

Student Body: 

Math majors and students in the sciences and engineering.

Background and Goals: 

Math 519 is a rigorous self contained introduction to ordinary differential equations intended for undergraduate math majors and advanced or graduate students from economics, engineering and physics. Topics will include theory of linear systems \[ \frac{dx}{dt} = Ax(t) + f(t) \] based on linear algebra, proofs of basic existence theorems for nonlinear systems of differential equations

\[ \frac{dx}{dt} = F(t, x(t)) \] as well as stability theory, bifurcations and applications to mechanical and biological systems.

Alternatives: 

Math 319 for a lower level introduction to Differential Equations

Subsequent Courses: 

N/A

Course Content: 
  • Systems of differential equations
  • Stability for linear systems. Fundamental matrix, periodic systems and Floquet theory.
  • Continuity and differentiability of solutions in initial conditions.
  • Flow of differential equations.
  • Qualitative behavior of nonlinear systems. Stability and Liapunov functions.
  • Periodic orbits, Poincare maps, attractors and Poincare-Bendixon Theorem.
  • Bifurcation for equilibria and periodic orbits (time permits).
  • Applications to Classical Mechanics and biological systems.
credits: 
3. (N-A)
semester: 
Spring
prereqs: 
see the UW course guide for current prerequisites:

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

(608) 263-3054

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