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: 

Provides a rigorous introduction to ordinary differential equations and dynamical systems. Enroll Info: Intended for math majors and advanced (or graduate) students in other disciplines.

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: 
(MATH 320, 340, 341 or 375) and (MATH 322, 376, 421 or 521) or graduate or professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

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

(608) 263-3054

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