Math 519–Ordinary Differential Equations

Links

• Topics and practice problems for the Final Exam
• The final exam project
• The course syllabus (a.k.a. the old course page.)
• Homework assignments: see below on this page.
• THE PROBLEMS PAGE
• Notes for the first (1 dimensional) part of the course:
  • Review of solution methods for certain kinds of diffeqs from calculus.
  • A theorem about first order linear equations
  • Picard’s existence proof
  • The uniqueness proof, and how to verify the Lipschitz condition.
  • How far can you extend the solution?
  • Dependence of the solution on parameters: the variational equation.
  • The Implicit Function Theorem
  • Bifurcation diagrams (how stationary solutions depend on parameters.)
  • The Poincaré map
• Notes for the second, linear, part:
  • Matrix/Linear Algebra glossary
  • Homogeneous Linear Systems and the matrix exponential
  • Complex eigenvalues
  • Miscellaneous comments on the Trace and Determinant
  • A list of two and three dimensional examples
    • MIT mathlet visualizing phase portraits of 2 dimensional linear homogeneous systems.
  • Vector and Matrix norms.
  • Linear Stability
  • The three room feedback problem
  • Coupled springs problem
  • The inhomogeneous equation; the variation of constants formula
• Sample problems for the first midterm
• Preparation for the second midterm

Homework Assignments

Week 1, due in class Monday January 25

Week 2, due in class Monday February 1

Week 3, due in class Monday February 8

Week 4, due in class Monday February 15

Week 5, due in class Monday February 22

Week 7, due in class Wednesday March 9

Week 8, due in class Wednesday March 16

Week 9, due in class Wednesday March 30

See also the Matrix Algebra Glossary for a very short description of perhaps forgotten linear algebra.

Week 10, Second Midterm

Week 11, due in class Wednesday April 20

Week 12, due in class Wednesday May 4