Math 511 - Ordinary differential equations

Details for Spring semester, 2025

• Time: 3:35 - 4:25 MWF, January 13th to May 2nd, 2025
• Location: McAllister 106
• Office hours will be Wednesdays, 1:30 - 2:30, or by appointment.
• Official course syllabus
• Textbooks: Ordinary differential Equations with Applications 3rd edition, by Carmen Chicone, 2024 (somebody please update openlibrary), but also see all these.
• Software: sympy (does allot but internal design issues mean it’s due for replacement with stronger/better language typing)

Lecture Contents by date

Homework

Topics

• Classification
• Derivation of Differential equations
• Elementary numerics and integration
• Geometric analysis
• Helmholtz-Hodge theory
• Constant solutions
• Duffing equation
• Linear systems
• Cayley-Hamilton
• Differential operators
• Green functions
• Forcing, Mathieu, and Messnier
• Series solutions
• Solution by quadrature and special functions
• Asymptotic and approximate solution
• Boundary value and eigenvalue problems
• Stability
• Bifurcation theory
• Limit cycles
• Stiffness, Quasisteady-state
• Averaging, Relaxation oscillators, multiscale expansions