Course Number
Next Offered
Spring 2022
Primary Program
Applied and Computational Mathematics
Applied Physics Laboratory
Mode of Study
Face to Face, Online, Virtual Live

This course examines ordinary differential equations from a geometric point of view and involves significant use of phase portrait diagrams and associated concepts, including equilibrium points, orbits, limit cycles, and domains of attraction. Various methods are discussed to determine existence and stability of equilibrium points and closed orbits. Methods are discussed for analyzing nonlinear differential equations (e.g., linearization, direct, perturbation, and bifurcation analysis). An introduction to chaos theory and Hamiltonian systems is also presented. The techniques learned will be applied to equations from physics, engineering, biology, ecology, and neural networks (as time permits).

Course Prerequisite(s)

EN.625.604 Ordinary Differential Equations or equivalent graduate-level ordinary differential equations class and knowledge of eigenvalues and eigenvectors from matrix theory. (Note: The standard undergraduate-level ordinary differential equations class alone is not sufficient to meet the prerequisites for this class.) EN.625.717 Advanced Differential Equations: Partial Differential Equations is not required.

Course Offering(s)


Advanced Differential Equations: Nonlinear Differential Equations and Dynamical Systems

01/24/2022 - 05/02/2022
Mon 7:20 p.m. - 10:00 p.m.
Notes: Students who wish to enroll and attend in Virtual Live (3VL only) courses in-person/on-site at Homewood or the Applied Physics Lab in the Spring 2022 term must upload their proof of COVID-19 and flu vaccination or receive an approve medical/religious exemption in the Vaccine Management System (VMS) system prior to their enrollment. Students who plan to attend Virtual Live (3VL) courses remotely must email [email protected] to indicate their status to “Off-campus" prior to their enrollment. For these courses, direct enrollment is not permitted for this term. Instead students must email [email protected] with their registration request, and our registration team will complete the enrollment once vaccination compliance has been verified. Note: Students will have until November 19, 2021 to become flu vaccine compliant.
Spring 2022
Mode of Study
Virtual Live
Applied Physics Laboratory