Course Number
625.718
Next Offered
Spring 2024
Primary Program
Applied and Computational Mathematics
Location
Online
Course Format
Online, Onsite, 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 Offerings

Open

Advanced Differential Equations: Nonlinear Differential Equations and Dynamical Systems

625.718.81
01/22/2024 - 05/07/2024
Semester
Spring 2024
Course Format
Online
Location
Online
Cost
$5,090.00
Course Materials