Course Title: Ordinary Differential Equations
Course Number: MATH 5410 - 1 / 6840 - 1
Instructor: Andrejs Treibergs
Home Page: http://www.math.utah.edu/~treiberg/M5412.html
Place & Time: M, T, W, F, 9:40 - 10:30 in LCB 121. (Live in person. Will also be ZOOM on line)
Office Hours: 11:45 - 12:45 M, T, W, F. (please email)
E-mail:
Prerequisites: Math 2250 or 2280 or consent of instructor.
Main Text: Morris Hirsch, Stephen Smale & Robert Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, 3rd. ed., Academic Press, 2013
ISBN 978-0-12-382010-5
Additional Texts:Annotated list of additional texts.
       1965 Obsession II by Julian Stanczak

 

 

Math 5410 - 1 Syllabus, pdf.

Math 5410 - 1 Homework

Supplementary Material, Solutions to Tests

In this one semester course in differential equations, we shall focus on ordinary differential equations and dynamical systems. This topic will continue in the Spring Semester course, Math 5470, Chaos Theory, taught by E. Cherkaev, will emphasize discrete dynamical systems. Although the nominal prerequisites are minimal, having some mathematical sophistication such as Math 3210-20 is highly encouraged.

We shall generally follow the Hirsch-Smale-Devaney text. We will emphasize applications taken from various subjects like mathematical biology, engineering, geometry and physics. Occasionally we'll refer to other texts and web resources. Topics include (depending on time):

  • Introduction to ODE. Applications. Review of calculus.
  • First order systems.
  • Linear algebra applied to linear systems.
  • Planar systems. Qualitative theory, Limit sets and attractors.
  • Existence, uniqueness and continuity theorems.
  • Poincare map.
  • Hamiltonian Systems.
  • Bifurcation. Chaos.

Last updated: 6 / 7 / 21