Course Title: |
**Ordinary Differential Equations** |

Course Number: |
MATH 6410 - 1 |

Instructor: |
Andrejs Treibergs |

Home Page: |
`http://www.math.utah.edu/~treiberg/M6417.html` |

Place & Time: |
M, W, F, 12:55 - 1;45 in LCB 218 |

Office Hours: |
11:45-12:45 M, W, F, in JWB 224 (tent.) |

E-mail: |
`treiberg@math.utah.edu` |

Prerequisites: |
Math 5210 or consent of instructor. |

Main Text: |
Ordinary Differential Equations by Thomas Sideris, Atlantis Press 2013 |

Additional Texts: | List of supplementary materials used in the course. |

Math 6410 - 1 Slides on the Hartman-Grobman Theorem.

## Home Pages of Previous Math 6410's

Math 6410 - 1 Fall 2016
Math 6410 - 1 Fall 2013

Math 6410 - 1 Fall 2012

Math 6410 - 1 Fall 2010

Math 6410 - 1 Fall 2009

Math 6410 - 1 Fall 2008

Math 6410 - 1 Fall 2002

In this first semester of a year long graduate course in differential
equations, we shall focus on ordinary differential equations and dynamical systems. The second semester, Math 6420 taught by P. Bressloff, will emphasize partial differential equations. In this course, along with the Math 6420, we shall try to cover the syllabus for the
qualifying exam in differential equations. Although some mathematical sophistication is required to
take the course, we shall provide any background materials needed by the class.

We shall begin by following Teschl's text. We cover existence, uniqueness and continuous dependence of solutions of ordinary differential equations, stability theory, bifurcation theory and periodic solutions. Occasionally we'll refer to more advanced texts. We shall discuss as many applications as we can.
Topics include (depending on time):

- Introduction to ODE. Applications. Review of calculus.
- Existence, uniqueness and continuity theorems.
- Linear
systems and stability. Liapunov's Method.
- Planar systems. Qualitative theory,
Lipunov stability. Limit sets and attractors.
- Bifurcation. Chaos.
- Averaging.
- Invariant manifolds and
linearizations. Hartman-Grobman theorem.
- Floquet Theory, periodic solutions and their stability.
- Sturm-Liouville Theory.
- Applications to physical and biological
systems. Charged particle, coupled pendula, planetary systems. Extensions to delay equations, integro-differential equations. Semigroup approach.

Last updated: 7 / 13 / 17