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

Course Number: |
MATH 6410 - 1 |

Instructor: |
Andrejs Treibergs |

Home Page: |
`http://www.math.utah.edu/~treiberg/M6412.html` |

Place & Time: |
M, W, F, 2:00 - 2:50 in LCB 215 |

Office Hours: |
10:40-11:30 M, W, F, in JWB 224 (tent.) |

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

Prerequisites: |
Math 5210 or consent of instructor. |

Main Text: |
James Hetao Liu, *A First Course in the Qualitative Theory of Differntial Equations*, Prentice Hall 2003. |

| This text is out of print.
How to obtain a copy. It is also on reserve at Mariott Library. You can access the list through the student portal. |

## Home Pages of Previous Math 6410's

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 D. Dobson, 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 backgroung materials needed by the class.

We shall follow Liu's text covering 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.
- 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: 5 / 7 / 9