MATH 6307 Ordinary Differential Equations 1
MWF 10:05-10:55, Skiles 270
Office Hours: MWF 11-12, Skiles 270.
The class text book is:
Nonlinear Differential Equation and Dynamical System
Springer, 2nd edition
I'll also use the lecture notes by prof. Jack Hale. The notes are linked below.
The notes are an update and extension of the book:
Ordinary Differential Equations.
Jack K. Hale
See th online syllabus.
will be two midterms and one final. The first midterm will be September
25 and the second October 30. Depending on the results of the first
midterm, the second midterm can be in the form of a take home
assignemet. During the class we will discuss the possibility of a
project based final exam. I will assign HW and collect them every 2 or
3 weeks. The final
grade will be based on HW (15%), midterms (40%) and final (45%).
- 1.1 Definition and Notation.
- 1.2 Existence and Uniqueness. (Notes: 1.1, 1.2 and 1.3)
- 1.3 Gronwall's Inequalities. (Notes: 1.4)
- 2.1 Phase Space, Orbits.
- 2.2 Critical Points and Linearization.
- 2.3 Periodic Solution
- 2.4 First Integral and Integral of Motion
- 2.5 Evolution of a Volume Element, Liouville Theorem
First Homework: from the textbook ex: 2.2, 2.4, 2.6, 3.2, 3.5. Homework due September 14.
- 3.1 Two Dimensional Linear System
- 3.2 Remark on Three-dimensional linea systems
- 3.3 Critical Point of Nonlinear System
Second Homework: from the textbook ex: 4.2, 4.5, 4.6, 4.8. Homework due October 23..
- 4.1 Bendixon's criterion
- 4.2 Geometric auxiliaries, preparation for the Poincare-Bendixon theorem.
- 4.3 The Poincare-Bendixon theorem.
- 4.4 Application of the Poincare-Bendixon theorem.
- 4.5 Periodic solution in Rn