Spring Semester 2018

Differential Equations I/II

Syllabus

Quick Links:

Class mailing list for announcements and discussion
Homework sheets
Class handouts

Summary:

Differential Equations is an topic which links pure mathematics with applications in physics, biology, electrical engineering, and others. The course will furnish a systematic introduction to ordinary differential equations in one and several variables, focusing more on qualitative aspects of solutions than on explicit solution formulas in those few cases where such exist. It will be shown how simple differential equations can lead to complicated and interesting, often "chaotic" dynamical behavior, and that such arise naturally in the "real world".

In the first part of the semester, we will discuss general existence and uniqueness results, the phase space for autonomous equations, critical points, periodic solutions, stability theory, nonautonomous linear equations, and bifurcations. In the second part of the semester, we will look at perturbation theory including multiple scales analysis, averaging, relaxation oscillations, and the theory of slow manifolds. Time allowing, the semester will conclude with an introduction to Hamiltonian dynamics and KAM theory.

Contact Information:

Instructor:	Marcel Oliver
Email:	m.oliver@jacobs-university.de
Phone:	200-3212
Office hours:	Tu 11:00, We 10:00 in Research I, 107
TA:	TBA

Time and Place:

Lectures:

Tu 15:45-17:00, Th 14:15-15:30 in West Hall 8

Textbook/Further Reading:

F. Verhulst, Nonlinear differential equations and dynamical systems, 2nd edition, Springer, 1996.
S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edition, Springer, 2003.
G. Teschl, Ordinary Differential Equations and Dynamical Systems, AMS, 2012.
L. Perko, Differential Equations and Dynamical Systems, 3rd edition, Springer, 2001.

Grading:

The final grade will be determined as follows:

Homework: 20%

Midterm Exam: 40%

Final Exam: 40%
The scores will be averaged as percentage grades with the given weights.
Homework will be given every week, it is due in class the following Tuesday.

Class Schedule (subject to change!)

Feb. 1., 2018:	Introduction, contraction mapping theorem, Picard-Lindelöf theorem
Feb. 6., 2018:
Feb. 8., 2018:
Feb. 13., 2018:
Feb. 15., 2018:
Feb. 20., 2018:
Feb. 22., 2018:
Feb. 27., 2018:
Mar. 1., 2018:
Mar. 6., 2018:
Mar. 8., 2018:
Mar. 13., 2018:
Mar. 15., 2018:
Mar. 20., 2018:
Mar. 22., 2018:
Apr. 3., 2018:	Midterm review
Apr. 5., 2018:	Midterm Exam
Apr. 10., 2018:
Apr. 12., 2018:
Apr. 17., 2018:
Apr. 19., 2018:
Apr. 24., 2018:
Apr. 26., 2018:
May 3, 2018:
May 8, 2018:
May 15, 2018:	Final exam review
TBA:	Final Exam, Room TBA

Last modified: 2018/02/05
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/spring2018/math361/index.html
Marcel Oliver (m.oliver@jacobs-university.de)

Homework:	20%
Midterm Exam:	40%
Final Exam:	40%