Math 420:
Ordinary differential equations

Lectures: MTWR 1:00-3:10pm in DRL 2C4
Instructor: Tobias Dyckerhoff
Office: DRL 4C9
Office hours: Tue/Thu 3:10-4:00pm
Phone: 215-898-6217
Email: tdyckerh AT math upenn edu

Announcements

Homework

Section	Problems
1.2	6,10,12,24,26,18
1.6	2,4,8,12,39,40,44
1.7	4,6,21	Quiz1
1.5	1,3,13,15,17,18
1.8	7,9,11,13
1.9	1,3,5,7,9,11,13,15,17
2.1	1-6,19
2.2	1-6,7,11,13,15,17
3.1	5,8,17,19,31,33
3.2	1,3,5,7,11,17	Midterm1
3.3	1,3,5,7,9
3.4	3,5,7,9,11,13,15,16,17,19,21,23
3.5	1,3,5,7,9,11,17,19,21	Quiz 2
5.1	1,3,5,7,9,11,13,15,17,18,19,21,23,25
5.2	1,3,11,13,15
5.3	1,3,5,7,9,11,13,15,17,19

Labs

Lab	due date
1.3	Monday, June 2
3.4	Monday, June 16

Course policies

About

The major focus of the course will be the analysis of dynamical systems and their applications to different fields of science (the type of applications will be based on your interest).

The syllabus will be roughly as follows.

basic methods of solving ODEs (more or less a quick review of 240/241 material)
linear dynamical systems (e.g. classification of planar linear systems)
non-linear dynamical systems
numerical methods (e.g. Euler, Runge-Kutta)
applications (according to interest)
projects in which you present an ODE-problem related to your field

Material

We will use Differential Equations (3rd edition) by Blanchard, Devaney, Hall as a textbook for the course.

Other useful books are

Ordinary Differential Equations (Arnold)
Differential Equations, Dynamical Systems and an Introduction to Chaos (Hirsch, Smale, Devaney)

Prerequisites

Math 240/241.

Homework/Quizzes/Exams

The course runs for 6 weeks. In the odd weeks we will write quizzes (Thursdays), in the even weeks we will write exams (on Thursdays).

Homework. I will assign homework at least once a week. You do not have to submit your work. BUT: The set of problems on the quizzes will literally be a subset of the assigned homework problems. So, if you do your homework you will automatically be well prepared for the quizzes.
Quizzes. In the odd weeks (1,3,5) on Tuesdays/Thursdays, I will take a short quiz in the first 10 minutes of class.
Labs. I will assign Lab projects on which you should work in groups of 2-3 members and submit your work in form of a short essay.
Exams. In the even weeks (2,4,6) on Thursdays, we will write exams. In weeks 2 and 4 we will write midterms, in the last week you will present your final projects.

Grading

Your final grade will be computed using the following weights

Quizzes: 10 %
Labs: 10 %
Midterm 1: 25 %
Midterm 2: 25 %
Final Project: 30 %

Grades will be posted on blackboard. The final grade distribution should be around 33% A, 33% B and 33% C, though in case of a general good performance I am willing to shift this distribution.

Math 420: Ordinary differential equations