Syllabus for Math 2574H --- Spring 2003



This is a one semester introduction to ordinary differential equations. In the first part of the course we will cover the theory of first and second order scalar equations. The second part will be devoted to first order linear systems. Finally, we will have a look at some nonlinear systems.


Differential Equations, by Polking, Boggess and Arnold. This book comes packaged with another book about using Matlab to solve differential equations (at no additional charge!). Occasionally I will cover topics which are not in the text or present a different approach to some topic.


Homework / Quizzes 20 %
Midterm Exams (20 % each) 40 %
Final Exam 40 %

All exams will be open book, open notes, calculators allowed.

Exam Dates:

 Midterm I Tuesday, February 25
 Midterm II Tuesday, April 7
 Final Monday, May 12, 1:30-4:30

For a general policy statement about grades, academic honesty and workload, go to: University Grading Policy Statement.


Below is a link for a Mathematica notebook which you can download and go through on your own in one of the campus computer labs.

Do-It_Yourself Lab download

You can also use the Java ODE solver at

Approximate Schedule:

 Week  Topics  Sections
1/21-1/24 ODEs and PDEs. Separable ODEs. 2.1-2.3
1/27-1/31 First order tricks and examples, Lab I 2.4-2.5
2/3-2/7 Existence theory, phase line, stability 2.7-2.9
2/10-2/14 Second-order linear ODEs 4.1-4.4
2/17-2/21 Forcing and resonance. 4.5-4.7
2/24-2/28 Midterm I, Numerical methods Ch. 6
3/3-3/7 First-order systems, linear systems Ch.8, 9.1
3/10-3/14 Eigenvalues, eigenvectors 9.2-9.3
3/17-3/21 Spring Break !  
3/24-3/28 More linear systems, matrix exp. 9.4-9.5
3/31-4/4 Fund. matrices, var. of parameters 9.6,9.8
4/7-4/11 Midterm II, Linearization of nonlinear ODEs 10.1-10.2
4/14-4/18 Phase portraits, periodic orbits 10.3-10.4
4/21-4/25 Nonlinear mechanics 10.5-10.6
4/28-5/2 More nonlinear systems 10.7-10.8
5/5-5/9 Special topics 10.7-10.8