Course Outline
Math 302 - Ordinary Differential Equations
Fall 2006
Instructor: Prof. John A. Pelesko
Office: 406 Ewing Hall, 831-1467, [email protected]
Course Web Pages: www.math.udel.edu/~pelesko,
Office Hours: MWF 9-10, F 3-4
Software: Maple
Textbooks: Elementary Differential Equations and Boundary Value
Problems, 8th Edition, Boyce & DiPrima
This is a course in ordinary differential equations. The focus of this course
will be on the applications of ordinary differential equations (ODE’s) to
problems from the physical, biological, and social sciences. You will find
that the tools we develop this semester are used by researchers in every
branch of science. You should also be aware that we will rely on material
you have studied in prior courses. In particular, your skills in algebra and
calculus should be sharp. If you feel rusty, a review is in order. In this
course, we will use Maple, you should ensure that you have access to Maple.
If you choose to take this class and develop your mathematical skills you
will need to:
• Read regularly and critically - You will have a text for this course,
notes that I will prepare, and outside references to consult. In order to
master the material it is necessary that you read these materials
regularly and critically.
• Attend Class - If you choose to take this class, you’ll need to attend.
Some portion of the material we cover will not be in your text. Don’t
decide to take this class without committing yourself to attending each
and every class.
• Complete Problem Sets - The heart of this course is the homework
problems. It is in doing the homework that you will master the
material. There will be 12 homework sets handed out during the
course of the semester. The due date for each homework assignment is
firm; no late homework will be accepted. You should write your
answers clearly. If I cannot understand an answer, it is wrong. In
addition, I will post homework sets that are not to be handed in, it is
your job to make sure you can do these as well.
Tentative Schedule:
Exam dates are firm. Lecture dates and topics will be adjusted as needed.
Week
Aug 28
September 4
September 11
September 18
September 25
October 2
October 9
October 16
October 23
October 30
November 6
November 13
November 20
November 27
December 4
Key events & topics
Introduction to ODE’s, modeling with 1st order equations.
Techniques of solving 1st order equations.
More modeling, population dynamics, numerical methods
Second order equations.
More 2nd order equations. Exam #1 on 9/29.
Applications of 2nd order equations.
Elements of nth order equations.
Series solutions, the Laplace transform.
Systems of ODE’s, review of matrices. Exam #2 on
10/25.
More matrix algebra, eigenvalues and eigenvectors.
Nonlinear equations and stability.
More nonlinear equations.
Numerical methods. Exam #3 on 11/22.
Boundary value problems.
More boundary value problems.
Assessment: Your final grade will depend on each of the components in the
course. In particular,
Homework/Problem Sets/Projects
40%
In-class exams (3 X 10%)
30%
Final Exam
30%