DIFFERENTIAL EQUATIONS
Math 1381, Spring 2007

Instructor: Dr. Rachel Hall
Office: 229 Barbelin
Office Hours: M 2:30-3:45, T 10-11:30, Th 2:30-3:45, and by appointment
Telephone: (610) 660-3096 (Office)
E-mail: rhall@sju.edu
URL: http://www.sju.edu/~rhall/DiffEq

Course Description: Differential equations are used to model the behavior of systems in the natural world, and predict how these systems will behave in the future. For instance, exponential growth (the rate of change of a population is proportional to the size of the population) is expressed by the differential equation dP/dt = kP. Newton's Law of Gravitation (acceleration is inversely proportional to the square of distance) translates to the equation y'' = -ky². Many more examples are found in the fields of physics, engineering, biology, chemistry, and economics.

The traditional course in differential equations focused on the small number of differential equations for which exact solutions exist. However, the methods used by scientists today have changed dramatically due to the computer. Although we will cover some of the analytic methods discussed in a traditional course, we will also emphasize qualitative and numerical methods that have been made practical through the use of computers.

Here are some words of wisdom from the web site of Bob Devaney, differential equations guru (and one of the authors of our text):

This is a course in ordinary differential equations. However, the course is by no means “ordinary.” In years past, before we had widespread access to computers and computer graphics, courses in ordinary differential equations consisted mainly in a series of special tricks to solve special differential equations. Unfortunately, most differential equations (and in particular most differential equations that arise in applications) cannot be solved explicitly by these or any other methods.

Today we all have access to high-speed computers and computer graphics. Like humans, computers cannot solve most differential equations that arise. However, they can give us an APPROXIMATE or NUMERICAL solution. For many purposes, this is good enough.

Unfortunately, computers make mistakes (sometimes because of round-off errors or sometimes because the differential equation is not suited to numerical approximation). So we always have to be careful when we solve differential equations this way. More importantly, the output of the computer is not a formula that we can use to compute values of our solutions. Rather, the output from the computer is a rather lengthy list of numbers. Most often, it is best to view this list geometrically as a phase line or plane or other geometric object.

All of this means that this will be a very different type of mathematics course. In this course you will rarely be asked to generate specific formulas for solutions of differential equations. Rather, you will be asked to understand the algorithms that lead to numerical solutions, to interpret the resulting pictures produced by the computer, and to relate these images back to the original application.

You will also be required to perform lengthy labs and submit written lab reports. Your homework problems and questions on exams will often involve essays rather than simple routine computations. And you will often have to use technology to come up with answers to questions that are posed. Most students in the past have found this kind of course quite challenging, but lots of fun. If you are used to the old style of mathematics courses, be prepared for something quite different and perhaps much more relevant to whatever your use for differential equations is.

(from http://math.bu.edu/INDIVIDUAL/bob/MA226/syllabus.html)

Prerequisite: Calculus III or instructor's permission.

Text: Blanchard, Devaney, and Hall, Differential Equations, Brooks/Cole, 1998. We will cover the first three chapters plus special topics from other chapters. This is a good, readable book, though it's not a “traditional” math book. You should read each section before the appropriate lecture. You will also need the CD-ROM that comes with the text.

Homework and labs: Homework assignments, labs, and policies are posted at http://www.sju.edu/~rhall/DiffEq/homework.html.  

Tests: There will be four 75-minute tests. Makeup tests will only be given to students who contact me within 48 hours of missing a test.  Students with a valid, verifiable reason for missing a test may take a makeup without penalty; those who have missed a test without a valid, verifiable reason may take a makeup with a 30% penalty.   The tests will not be cumulative.

Grades: Grades will be weighted as follows: 60% for the four test grades, 35% for homework and labs, and 5% for class participation. There will be about 10 homework assignments and 3 labs. The grading scale is 94-100% A, 90-93% A-, 87-89% B+, 84-86% B, 80-83% B-, 77-79% C+, 74-76% C, 70-73% C-, 67-69% D+, 60-66% D, and below 60% F. Grades may be curved at the end of the semester.

Academic Honesty: Dishonesty includes cheating on a test, falsifying data, misrepresenting the work of others as your own (plagiarism), and helping another student cheat or plagiarize. Academic dishonesty will result in a grade of zero on that particular assignment or failure of the course. For complete information about the University's policy on Academic Honesty, consult the Student Handbook 2006-2007.

Attendance: Class attendance is mandatory.  Although I do not have a rigid cut policy, anyone who has missed lots of classes and is doing poorly in the course should not expect much sympathy from me.  If you do miss a class, it is your responsibility to make up the material and make sure your homework is turned in on time.