## General Course Information

A Little Philosophy and a Warning: 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.