I apologize for the outage on the site yesterday and today. Lamar University is in Beaumont Texas and Hurricane Laura came through here and caused a brief power outage at Lamar. Things should be up and running at this point and (hopefully) will stay that way, at least until the next hurricane comes through here which seems to happen about once every 10-15 years. Note that I wouldn't be too suprised if there are brief outages over the next couple of days as they work to get everything back up and running properly. I apologize for the inconvienence.
August 27, 2020
Chapter 1 : Basic Concepts
There isn’t really a whole lot to this chapter it is mainly here so we can get some basic definitions and concepts out of the way. Most of the definitions and concepts introduced here can be introduced without any real knowledge of how to solve differential equations. Most of them are terms that we’ll use throughout a class so getting them out of the way right at the beginning is a good idea.
During an actual class I tend to hold off on a many of the definitions and introduce them at a later point when we actually start solving differential equations. The reason for this is mostly a time issue. In this class time is usually at a premium and some of the definitions/concepts require a differential equation and/or its solution so we use the first couple differential equations that we will solve to introduce the definition or concept.
Here is a quick list of the topics in this Chapter.
Definitions – In this section some of the common definitions and concepts in a differential equations course are introduced including order, linear vs. nonlinear, initial conditions, initial value problem and interval of validity.
Direction Fields – In this section we discuss direction fields and how to sketch them. We also investigate how direction fields can be used to determine some information about the solution to a differential equation without actually having the solution.
Final Thoughts – In this section we give a couple of final thoughts on what we will be looking at throughout this course.