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.