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Unformatted text preview: Differential Equations 2005 Paul Dawkins http://tutorial.math.lamar.edu/terms.asp 1 This document was written and copyrighted by Paul Dawkins. Use of this document and its online version is governed by the Terms and Conditions of Use located at http://tutorial.math.lamar.edu/terms.asp . The online version of this document is available at http://tutorial.math.lamar.edu . At the above web site you will find not only the online version of this document but also pdf versions of each section, chapter and complete set of notes. Preface Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn how to solve differential equations or needing a refresher on differential equations. Ive tried to make these notes as self contained as possible and so all the information needed to read through them is either from a Calculus or Algebra class or contained in other sections of the notes. A couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. 1. Because I wanted to make this a fairly complete set of notes for anyone wanting to learn differential equations I have included some material that I do not usually have time to cover in class and because this changes from semester to semester it is not noted here. You will need to find one of your fellow class mates to see if there is something in these notes that wasnt covered in class. 2. Because I want these notes to provide some more examples for you to read through, I dont always work the same problems in class as those given in the notes. Likewise, even if I do work some of the problems in here I may work fewer problems in class than are presented here. 3. Sometimes questions in class will lead down paths that are not covered here. I try to anticipate as many of the questions as possible in writing these up, but the reality is that I cant anticipate all the questions. Sometimes a very good question gets asked in class that leads to insights that Ive not included here. You should always talk to someone who was in class on the day you missed and compare these notes to their notes and see what the differences are. 4. This is somewhat related to the previous three items, but is important enough to merit its own item. THESE NOTES ARE NOT A SUBSTITUTE FOR ATTENDING CLASS!! Using these notes as a substitute for class is liable to get you in trouble. As already noted not everything in these notes is covered in class and often material or insights not in these notes is covered in class. Differential Equations 2005 Paul Dawkins http://tutorial.math.lamar.edu/terms.asp 2 Basic Concepts Introduction There isnt 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. here can be introduced without any real knowledge of how to solve differential equations....
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