DE_Basic_Concepts

# DE_Basic_Concepts - DIFFERENTIAL EQUATIONS Basic Concepts...

This preview shows pages 1–6. Sign up to view the full content.

DIFFERENTIAL EQUATIONS Basic Concepts Paul Dawkins

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Differential Equations © 2007 Paul Dawkins i http://tutorial.math.lamar.edu/terms.aspx Table of Contents Preface . ............................................................................................................................................ 2 Basic Concepts . ............................................................................................................................... 1 Introduction . ............................................................................................................................................... 1 Definitions . ................................................................................................................................................. 2 Direction Fields . ......................................................................................................................................... 8 Final Thoughts . ........................................................................................................................................ 19
Differential Equations © 2007 Paul Dawkins ii http://tutorial.math.lamar.edu/terms.aspx 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. I’ve 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 wasn’t covered in class. 2. In general I try to work problems in class that are different from my notes. However, with Differential Equation many of the problems are difficult to make up on the spur of the moment and so in this class my class work will follow these notes fairly close as far as worked problems go. With that being said I will, on occasion, work problems off the top of my head when I can to provide more examples than just those in my notes. Also, I often don’t have time in class to work all of the problems in the notes and so you will find that some sections contain problems that weren’t worked in class due to time restrictions. 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 can’t anticipate all the questions. Sometimes a very good question gets asked in class that leads to insights that I’ve 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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Differential Equations © 2007 Paul Dawkins iii http://tutorial.math.lamar.edu/terms.aspx
Differential Equations © 2007 Paul Dawkins 1 http://tutorial.math.lamar.edu/terms.aspx Basic Concepts Introduction

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/11/2011 for the course MATH 244 taught by Professor Boyce during the Fall '08 term at Rutgers.

### Page1 / 24

DE_Basic_Concepts - DIFFERENTIAL EQUATIONS Basic Concepts...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online