DE_Complete

# DE_Complete - DIFFERENTIAL EQUATIONS Paul Dawkins...

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Unformatted text preview: DIFFERENTIAL EQUATIONS Paul Dawkins Differential Equations © 2007 Paul Dawkins i http://tutorial.math.lamar.edu/terms.aspx Table of Contents Preface . ............................................................................................................................................ 3 Outline . ........................................................................................................................................... iv Basic Concepts . ............................................................................................................................... 1 Introduction . ............................................................................................................................................... 1 Definitions . ................................................................................................................................................. 2 Direction Fields . ......................................................................................................................................... 8 Final Thoughts . ........................................................................................................................................ 19 First Order Differential Equations . ............................................................................................ 20 Introduction . ............................................................................................................................................. 20 Linear Differential Equations . .................................................................................................................. 21 Separable Differential Equations . ............................................................................................................. 34 Exact Differential Equations . ................................................................................................................... 45 Bernoulli Differential Equations . ............................................................................................................. 56 Substitutions . ............................................................................................................................................ 63 Intervals of Validity . ................................................................................................................................ 72 Modeling with First Order Differential Equations . .................................................................................. 77 Equilibrium Solutions . ............................................................................................................................. 90 Euler’s Method . ........................................................................................................................................ 94 Second Order Differential Equations . ...................................................................................... ....
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## This note was uploaded on 02/25/2010 for the course MATH 2070 taught by Professor Pual'snotes during the Fall '10 term at Lamar University.

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DE_Complete - DIFFERENTIAL EQUATIONS Paul Dawkins...

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