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 Eulers Method . ........................................................................................................................................ 94 Second Order Differential Equations . ..................................................................................... ....
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This note was uploaded on 05/08/2009 for the course AAE 580 taught by Professor Nnjkl during the Spring '09 term at Ohio State.

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DE_Complete - DIFFERENTIAL EQUATIONS Paul Dawkins...

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