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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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DE_Complete - DIFFERENTIAL EQUATIONS Paul Dawkins...

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