Transcription of ORDINARY DIFFERENTIAL EQUATIONS
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ORDINARY DIFFERENTIAL EQUATIONS
ORDINARY DIFFERENTIAL EQUATIONSGABRIEL NAGYM athematics Department,Michigan State University,East Lansing, MI, 16, is an introduction to ORDINARY DIFFERENTIAL EQUATIONS . We describe themain ideas to solve certain DIFFERENTIAL EQUATIONS , like first order scalar EQUATIONS , secondorder linear EQUATIONS , and systems of linear EQUATIONS . We use power series methodsto solve variable coefficients second order linear EQUATIONS . We introduce Laplace trans-form methods to find solutions to constant coefficients EQUATIONS with generalized sourcefunctions. We provide a brief introduction to boundary value problems, Sturm-Liouvilleproblems, and Fourier Series expansions. We end these notes solving our first partialdifferential equation, the Heat Equation. We use the method of separation of variables,hence solutions to the partial DIFFERENTIAL equation are obtained solving infinitely manyordinary DIFFERENTIAL NAGY ODE August 16, 2015 IContentsChapter 1.
Summary. This is an introduction to ordinary di erential equations. We describe the main ideas to solve certain di erential equations, like rst order scalar equations, second order linear equations, and systems of linear equations. We use power series methods to solve variable coe cients second order linear equations. We introduce Laplace trans-
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