Author: Nagy, G.
Title: Ordinary Differential Equations. Mathematics Department, Michigan State University, East Lansing, MI, 48824.
Accessed 16 August 2016.
This is a work in progress, but the 331 page first attempt holds forth with theory and good narrative as well as several exercise sets and a reasonable reference section. We quote from the author’s Summary. Indeed, the version which is currently up is dated 10 April 2016.
“This is an introduction to ordinary differential equations. We describe the main ideas to solve certain differential equations, like first order scalar equations, second order linear equations, and systems of linear equations. We use power series methods to solve variable coefficients second order linear equations. We introduce Laplace transform methods to find solutions to constant coefficients equations with generalized source functions. We provide a brief introduction to boundary value problems, Sturm-Liouville problems, and Fourier Series expansions. We end these notes solving our first partial differential equation, the Heat Equation. We use the method of separation of variables, hence solutions to the partial differential equation are obtained solving infinitely many ordinary differential equations.”
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