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One semester introductory course on differential equations aimed at engineers. The book originated as class notes for Math 286 at the University of Illinois at Urbana-Champaign in the Fall 2008 and Spring 2009 semesters. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. The Laplace transform and power series are not usually covered in Math 286. See http://www.jirka.org/diffyqs/ for more information.