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According to the author,"This free online book (e-book in webspeak) should be usable as a stand-alone textbook or as a companion to Edwards and Penney, Differential Equations and Boundary Value Problems. I developed and used these notes to teach Math 286/285 at the University of Illinois at Urbana-Champaign. Sample Dirichlet problem solution The aim is to provide a low cost, redistributable, not overly long, high quality textbook that students will actually keep rather than selling back after the semester is over. Even if the students throw it out, they can always look it up on the net again. You are free to have a local bookstore or copy store make and sell copies for your students. See below about the license. Another reason is to allow modification and customization for a specific purpose if necessary. If you do modify these notes, make sure to mark them prominently as such to avoid confusion. This aspect is also important for longevity of the book. The book can be updated and modified even if I happen to drop off the face of the earth. You do not have to depend on any publisher being interested as with traditional textbooks. While the textbook may be used by itself, it is can also be used in conjunction with the IODE software. IODE is a free software package for experimenting with basic ODEs developed at University of Illinois specifically for teaching this course. IODE works with both Matlab (proprietary) and Octave (free). The IODE website has several extra projects for the students to work through as homework. The graphs in the book are done using the Genius software. Temperatures of object with ambient temperature oscillating Table of contents: Introduction 1. First order ODEs 2. Higher order linear ODEs 3. Systems of ODEs 4. Fourier series and PDEs 5. Eigenvalue problems 6. The Laplace transform"

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