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I'm looking for a good book that serves well as an introduction to the study of differential equations. I don't want it to be about applications since I'm currently not particularly interested in anything but pure mathematics. I want topics like existence, uniqueness, Laplace transformation, solutions in terms of power series and moderately difficult non-linear equations to be covered rigorously. I want many assignments as well. A bonus would be if Fourier series and simple partial differential equations are covered but this is not mandatory. Preferably I would like the price to not exceed \$$100$. If there is a free pdf that would be wonderful.

Not a duplicate since I am more specific with what I want.

David
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  • No, I have already checked that one and it does not include my specifications. – David Dec 16 '16 at 02:22
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    You might want to peruse: Differential Equations 3rd Edition by Shepley L. Ross (800-page one) , ODEs and Dynamical Systems by Teschl, ODEs by V.I. Arnold, but tough request. – Moo Dec 16 '16 at 02:52
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    I agree with @Moo. Teschl is a good choice, he has an online copy of his book. https://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf – Chee Han Dec 16 '16 at 03:26
  • For a good introduction to ODE:http://tutorial.math.lamar.edu/Classes/DE/DE.aspx ; For a good introduction to PDE: Farlow: Partial Differential equations for scientists and engineers. – qmd Dec 16 '16 at 10:23
  • @Moo thank you very much. – David Dec 16 '16 at 12:05

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