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I have taken a lot of math in university, but chose to omit differential equations. Unfortunately, now I have to read computer science proofs that use them, mostly ODEs, and this is always a struggle. What textbook(s) should I read to take me from the basics to practical use of the theory?

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I am mildly surprised to learn that ODEs show up in theoretical computer science. Would you mind giving some examples? – Pete L. Clark Feb 7 '12 at 23:25
@PeteL.Clark,"The O.D.E. Method for Convergence of Stochastic Approximation and Reinforcement Learning", "Cellular Networks: Theory". – Don Reba Feb 8 '12 at 1:16
$@$Don: thanks for the references. – Pete L. Clark Feb 8 '12 at 2:28
up vote 4 down vote accepted

If you are looking for practical solving of differential equations I recommend :

  • Advanced Mathematical Methods for Scientists and Engineers by Carl M. Bender and Steven A.Orszag.

  • Methods of Mathematical Physics R.Courant and D. Hilbert two volumes.

The second positions is absolutely the best ever written textbook on differential equations.

Maybe not so practical for solving special types of ODE's but still close to applications is

  • Ordinary Differential Equations by V.I.Arnold

Another quite well written textbook dealing with differential equations is

  • Dynamical Systems with Applications using Mathematica by Stephen Lynch

This book however mainly describes qualitavie methods for dynamical systems, but there are many good examples.

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Thank you. I've gone through the prefaces and tables of contents of these books, and they all look great. I want to read them all. Arnold's book, in particular, deals with the subject matter I am most interested in. There is even a Kindle version, so I can get it right away. – Don Reba Feb 12 '12 at 14:13
I would add another good books by V.I.Arnold : "Mathematical methods of Classical Mechanics" and "Theory of differential equations". Both are very good, though rather hard to read them quickly. They deal with all range of mathematics concerning differential equations. – Artes Feb 12 '12 at 18:15

Boyce and DiPrima, Elementary Differential Equations, Eighth Edition. Website.

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The books which I referred are:

  • Ordinary differential equations by E. Coddington.

  • Differential Equations With Applications and Historical Notes by George F. Simmons. This book is a classic and at the end of each chapter has historical notes of Mathematicians which is fun to read.

  • An online book published by the AMS is available here. I basically learn't the proofs of Gronwall's equality from here and used it as a reference book.

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