Book for ODEs and numerical solution I would like to ask you information for a book. I want to (self) study ordinary differential equation and their numerical solution (with MATLAB). I am not a math student (life science) so I want a more applied math book (not something very basic and without theory, but not a very theoretical book without real world examples)...
Moreover, I also want to be able to solve ODEs with MATLAB and doing some simulation, so I would like a book that combine ODEs theory with numerical solution in MATLAB.
I found the book of Robinson but I do not know if it is too much easy!
Thanks for your help and have a nice day.
 A: For a short introduction see these Notes.
There is also a book:
Using Matlab for Differential Equations (MATLAB Curriculum Series)
which is a bit outdated (1995), but most of the basic stuff does not need update.
A: I would recommend Elementary Differential Equations and Boundary Value Problems (Amazon link) by Boyce and DiPrima. If you want to buy it, it is really easy to get a previous edition inexpensively from Amazon (I got the 8th edition a couple of years ago with CD for $7–8).
I have been using it and I found it great for your purposes, it has theory, but also a lot of examples, some of them from life sciences. It has also a great chapter on Numerical Methods (the book is not entirely devoted to them). It gives you just the algorithm for the resolution of the equation (Euler, Runge-Kutta, ...) and you would have to implement it yourself in Matlab, but it's quite well explained so it's very easy to do it.
A: One of the great advantages of MATLAB is that many of the methods for solving ODE are implemented. For example Runge-Kutta is the ode45 routine and many more.
In my opinion I think the best option is to learn the basic theory using the book that Adolfo has recommended you, because it is a very, very good book.
Once you have learned the basic equations and numerical methods. The Matlab help documentation will teach you how to apply the methods you have learned but using matlab routines, which will avoid tedious programming numerical methods, and you will be sure that in your calculations you dont have programming errors. 
And finally one of the most important things you should learn is to reduce an ODE to order 1, because it can solve many equations, this is very important when you are modelling a system.
I hope this helps you solve your doubt.
