Textbook Recommendation Needed

[sampahmel]

I already finished a undergraduate ODE course that uses Elementary Differential Equations and Boundary Value Problems by Boyce.

And I'm now seeking for a book or lecture notes that teaches something beyond what is usually learned in a first course of ODE, but at the same time, the material should not be too advanced as I am facing a time constraint.

Specifically, I'm looking for topics like local and global solution (which I didn't learn much in the 1st course), Cauchy problem, Peano's Theorem, Cauchy-Lipschitz Theorem and so on.

I'm also looking for something more of a calculation nature than theorem-proof-theorem-proof type (which is why I was asking for something not too advanced) as right now I'm just trying to learn some "basics" for a project.

Thank you for reading.

 

[gtoguy97]

One book that may be of use to you is Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers by D.W. Jordan and P. Smith. This book covers topics such as local and global solution, Cauchy problem, Peano's Theorem, Cauchy-Lipschitz Theorem, and more. It also provides calculation techniques for these topics, which may be useful for your project. Additionally, the book is not overly advanced and should be accessible for someone with an understanding of first-order ODEs.