I am thinking of picking up an introductory course on Differential Equations. I have 3 books on my mind.
- An introduction to ordinary differential equations - Earl A. Coddington
- Differential Equations: With Applications and Historical Notes - George F. Simmons
- Differential Equations and Boundary Value Problems - C. Edwards and David E Penney
I am confused as to which book would be ideal for me. I know all these are great books, hence the confusion. Coddington seems concise and rock solid. Simmons, on the other hand, seems very intuitive but less rigorous and more applied. Don't know much about the third one. It's on my University's recommendation list.
I am a little more theoretically inclined (have read a bit of Analysis and the basic structures of Proofs) but would like to get a little applied touch too and learn the different ways of tackling and solving differential equations.
I have the updated book by Simmons and Krantz - Differential Equations: Theory, Technique, and Practice. George F. Simmons and Steven G. Krantz. The presentation in the book is not completely rigorous, but they still cover existence and uniqueness theorems. I compared the contents of Coddington's book with that of Simmons' book and the latter covers much more material (Laplace and Fourier transforms, PDEs, calculus of variations, non-linear theory and introduction to chaos off the top of my head) Also, Simmons is an excellent expositor and the historical notes and examples drawn from mechanics and physics make the book an excellent introductory text.
Also, there is another book by Coddington - Theory of Ordinary Differential Equations which is rigorous and is a classical reference on the subject. However, it may not be suited as a first text.