ODE introduction textbook Unfortunately I have reached the maximum number of math classes I can take for my undergraduate degree.  I still wish to study basic ODEs and basic number theory.  What is a good textbook with an introduction to these?  I would prefer a textbook that is not super rigorous or formal since I will be studying it on my own time.
Thank you.
 A: I think these two are quite good:
Elementary Differential Equations with Boundary Value Problems (Edwards &Penney)
An Introduction to the Theory of Numbers (G Hardy)
A: For learning ODE's, a popular undergraduate book is 

1.)Differential Equations with Boundary Value problems-Polking, Bogges, Arnold.

If you want to see many examples, I recommend you get the 

2.)Schaum's Outline on Differential equations-Bronson,Costa.

From personal experience I highly recommend both of these books. If you want to see slightly more advance topics with a geometric taste I recommend

3.) Ordinary Differential Equations-V.I. Arnold

As for Number theory, if you want a computational approach, consider

1.) Elementary Number Theory-Burton

For a more theoretical approach,

2.) A classical Introduction to Modern Number theory-Rosen, Ireland
  3.) Introduction to Analytic Number Theory-Apostol

A: Nonlinear Dynamics and Chaos
by Steven Strogatz is a great book if you want to get a feel for how differential equations work. Wonderful explanations, fun exercises, and lots of interesting applications. (But don't expect any proofs of existence and uniqueness theorems and such things.)
A: Some books that I think work quite well and very well laid out in formatting and examples and exercise are the following two books:
1) Differential Equations & Linear Algebra, Third Edition: Edwards and Penney
2)  Elementary Number Theory, Fifth Edition: Kenneth Rosen
There is a sixth edition out now on the Rosen's Number Theory book, but I would guess that there is not much change to it, but I can be unsure. The material should be still relevant in the Fifth with respect to the newer edition.
Okay, I hope that this helps out with your journey to self-learn. 
Good~Luck and happy studying.  :)
A: There are two books I know of that deal with differential equations & include a chapter on the calculus of variations at an introductory level as well which you 
might enjoy.
1) Differential Equations and Their Applications - Zafar Ahsan
2) Differential Equations & the Calculus of Variations - Lev Elsgolts
Another book exclusively devoted to ODE's is Tenenbaum/Pollard Ordinary Differential Equations.
The NPTEL video lectures here are wonderful, do module 1 & 2 simultaneously (beginning with, & with more emphasis on, module 2).
The UCCS video's here use different books, you might like to buy one of the
books & work along with the videos on there. Similarly the videos on number theory in that link use a book you might like to buy & read along with the lectures on there. 
A: *

*An Introduction to Ordinary Differential Equations-Earl A. Coddington

*Fundamentals of Number theory-William J. Leveque

