ODE introduction textbook

Question

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.

Answer 1

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)

Answer 2

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.)

Answer 3

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. :)

Answer 4

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.

Answer 5

1. An Introduction to Ordinary Differential Equations-Earl A. Coddington
2. Fundamentals of Number theory-William J. Leveque

Answer 6

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