Suggestions for Differential Equations Text

[Jow]

As a high school student, I enjoy studying mathematics on my spare time. Having recently worked through a textbook on vector calculus, I am in need of a textbook that will give me a solid introduction to differential equations.

Any suggestions will help my search; however, I would prefer a book that will give me a good intuitive understanding of topics, rather than a highly rigorous book.

Also, I suspect it will help narrow down your suggestions if I give you a list of topics I am familiar with. I am competent in elementary calculus, I have a decent understanding of multivariable/vector calculus and I have some knowledge of linear algebra.

If you know of any textbook that will aid my studies I would greatly appreciate it if you shared the title and author (also, why it would be a good book, if you feel so inclined).

 

[Poley]

Differential Equations, Dynamical Systems, and an Introduction to Chaos is great for developing an intuitive, geometric understanding of differential equations. It's a little less rigorous than other choices but this might be what you are looking for. Another choice is Ordinary Differential Equations by Arnold, which like the previous is an intuitive, geometric approach but this time with some more rigor and detail. (Be aware that Arnold demands strong preparation in linear algebra.)

These two texts are primarily studies of the "qualitative theory" of differential equations; neither of will teach you much of the gritty details of actually finding analytic/numerical solutions to DEs. If that's what you're interested in instead, then I'd recommend Ordinary Differential Equations by Tenenbaum or Differential Equations and Boundary Value Problems by Edwards and Penney.

Finally I'll recommend Differential Equations and Their Applications, which is at a lower level than HSD or Arnold but still good if you want a more basic introduction.

 

[verty]

Differential Equations - Stroud & Booth looks good. In particular, it has good coverage of topics, for example, Bessel functions and Laplace and Z transforms.

There are other less expensive books that are more traditional but I chose to recommend this one.

 

[jasonRF]

I don't know what the best book for you is, but if you go for Edwards and Penney (or any similar book) I would recommend used copies of old editions for cheap. For example:
https://www.amazon.com/dp/0130652458/?tag=pfamazon01-20

jason

 

[Dr Transport]

Boyce and DiPrima

https://www.amazon.com/dp/047003940X/?tag=pfamazon01-20

 

[djh101]

For nonlinear differential equations, I liked Strogatz quite a bit (although we had a substitute one day that couldn't condemn him enough). A nonlinear book will give a good introduction to analyzing differential equations by their behavior and modelling systems (although I suppose a mathematical modelling book might be better suited to that if you aren't as interested in bifurcations and chaos).

For a good introduction to ordinary differential equations in general, Tenenbaum (published by Dover) will be well suited. I actually found myself reading through Tenenbaum for Laplace and Heavyside as opposed to our assigned book (Simmons). Good explanations with proofs and lots of examples and practice problems, although a slight annoyance is that he doesn't use the metric system in application problems. Fourier series are also not covered, which I found to be a little bit disappointing.

Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity)
Ordinary Differential Equations (Dover Books on Mathematics)