Looking for good intro book on differential equations

Question

I am looking for a good book to study ordinary differential equations.

My background is that I have successfully completed calculus 1 through 3. So this included derivatives and integrals, multivariable , taylor series, some vector calculus etc.

I have also had two semesters of linear algebra which included basic geometry, matrices, vector spaces, linear transformations, inner product spaces etc.

I am looking for either a good book for self study, or/ and one with good problems.

I am also very open to hearing any opinions on the course in general. Is there anything I should make sure I am completely brushed up on? I have heard a few mixed reviews about the class. Some have said that the class is easy but "boring" and others have said it can be quite difficult.

Anyways, hope all is well, Thanks!

Answer 1

I would strongly recommend taking some time to study Fundamentals of Differential Equations (8th Edition) by Nagle, Saff, and Snider. (Notice that this actually is a PDF file, not just an Amazon link!)

This is the best book I've ever encountered in any math class by far. Nagle takes the time to explain a wide variety of problems and solutions step-by-step with some of the clearest explanations possible. Any time you spend with this book (particularly for 2nd-order ordinary differential equations in Chapter 4) will pay itself over many times.

Answer 2

Well, I'll give my two cents.

I like An Introduction to Linear Analysis, from several authors, a lot. Do not be mistaken by the name, they talk a lot about ODE's. And the first and second chapters are a quick review of linear algebra. I think it is a well-suited book for self-study.

I also heard people talk good things about Elementary Differential Equations, from Boyce and Di Prima. Might be worth taking a look.

When I took the course, the professor said she used this book from Brauer and Nohel to prepare the lectures. It was an introductory course on ODE's, so I think you may also profit from taking a look at this one.