Book Recommendation - Introductory Differential Equations

[niehaoma]

Anyone have a great recommendation for a textbook on 1st semester/year/undergraduate differential equations? I would like for:

1. The books style to cater to auto-didactic learning.
2. Emphasis on engineering problems/applications and/or emphasis towards engineering students. (i.e. non-math major)

There are numerous books on Amazon, most with avg reviews. I am a highly visual learner, so as much as I hate to admit it, nice new books with fancy graphics suit my learning style compared to monochromatic books of yesteryear.

If you do provide a recommendation, could you please state "why" it is a good/great book. I would also like coverage of Laplace and Fourier (or a separate recommendation for these topics).

Thank you in advance.

EDIT:
The following book seems to be fairly multi-facted, with good reviews for previous edition. Anyone use this book?
https://www.amazon.com/dp/0470458364/?tag=pfamazon01-20

 

[hunt_mat]

How about engineering mathematics and further engineering mathematics by K. A. Stroud?

 

[niehaoma]

I actually have both of those books. Working within the first one now. However, I am looking for some recommended alternatives.

 

[hunt_mat]

I think strouds book is utterly brilliant, differential equations aren't really a pictorial type of maths, the only motivation is from physical applications. The standard one that is usually given is Elementary Differential Equations by Boyce and DePrima.

 

[sponsoredwalk]

I've painfully, & I really mean painfully, come to the realization that every book on this
subject is deficient in a serious way. This book is one of the best in terms of content as
you can see from the contents page but still it's deficient in terms of theory. This book
makes up for the lack of theory, but still it's deficient - deficiencies I only discovered
because of merciless browsing of online class slides where lecturers offer up theorems
not in either book that just make sense.

Mix the theory at the start of this .pdf with the theory at the start of Goursat's book &
you've got more cogency than is explained in any of the above mentioned books. Then
throw in some of the theory from the books I've mentioned along with some of the
theorems in the .pdf's on this website, some theorems from this book & http://www.out.ac.tz/avu/images/Mathematics/Differential%20Equations/Differential%20Equations.pdf & then
you have, unless I'm mistaken, a coherent view of elementary differential equations that
no book I have found thus far has given. Note that this is all content that refrains from
the theory more advanced books contain, this is the elementary theory that just makes
the basics hang together (so that it's not just a collection of tricks)! I think that conveys
a good deal of info & hopefully you find it helpful, if anybody has any good sources to add
I know I'd really appreciate it

 

[niehaoma]

@sponsoredwalk,

I just wanted to say thank you for taking the time to put that post together. Greatly appreciated. I ordered a book by Kreyszig; hopefully it will be informative, combined with Stroud.

 

[saim_]

You should also try Morris Tenebaum's "Ordinary Differential Equations". I really liked this book. We were actually assigned Kreyszig's Advanced Engineering Math, also quite a decent text but a little too light on theory for my taste.