Need opinions on my differential equations book

Mathgician

I was wondering what you guys think of my textbook.
My textbook is called:

A First Course in Differential Eqations (Eight Edition)

Author: Dennis G. Zill

ISBN: 0534418783

I have been using this book for my DE class, and I do not feel like I am really learning anything. This class is very different from my other math classes, I learn methods that I am not getting a solid explanations for. Most people I've gone for help that has taken this class before have forgotten most of the materials that has been tought in this class. I want to get the most out of my DE class, is there another book you guys suggest that will help me understand DE and not forget it?
Also, another question, is the first differential equations course just a beginning course that does not go indepth? I just don't feel like I am learning anything or in other words getting any insights. Tell me your experience people.

srikanth.isro

You can try Schaum's outline series on Differential equations. It gives a lot of worked out problems with application.

Mathgician

I'm not saying I am having problems with the course that I cannot keep up, in fact I think it isn't very difficult at all. I haven't been faced with any challenges from the class to get any insights as I would in a calc class. I am doing the problems, but it just seem very mechanical process.

AiRAVATA

Try Braun's book.

Chris Hillman

For a moment there I thought you were saying you were teaching the course with an assigned textbook. Anyway, I happen to think that's a fine book and I don't see why you dislike it. Depending upon what applications interest you, there are plenty of alternatives, such as Differential Equations : A Dynamical Systems Approach by John H. Hubbard and Beverly H. West.

Yes. OK, now I think I do see what you dislike about Zill's book: it's a "cookbook". That is, he presents a whole bunch of techniques for solving various kinds of problems but doesn't attempt to philosophize or to explain many deep principles. For most students, that is just the right approach. And if you dislike it, you'll hate Braun's Schaum Outline book even more! Why not go with the flow (no pun intended), learn the techniques, and plan on some self study this summer with Cantwell, Introduction to Symmetry Analysis? This book explains a general principle (symmetry of the ODE or PDE itself) which lies behind the techniques you learned from Zill. IOW, relax, you're learning much more than you yet realize.

AiRAVATA

Braun's book is not a Shaums outline!!!

I love the first book of Hubbard and West. The fence-funnel approach to existence and flow behavior is simply fantastic.

Chris Hillman

Did you know that Hubbard and Douady discovered an important theorem which involves symbolic dynamics and the "field lines" of an electrically charged Mandlebrot set?

AiRAVATA

I've read that one of his most important works was that Mandelbrot set is connected.

I remember that one day I was looking for comparison theorems for ODE's, and I came across a great paper for undergrad students where, using simple arguments like fence-funnel theory, he was able to deduce in great clarity the behavior of a dynamical system. I have been trying to find it to post the link here, but haven't been able to.

Mathgician

Right on! You know exactly how I feel about the course I am taking that is being supplemented with this "book of techniques," makes me feel like how I felt when I was taking beginning algebra, techniques, but no insights. I really appreciate your input and thank you, you understand very well what I am trying to say.

Chris Hillman

With Douady, yes. (Hubbard was my undergraduate advisor at the time he was working with Douady, BTW!)

By all means post the link if you find it.

Thanks! I hope you took my point that if you change your expectations you can enjoy the course on its own terms. Once you understand that you need to learn the recipes before you can appreciate how marvellous it is that Lie was able to find a single principle underlying almost all of them, you can have fun simply learning to cook.

AiRAVATA

Found it!!!

A New Look at the Airy Equation with Fences and Funnels
John H. Hubbard, Jean Marie McDill, Anne Noonburg, Beverly H. West
The College Mathematics Journal, Vol. 25, No. 5 (Nov., 1994), pp. 419-431
doi:10.2307/2687507

To bad there are no figures, but here is the full reference (for those of you lucky enough to have journal access).