Need opinions on my differential equations book

In summary: 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
  • #1
Mathgician
78
0
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.
 
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  • #2
You can try Schaum's outline series on Differential equations. It gives a lot of worked out problems with application.
 
  • #3
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.
 
  • #4
Try Braun's book.
 
  • #5
Don't like "cookbooks"?

Mathgician said:
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.

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.

Mathgician said:
This class is very different from my other math classes, I learn methods that I am not getting a solid explanations for...is the first differential equations course just a beginning course that does not go in depth?

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.
 
  • #6
Braun's book is not a Shaums outline!

Used in undergraduate classrooms across the country, this book is a clearly written, rigorous introduction to differential equations and their applications. Fully understandable to students who have had one year of calculus, this book differentiates itself from other differential equations texts through its engaging application of the subject matter to interesting scenarios. This fourth edition incorporates earlier introductory material on bifurcation theory and adds a new chapter on Sturm-Liouville boundary value problems. Computer programs in C, Pascal, and Fortran are presented throughout the text to show the read how to apply differential equations towards quantitative problems.

I love the first book of Hubbard and West. The fence-funnel approach to existence and flow behavior is simply fantastic.
 
  • #7
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?
 
  • #8
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.
 
  • #9
Chris Hillman said:
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.

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.
 
  • #10
AiRAVATA said:
I've read that one of his most important works was that Mandelbrot set is connected.

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.

Mathgician said:
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.

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.
 
  • #11
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1. What is the overall structure of the book?

The book is divided into several sections, each focusing on a specific aspect of differential equations. The first section introduces the basic concepts and techniques, followed by sections on first-order and higher-order equations, systems of equations, and applications. Each section includes clear explanations, examples, and practice problems.

2. Is the book suitable for beginners?

Yes, the book is designed for students with little to no background in differential equations. It starts with the fundamentals and gradually builds upon them, making it accessible for beginners. However, some knowledge of calculus is recommended.

3. What kind of exercises and problems are included in the book?

The book includes a variety of exercises and problems, including conceptual questions, computational problems, and real-world applications. The exercises are designed to reinforce the concepts and techniques learned in each section, and the problems range from straightforward to challenging.

4. Are there any additional resources or materials available?

Yes, the book includes online resources such as practice quizzes, interactive simulations, and video lectures. These resources are meant to supplement the material in the book and provide additional practice and support.

5. How does this book compare to other textbooks on differential equations?

This book offers a unique approach to teaching differential equations, focusing on conceptual understanding and real-world applications. It also includes a variety of resources and exercises for students to practice and apply their knowledge. Additionally, the book is written in a clear and concise manner, making it easy to follow and understand.

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