Customer Reviews

A Modern Introduction to Differential Equations, Second Edition

5 star:		(2)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

Off course, what else can anyone expect from the mind of Dr. Ricardo??? I just wish he had already published this book when I was still in my Undergraduate years as a Physics Major. Or perhaps even better: When I used to sit in his classroom. I owe my mathematical skills to the same teaching techniques I see when I read his book: The ability of Dr. Ricardo to explain complex subjects in a simple way, so different from many other instructors, especially at the undergraduate level. That is, not only the ability to get students to see the practical application of mathematical concepts, but to motivate them to do interesting work. I took my differential equations with another teacher, using the De Prima textbook, (a classic) long before Dr. Ricardo published his work. Nevertheless, I just purchased his book, it is part of my library and will remain there as a source of teaching ideas. Reading his work was like if I was still seating at his calculus class.

Also recommended: De Prima: 'Differential Equations and Boundary Value Problems' Powers: 'Boundary Value Problems' Tromba: 'Vector Calculus' Arfken: 'Mathematical Methods For Physicists'

This is primarily a response to the startling denunciation in one of the other reviews.

In the last analysis, it isn't hard to learn the particular tricks you need to solve everybody's favorite exam questions--Tennenbaum or the Schaum Series books (Lipschutz? Spiegel?) will help you do that. Many students should go that route, particularly those who have a firm commitment to being able to perform at a minimal level, without being distracted by concepts at all. (This is humor; I do not subscribe to this theory personally. It is sad that I feel obliged to point this out...)

Slope fields are a MAJOR tool to understand what is going on in a differential equation. The fact that software is now easily able to produce slope fields is a FABULOUS advantage to living in these times. Another tool is phase space; I shudder to think what the reviewer would think of that! A semester of classical mechanics should cure people who do not understand the value of phase space.

Unfortunately, most instructors --including myself-- continue to feel obliged to set examinations in which slope fields do not figure largely. A test containing lots of graphics is beyond the scope of what most instructors are willing to do. (I think I've just persuaded myself to try it!) As a result, the typical student is more concerned with the algebraic aspects of the subject (which are admittedly fascinating), rather than the conceptual aspects of the subject. This probably includes the vast number of low-level engineers who do not aspire to use more than 6.7 differential equations in their entire lives, and so do not need to get involved in the concepts too heavily.

At the more advanced level, I suspect that engineers do certainly need to engage in the more subtle and sophisticated aspects of differential equations, dynamical systems and control systems. Unfortunately, they probably do not know what they will encounter as adults while in their sophomore years! Trust me: ODEs are a lot more than algebra.

Ricardo's book is what I intend to adopt. I hope my students will not review the book until the end of the semester!

Arch

I took ODE class 15 years ago and never had to use it in practice. Now, due to a nature of work I have to go back and refresh my knowledge. This is excellent book for student or anyone who wants to understand how to solve and apply differential equations in real life.
My old professor used dry, formal approach to just manipulate equations and never really taught real life use cases.
Unlike most of textbooks I've seen, this book is self contained, no question is left unanswered. I mean really no question.
If topic is not covered in the main text, author provides all the necessary information in appendix, you will even find introduction to vector algebra and complex numbers. You will never see vague explanation or do it yourself calculation for any formula derivation that is not trivial.
Excellent work. I wish I had a chance to use this textbook long time ago when I took my ODE class.

I found this book to be of limited usefulness primarily because it falls into the same trap that seemingly all math textbooks in the US have; over dependance on technology. Over and over again the author tells you to use the mathematic software package of your choice to explore slope fields of some equation. I really don't care about the slope field, maybe I will after I understand how to find particular solutions to nonhomogenous equations (which was not explained well at all imho). Overall, the text doesn't spend alot of time explaining things, and when it does it's not very enlightening. I found the problem sets lacking and the solutions manual wasn't much help. A much better book is the Dover Ordinary Differential Eqn book by Tannenbaum. First published in 1964 (iirc) it's a far superior book.