Customer Reviews

Differential Equations with Boundary-Value Problems

5 star:		(9)
4 star:		(6)
3 star:		(1)
2 star:		(7)
1 star:		(10)

 

 

This is a book from the old school of ODE's. The absolute focus of this book is analytical methods and beats the algebra and integration drum to the exclusion of anything else. If you want to learn how ODE's were solved 25 years ago then this book is for you. If you are looking for a book that deals with more modern theory, or handles modeling in a constructive manner then this book is NOT a good choice.

I am a graduate student in mathematics so I've been through my share of textbooks. To this day, I have not found one quite as inconsistent as this one. Some sections are flawless; the author is elegant in his explanation, the examples are clear and relevant, and the problems serve their purpose. However, the poorly written sections (and trust me, there are plenty of them) far outweigh what little beauty lies in this textbook. Anyone who wishes to meticulously plow through this book will know what I'm talking about. The most depressing thing about it all is that I can't seem to find a book (on DE's) that's any better! So to you mathematicians out there: write a decent book on Differential Equations; you might become a millionaire. However, as mentioned earlier, this book will weigh down anything, even in the strong winds of Lubbock.

I bought this book to show me how they got the answers to some of the problems in the text book. I was very dissappointed when I recieved it to find that all it did was basically give only some answers and a few clues as to how they got them. Does not help you at all.

Zill and Cullen's book is disappointing for quite a few reasons:

First, the book is written in such a way as to include too little details on a large number of topics. The book contains 15 chapters. The last 5 deal with partial differential equations, and are more than likely not covered in most classes in which this book is intended to be used for. These chapters aren't even covered in elite ODE classes (such as the one offered at MIT). However, these 5 chapters do not contain enough information on partial differential equations that this book can be used for a separate class on PDEs. Therefore, the last 5 chapters just add to the cost of an already expensive book... (Its retail price is 11 times the retail price of Dover's classic ODE book!)

The aspect of this book which angers me the most is as follows: the "proofs" are, for the most part, plug-and-chug! The authors sometimes assume that a complicated formula for solving differential equations works, and then "prove" it by plugging it into the differential equation. Although this is a legitimate way to prove a formula, there are two things wrong with it: First, there are more intelligible ways to prove a certain formula than to calculate third derivatives, collect terms, use trigonometric identities, and show that the resulting equation is an identity. Second, the reader has NO idea where the formula came from! All the reader is left with is the knowledge that the formula works. However, without the knowledge of a formula's origin, it is very easily forgettable!

A classic example of this is in chapter 5.1, where the authors claim that the equation: y = Acos(wt) + Bsin(wt) can be written as Ccos(wt + D). To "prove" this, the authors start with the equation that is trying to be proved (the right hand side), and use trigonometric identities to show that it equals the left hand side... In my opinion, this makes no sense at all... When solving differential equations, all methods will yield the left hand side of that equation. Although the authors have shown that the formula works, it still requires that the reader memorize 3 formulas which are still of some mystical origin! I'm aware of two very natural methods which will convert the left hand side into the right hand side. This book contains neither of them.

In addition, the authors (for some reason) shy away from the use of complex numbers. Instead of showing, in an organized fashion, that complex numbers dramatically aid solving differential equations, they mention Euler's formula a few times, and create "cases" for the reader to memorize in case he/she ever runs into a complex number... Differential equations is not an introductory course in mathematics, and readers of this book are assumed to be able to think mathematically. A one-dimensional memorization approach of differential equations is pretty useless...

If possible, stay away.

The student solutions manual only gives very vague hints at solving a few problems and almost never the most important problem of a set, the first problem. I spent an unbelievable amount of time trying to figure out how to rewrite the problem in the form that was shown in the solutions manual. DO NOT WASTE YOUR MONEY.

I used this book for an "online course" where we never met the instructor. Fortunately the book makes it easy to learn the material without having an expert by your side to guide you.

This book's example problems are impossible to follow. They skip way to many steps, making learning from the text near-impossible. If using text, pay attention to prof. in class, as you won't learn anything from book, except confusion.

How about showing some examples that are relevant to the homework at the end of each chapter? This book is making my life hell, because it expects WAY too much of the student. If you want a book with paragraph after paragraph of written text trying to explain math instead of clear examples citing the steps to take to solve a particular problem, this book is for you! If you enjoy pulling out your hair in frustration, order the solutions manual too! The solution manual is CRAP. You would expect for it to show, step-by-step solutions, but it's just as vague as the rest of the book itself. The people that wrote this book did not have the student in mind while writing it. I had to purchase another book to understand differential equations and use this one ONLY because my professor assigns homework from it; otherwise, I would never open this book. I plan on burning this book, as I do not feel comfortable selling it to another human being. By the way, the other book I use and completely recommend is: Ordinary Differential Equations by Tenenbaum. Avoid this book to learn from if you can. If you cannot avoid this book, buy another book on the subject and do not waste your money on the "solutions manual".

I ordered what I thought was the paperback version of the textbook, and what arrived was the student resource manual. If that is what you're after, great, but don't think that the paper back version is the textbook, it's not.

Though some of the reviews mention the examples in the book are hard to follow, I found the examples made learning DE really simple if your classes/profs follow the book closely. Perhaps it is just personal learning/study styles, but since I fall asleep in class often, I rely heavily on the examples in the book and learn by myself a few days before the exams.

I can't disagree that the book does skip steps in the example from time to time (but maybe it is because those are considered trivial calculus knowledge? and DE is normally taken after finishing calculus). One thing I really like about the book is that once it gives a concept/theorem it is followed by an example that demonstrates how to solve a problem of that type.

As for the problems given at the end of section, I never really sat down and went over each problem, so I am not too familiar in reviewing how the problems are. For the problems I did go over, they are fairly straight forward.