Customer Reviews

Differential Equations Demystified

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

 

 

Differential Equations Demystified is written by Steven Krantz, the author of the not-so-popular Calculus Demystified. Admittedly, this book is not any more user friendly than Calculus demystified; he spends no time explaining jargon in informal language; he constantly uses different notation for derivatives, etc. But at this level, at least, it is more acceptable. Any reader tackling the subject of differential equations with any seriousness will have to face rigors of mathematical language at some point.

Surprisingly Krantz claims in his introduction that anyone who has finished Caculus Demystified will be prepared for this book. Unfortunately by page fifteen he is using concepts from multivariable calculus (partial derivatives) that, if I'm not mistaken, were not covered in Calculus Demystified. Unless you are confident in your mathematical skills I would recommend brushing up your multivariable calculus before tackling this text.

For the most part, however, the book proceeds in typical fashion. The reader will be introduced to most of the key topics covered in a typical college Diff Eq class including first and second order differential equations, series solutions, and other basic topics. If you're just looking to get the "flavor" of Diff. Eqs then this book will suffice. However, do not expect to come away from this book with a deep knowledge of the subject matter. He concisely covers most of the basic procedures for solving and manipulating standard ordinary differential equations, and doesn't bog the reader down in much theory. Answers are provided in the back of the book for most of the problems in each chapter.

However, for readers who want a more thorough introductory look at applied differential equations I know of no better introduction than Tenenbaum's Ordinary Differential Equations. Tenenbaum does an excellent job of introducing the theory behind the equations and covers many of the fine details that Krantz leaves out. Another strength of Tenenbaum is his resistance to undue formalism. He takes the time to flesh out the motivation behind each topic with historical asides and physical applications. Krantz does not do this. Seeing as both books are selling for the roughly the same price [...] I see little justification in recommending this work over Tenenbaum's. The only circumstance under which I would recommend Krantz is to the reader who needs a concise and breezy introduction to the methods of Differential Equations. For deeper understanding consult Tenenbaum. And if you are looking for a source for solved practice problems I would direct you to Differential Equations Prolem Solver which has thousands of solved problems.

Overall, a solid, concise effort. But when compared to other books in its league like "Calculus for Dummies" and "How to Ace Calculus" it falls a bit short.

PS: For a great informal brush up on Multivariable caclus I recommend "How to Ace the rest of Caculus".

I teach this subject. The book is perfect for a first course whose purpose is to introduce foundational topics from both ordinary and partial differential equations. Not a lot of theory, but I find that the theory undergirding a technique is a lot more palatable when the student has confidence in his ability to use that technique in practice. DE Demystified gets right to the point, presents the method, and then gives examples and practice problems. I learn math by doing it and this book is just what I was looking for. Several other books are available in the classroom for students who choose to go more in depth on any particular topic, and I use other resources for additional problems and to code programs for numerical solutions. But this is the book the students must buy and bring to class. I really like the presentation in DE Demystified.

I bought this book because I am considering getting a graduate degree in math, so I thought it would be useful as a book to brush up with. This book is highly readable and the examples are laid out well. There are ample exercises to test your knowledge of the various techniques for solving diff eqs, answers are included also. It is quite a bit better than the text that was used in engineering school.

I read some of the other reviews before writing this, and -- with all due respect, etc. etc. -- I think some of the other reviewers are missing the point of the entire series (Demystified) books.

The book is intended as a short, pithy, introduction to the topic. It makes no pretense of providing in-depth coverage, either of theory, or of all possible topics. This series of books is intended to provide a survey of many, but not all, commonly used techniques in a field; and it is intended to provide relatively simple examples and exercises so that the self-teaching student can get his/her feet wet.

I've just finished two chapters (and skimmed the rest), and so far I'm very pleased with the level of the treatment. You do need some prior calculus background, but if you have that, the book should be easy to follow. My own background was undergraduate physics, and, years later, I've decided to brush up. The book provides excellent review, as well as introducing me to topics I never quite "got" back in college.

If you want in-depth theory, or more comprehensive coverage of various techniques, or more advanced and challenging examples/home work problems, *or* conditions for solubility, go buy a standard, $100 college textbook on DiffEQs. However, if you want an accessible, inexpensive, brief but not overly-brief treatment of the fundamental techniques of solving differential equations, this book is very good. (By the way, the book includes the basics for at least some partial differential equations, as well as ordinary differential equations.)

Is it perfect? No. There is one subsection, for example, on using DiffEQs to make the connection between Newton's laws and Kepler's laws, and that particular subsection is not entirely clear. But I can forgive an occasional rough spot in a book that is overall clearly written, and well-designed for the self-study student.

I gave this book such a low rating because it falls way short of the expectations of its intended audience. This book is terrible choice for someone who knows nothing about differential equations and wants to teach themself. The examples and explanations and derivations are difficult to follow and not really any different from what you would find in a typical college textbook. I was hoping to find a book that explained differential equations in plain, simple English and avoided using jargon and confusing symbols. I was disappointed. The author also skips a lot of steps in the examples. The answers in the back of the book are not very well explained. The book is full of problems titled "Now you try" but the answers are not given. How am I supposed to know if I did it right? I feel that the author's mathematical formalism and usage of symbols was out of place. I see nothing wrong with explaining things using language like "now you take this thing here, and derive it, then multiply by this other over here... etc". If you can follow the author, you probably don't need this book in the first place. This book is no more user friendly than a typical 800 page textbook, just shorter and soft cover.

This book is a good preliminary intro into ODE's. It does not cover a majority of the higher order solution systems covered in a basic engineering diffy Q class, so beware if that is what youre looking for.

Except for the interesting treatment of Kepler's equations in chapter 2, there is not much to reccommend this version over others. This is a greatly stripped-down rehash of the standard fare: problems, exams and all. I was greatly underwhelmed. Demystification requires at the very least minimal discussions of some of the applications and the nature and utility of differential equations to other areas of mathematics. I found none of that here and thus expected a lot more. Instead of Demystification, it should just be called a "rehashed summary of differential equations."

Avoid this book if you are a math student and need a more rigorous approach that deals with the Lipschitz condition etc. This book doesn't cover the necessary conditions under which one can find a solution, Picard's iteration, or the method of Frobenius, all of which are needed in most math-major type of ODE classes.

If you need a quick reference, Schaum's provides more bang for your buck.