Differential Equations With Boundary-Value Problems Fourth Eddition By Dennis G. Zill, Michael R. Cullen - Publisher: Thomson Brooks/Cole
- Number Of Pages: 768
- Publication Date: 1996-06-30
- ISBN-10 / ASIN: 0534955800
- ISBN-13 / EAN: 9780534955809
Product Description: This Fourth Edition of the expanded version of Zill's best-selling A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING
APPLICATIONS places an even greater emphasis on modeling and the use of technology in
problem solving and now features more everyday applications. Both Zill texts are identical through the first nine chapters, but this version includes six additional chapters that provide in-depth coverage of boundary-value problem-solving and
partial differential equations, subjects just introduced in the shorter text. Previous editions of these two texts have enjoyed such great success in part because the authors pique students' interest with special features and
in-text aids. Pre-publication reviewers also praise the authors' accessible writing style and the text's
organization, which makes it easy to teach from and easy for students to understand and use. Understandable, step-by-step solutions are provided for every example. And this edition makes an even greater effort to show students how the mathematical concepts have relevant, everyday applications.
Among the boundary-value related topics covered in this expanded text are: plane autonomous systems and stability; orthogonal functions;
Fourier series; the Laplace transform; and elliptic, parabolic, and hyperparabolic partial differential equations, and their applications.
Summary: Not a bad book
Rating: 4 I bought the book for my differential equations class. It seems that I bought an earlier edition since one of the chapters is missing. That's my fault not the seller's though.
Summary: Good instruction on differential equations
Rating: 5 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.
Summary: If you absolutely must have this book
Rating: 2 This text is unnecessarily difficult to follow. There are
paperbacks which have far better explanations, footnotes, and lay better groundwork. One such is Morris Tenenbaum and Harry Pollard's Ordinary Differential Equations (which incidentally costs $25 brand new, not $180.) But I'll bet your teacher wanted you to suffer as much as he/she did, and so in selecting a text, it was important that it be written by misanthropes. Do not bother getting the solutions manual from your bookstore. It omits all the problems you'll have trouble with. Get a supplementary text, one that really demonstrates the problems and their solutions. Tenenbaum's is the best I've found, and there is also "DE for Dummies" by IDG, which is a quick-and-dirty for methods that your teacher doesn't want to spend much time on.
Summary: Very disappointing.
Rating: 2 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.
Summary: diffcult text for the DE student
Rating: 2
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