Differential Equations, Student Solutions Manual: An Introduction to Modern Methods and Applications [Paperback]

James R. Brannan (Author), William E. Boyce (Author)

Book Description

Publication Date: February 2, 2007 | ISBN-10: 0470125535 | ISBN-13: 978-0470125533 | Edition: 1

Differential Equations: An Introduction to Modern Methods and Applications is a textbook designed for a first course in differential equations commonly taken by undergraduates majoring in engineering or science. It emphasizes a systems approach to the subject and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. Section exercises throughout the text are designed to give students hands-on experience in modeling, analysis, and computer experimentation. Optional projects at the end of each chapter provide additional opportunitites for students to explore the role played by differential equations in scientific and engineering problems of a more serious nature.

Editorial Reviews

About the Author

William E. Boyce received his B.A. degree in Mathematics from Rhodes College, and his M.S. and Ph.D. degrees in Mathematics from Carnegie-Mellon University. He is a member of the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. He is currently the Edward P. Hamilton Distinguished Professor Emeritus of Science Education (Department of Mathematical Sciences) at Rensselaer. He is the author of numerous technical papers in boundary value problems and random differential equations and their applications. He is the author of several textbooks including two differential equations texts, and is the coauthor (with M.H. Holmes, J.G. Ecker, andW.L. Siegmann) of a text on using Maple to explore Calculus. He is also coauthor (with R.L. Borrelli and C.S. Coleman) of Differential Equations LaboratoryWorkbook (Wiley 1992), which received the EDUCOMBest Mathematics Curricular InnovationAward in 1993. Professor Boyce was a member of the NSF-sponsored CODEE (Consortium for Ordinary Differential Equations Experiments) that led to the widely-acclaimed ODE Architect. He has also been active in curriculum innovation and reform. Among other things, he was the initiator of the "Computers in Calculus" project at Rensselaer, partially supported by the NSF. In 1991 he received the William H.Wiley Distinguished FacultyAward given by Rensselaer. --This text refers to the Hardcover edition.

Product Details

• Paperback: 384 pages
• Publisher: Wiley; 1 edition (February 2, 2007)
• Language: English
• ISBN-10: 0470125535
• ISBN-13: 978-0470125533
• Product Dimensions: 10.7 x 8.6 x 0.8 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 2.9 out of 5 stars  See all reviews (13 customer reviews)
• Amazon Best Sellers Rank: #436,481 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

11 of 11 people found the following review helpful:

1.0 out of 5 stars As an instructor to other instructors and students alike: "RUN AWAY AS FAST AS YOU CAN!", March 31, 2011

By 

Robert D. Wooster - See all my reviews
(REAL NAME)   

This review is from: Differential Equations: An Introduction to Modern Methods and Applications (Hardcover)

This review is of the first edition (with the dam on the cover).

Short version: This book is terrible, stay away.

Less short version: I have taught a first course on differential equations out of several different books and this one is easily the worst. Differential equations is a beautiful topic, for many practical and theoretical reasons. This book does not in any way portray this spirit, and is probably scaring away talented young minds from pursuing mathematics and engineering. I can't wait to burn my (free) instructor's copy. My major issues with this book are:

1. My biggest complaint is that this book is obscenely overpriced for what you get. None of this material is new or specialized, it can all be found on the web for free. MIT has open courseware on differential equations with a far better presentation for example.

2. The book is poorly written #1: The notation used throughout the book ranges from atrocious to flat out ambiguous. For example, on p. 340 the author defines the indicator of the interval [c,d) by u_{cd}(t), where u_{a}(t) is the Heaviside function, which turns on from 0 to 1 at t=a. With this notation there is no difference in how the indicator of [2,3) and the Heaviside at t=23 are written, they both are u_{23}(t). This is a bad practice, and beginning students in mathematics and engineering should not be exposed to this practice.

3. The book is poorly written #2: Most of the sections of the book read like someone doing various problems taken from various topics for no rhyme nor reason. There is little to no discussion about building intuition of DEs or about how the topic in question fits in with the bigger picture. The sections on the "theory" are particularly bad. The Wronskian determinant is overused (even in the 2D case!) and not properly introduced, with no reason given as to why we need a fundamental set of solutions or what that even means. A good textbook first motivates new material, then highlights the important points through the use of instructive examples. Each example should have a specific purpose which shed light on the strengths and limitations of a particular theorem or technique. Furthermore this specific purpose in choosing the example should be clearly explained to the student before and after the example. The book by Blanchard, Devany, and Hall does a much better job of this overall, even though it's long-winded and "fluffy" at times (and extremely overpriced as well).

4. The book is poorly written #3: The exercises at the end of the section are dull and unimaginative, most just involve excessive calculations with no real educational value. Doing homework problems is where much of the learning process should take place, with this book it's a lesson in pain tolerance and boredom.

5. The answers to both odd and even problems are in the back. I prefer books that don't have ALL the answers, the temptation for most students is too great and this becomes a crutch.

6. Much of this book is "borrowed" from Boyce and DiPrima's "Elementary Differential Equations and Boundary Value Problems", which is a better book (but still overpriced, see the pattern?). In fact it is pretty easily to tell which sections come from that book because those are the sections that are somewhat readable.

7. There are errors that I hope are just misprints. For example, in Example 1 of section 6.3 on p. 414 the authors compute the vectors in the eigenspace for a repeated eigenvalue. In particular the eigenspace is written as an arbitrary linear combination of two basis vectors. They then go on to form two new vectors by choosing two particular linear combinations of the basis vectors (no reason given as to why those particular linear combinations were chosen) and say they are doing it to get a pair of linearly independent eigenvectors. The basis vectors they had WERE already linearly independent. My guess is that they wanted two orthogonal vectors. Why they would want to do this in the first place, I have no idea. There is no reason given. And again it is just a guess because there is no motivation given for anything done in this book.

The only good thing I can say about the book is that it includes some of the topics that engineering students will see in future courses that other introductory books do not. However this offers no advantage because the topics are poorly covered. A better alternative is Kreyszig's "Advanced Engineering Mathematics", but be sure to buy a used less expensive copy.

In conclusion, do not choose this book (if you have a choice). If you are a student shackled by the chains of bloodthirsty publishers, like Wiley in this case, my heart goes out to you. Speak up and do not tolerate this nonsense! There are good alternatives including (but of course not restricted to) some of the yellow Springer books, MIT opencourseware, even one of the other overpriced Intro to DE books (I like Blanchard, Devany, and Hall better than most for having clearer mathematics, and great examples and problems, Boyce and DiPrima is also better). As you can tell from this review I won't be nominating this book for any "Textbook of the Year" awards, and although this review is very harsh I hope you find it substantive. I also hope this review is helpful to you and saves you some frustration and $$$.

8 of 8 people found the following review helpful:

1.0 out of 5 stars Horrible Book, March 22, 2009

By 

Michael B. Stone (Atlanta, GA) - See all my reviews
(REAL NAME)   

This review is from: Differential Equations: An Introduction to Modern Methods and Applications (Hardcover)

Never before have I encountered a [Math] book with as many words as the one that I am currently writing a review for. Rather than show the reader visually of why things are, the authors have taken it upon themselves to take the approach of explaining via verbose text why things are. While some may find this a better approach, the fact that there exists very little examples proves this method futile and frustrating. The ONLY thing salvageable from this book is the inclusion of the answers in the back of the book. Even then, if one wants to truly learn differential equations, another book should be sought.

11 of 12 people found the following review helpful:

1.0 out of 5 stars Terrible Book, September 6, 2008

By 

Bill - See all my reviews

This review is from: Differential Equations: An Introduction to Modern Methods and Applications (Hardcover)

This book is poorly written, overly verbose, and poorly structured. After having consulted some other references, having figured out how to do the problems, and having completed the assigned problems, I am still unable to make ANY sense at all out of the book's explanations. Another specific criticism: In just about every section, the author introduces some new method or theorem in the problems, leaving the exercise to the reader. These introductions are very incomplete, and leave students groping in the dark. Then there are additional problems, "Using the method of problem x, solve..." Quite frustrating. Seriously, textbook publishers give free books to instructors... Do they look at them before making a selection? And for the price of this book, I expect to be able to learn differential equations just by putting the book under my pillow at night.