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This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; it does not concentrate on traditional manual methods but rather on new computer-based methods that lead to a wider range of more realistic applications. The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the book. For mathematicians and those in the field of computer science.
- Sales Rank: #867975 in Books
- Brand: Brand: Prentice Hall
- Published on: 2003-06-28
- Original language: English
- Number of items: 1
- Dimensions: 10.26" h x 1.40" w x 8.20" l,
- Binding: Hardcover
- 727 pages
Features
- Used Book in Good Condition
From the Publisher
Reflecting the shift in emphasis from traditional methods to new computer-based methods, this text -- in classic Edwards and Penney style -- focuses on the mathematical modeling of real-world phenomena as the goal and constant motivation for the study of differential equations. It offers a fresh computational flavor in figures, examples, problems, and projects throughout, and features a broad range of real-world applications. The book also covers topics not found in other similar texts.
From the Back Cover
This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; it does not concentrate on traditional manual methods but rather on new computer-based methods that lead to a wider range of more realistic applications. The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the book. For mathematicians and those in the field of computer science.
About the Author
C. Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and recently retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow. He has received numerous teaching awards, including the University of Georgia's honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution's highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence. His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics. In addition to being author or co-author of calculus, advanced calculus, linear algebra, and differential equations textbooks, he is well-known to calculus instructors as author of The Historical Development of the Calculus (Springer-Verlag, 1979). During the 1990s he served as a principal investigator on three NSF-supported projects: (1) A school mathematics project including Maple for beginning algebra students, (2) A Calculus-with-Mathematica program, and (3) A MATLAB-based computer lab project for numerical analysis and differential equations students. David E. Penney, University of Georgia, completed his Ph.D. at Tulane University in 1965 (under the direction of Prof. L. Bruce Treybig) while teaching at the University of New Orleans. Earlier he had worked in experimental biophysics at Tulane University and the Veteran's Administration Hospital in New Orleans under the direction of Robert Dixon McAfee, where Dr. McAfee's research team's primary focus was on the active transport of sodium ions by biological membranes. Penney's primary contribution here was the development of a mathematical model (using simultaneous ordinary differential equations) for the metabolic phenomena regulating such transport, with potential future applications in kidney physiology, management of hypertension, and treatment of congestive heart failure. He also designed and constructed servomechanisms for the accurate monitoring of ion transport, a phenomenon involving the measurement of potentials in microvolts at impedances of millions of megohms. Penney began teaching calculus at Tulane in 1957 and taught that course almost every term with enthusiasm and distinction until his retirement at the end of the last millennium. During his tenure at the University of Georgia he received numerous University-wide teaching awards as well as directing several doctoral dissertations and seven undergraduate research projects. He is the author of research papers in number theory and topology and is the author or co-author of textbooks on calculus, computer programming, differential equations, linear algebra, and liberal arts mathematics.
Most helpful customer reviews
4 of 4 people found the following review helpful.
Average, Could use more worked examples
By A Customer
Luckily I had a very good professor for this class, so I didn't need to depend on the text as much as I might have to in other classes. As an engineering student, I don't ignore theory, but I do need a few more worked examples for the text to be really useful for me. Don't get me wrong, I appreciate rigor and I do like mathematics for its own sake, but, I could have used a little more emphasis on applications than this text provided.
8 of 8 people found the following review helpful.
A good differential equations textbook
By A Customer
I think the strength of this textbook is the amount of material it encompasses: this book is used in two separate courses in my school--introduction to DE and engineering analysis. I didn't appreciate the textbook so much until I completed my differential equations course and then looked back at the sections on mechanical vibrations to review for my physics course. I then realized that the explanations and derivations were extremely satisfying, much more than your average introductory physics text. Also, the emphasis on the qualitative aspects of DEs, such as slope fields and phase portraits, aid in the coneptual understanding of the otherwise rigorous computation aspects of the topic. My only complaint is that the proofs could've been done in a more understandable manner.
19 of 20 people found the following review helpful.
Just Plain Not Good
By Undergrad
This book has several problems.
1. There are numerous typos in the text as well as in the solutions printed in the back of the book (and in the solutions manual). It can be very frustrating to puzzle over a problem for a long time only to find you were right and the book was wrong.
2. Several important techniques are only explained as short paragraphs in the exercise section (ie Euler Equation substitution, Reduction of Order, and others). You are left to try and figure out how to apply the vague instructions by looking at the solutions manual or asking someone else. I found this to be the biggest problem with the book.
3. The end of each example or concept is marked by a small red box in the margin of the page. These boxes are easy to miss so the distinction between example and theory, as well as between different aspects of the theory will become blurred unless you pay close attention to when the red boxes appear. Consequently results derived from theory and results derived from specific examples tend to blend together.
4. Often the authors add length to problems by providing the given values in non-SI units and the constants of nature in SI units. While this isn't a serious problem with the book, it would make the book needlessly annoying if you were using it for self study.
For the class that required this book I ended up checking out a different textbook on differential equations from the library to learn from. I only used this one for the questions we were assigned. If you have any choice in the matter I would recommend getting a different book.
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