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Differential Equations Problem Solver, by Editors of REA, David Arterburn
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REA’s Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems.
The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.
The Differential Equations Problem Solver is the perfect resource for any class, any exam, and any problem.
- Sales Rank: #744786 in eBooks
- Published on: 2012-06-14
- Released on: 2012-06-14
- Format: Kindle eBook
About the Author
James Ogden is the chair of the Department of Marketing at Kutztown University in Kutztown, Pennsylvania. He has formerly taught at Cedar Creek College, Central Michigan University, and the University of Northern Colorado, among others. Dr. Ogden received his Ph.D. in College Student Personnel Administration from the University of Northern Colorado, and his M.S. in Marketing from Colorado State University.
Excerpt. © Reprinted by permission. All rights reserved.
WHAT THIS BOOK IS FOR
Students have generally found differential equations a difficult subject to understand and learn. Despite the publication of hundreds of textbooks in this field, each one intended to provide an improvement over previous textbooks, students of differential equations continue to remain perplexed as a result of numerous subject areas that must be remembered and correlated when solving problems. Various interpretations of differential equations terms also contribute to the difficulties of mastering the subject.
In a study of differential equations, REA found the following basic reasons underlying the inherent difficulties of differential equations:
No systematic rules of analysis were ever developed to follow in a step-by-step manner to solve typically encountered problems. This results from numerous different conditions and principles involved in a problem that leads to many possible different solution methods. To prescribe a set of rules for each of the possible variations would involve an enormous number of additional steps, making this task more burdensome than solving the problem directly due to the expectation of much trial and error.
Current textbooks normally explain a given principle in a few pages written by a differential equations professional who has insight into the subject matter not shared by others. These explanations are often written in an abstract manner that causes confusion as to the principle's use and application. Explanations then are often not sufficiently detailed or extensive enough to make the reader aware of the wide range of applications and different aspects of the principle being studied. The numerous possible variations of principles and their applications are usually not discussed, and it is left to the reader to discover this while doing exercises. Accordingly, the average student is expected to rediscover that which has long been established and practiced, but not always published or adequately explained.
The examples typically following the explanation of a topic are too few in number and too simple to enable the student to obtain a thorough grasp of the involved principles. The explanations do not provide sufficient basis to solve problems that may be assigned for homework or given on examinations.
Poorly solved examples such as these can be presented in abbreviated form which leaves out much explanatory material between steps, and as a result requires the reader to figure out the missing information. This leaves the reader with an impression that the problems and even the subject are hard to learn - completely the opposite of what an example is supposed to do.
Poor examples are often worded in a confusing or obscure way. They might not state the nature of the problem or they present a solution, which appears to have no direct relation to the problem. These problems usually offer an overly general discussion - never revealing how or what is to be solved.
Many examples do not include accompanying diagrams or graphs, denying the reader the exposure necessary for drawing good diagrams and graphs. Such practice only strengthens understanding by simplifying and organizing differential equations processes.
Students can learn the subject only by doing the exercises themselves and reviewing them in class, obtaining experience in applying the principles with their different ramifications.
In doing the exercises by themselves, students find that they are required to devote considerable more time to differential equations than to other subjects, because they are uncertain with regard to the selection and application of the theorems and principles involved. It is also often necessary for students to discover those "tricks" not revealed in their texts (or review books) that make it possible to solve problems easily. Students must usually resort to methods of trial and error to discover these "tricks," therefore finding out that they may sometimes spend several hours to solve a single problem.
When reviewing the exercises in classrooms, instructors usually request students to take turns in writing solutions on the boards and explaining them to the class. Students often find it difficult to explain in a manner that holds the interest of the class, and enables the remaining students to follow the material written on the boards. The remaining students in the class are thus too occupied with copying the material off the boards to follow the professor's explanations.
This book is intended to aid students in differential equations overcome the difficulties described by supplying detailed illustrations of the solution methods that are usually not apparent to students. Solution methods are illustrated by problems that have been selected from those most often assigned for class work and given on examinations. The problems are arranged in order of complexity to enable students to learn and understand a particular topic by reviewing the problems in sequence. The problems are illustrated with detailed, step-by-step explanations, to save the students large amounts of time that is often needed to fill in the gaps that are usually found between steps of illustrations in textbooks or review/outline books.
The staff of REA considers differential equations a subject that is best learned by allowing students to view the methods of analysis and solution techniques. This learning approach is similar to that practiced in various scientific laboratories, particularly in the medical fields.
In using this book, students may review and study the illustrated problems at their own pace; students are not limited to the time such problems receive in the classroom.
When students want to look up a particular type of problem and solution, they can readily locate it in the book by referring to the index that has been extensively prepared. It is also possible to locate a particular type of problem by glancing at just the material within the boxed portions. Each problem is numbered and surrounded by a heavy black border for speedy identification.
Most helpful customer reviews
28 of 28 people found the following review helpful.
I doubt that there's a better supplemental DE book out there
By Fugazi
I used this book for an introductory differential equations course. With the help of this book, I was completely prepared for everything the professor threw at us and more.
Some of the problems are simple and should help to reinforce the basic concepts learned from another book. Learn the fundamentals from some other book (or even a professor), and refine your thought processes using this one. There are some basic explanations of concepts and problem types, but most of the space is devoted to problems and solutions, as you may have guessed. If I had trouble with a problem from another book, I could almost always find a similar one in the REA book. A few problems are extremely difficult or involved, but the book leads you through every step of every problem. I was blown away by the depth of a few problems, but following the reasoning in this book really helped me to develop a better "feel" for the subject.
Yes, the font looks like something from your mother's typewriter, but the book is very sensibly organized into a (huge) number of chapters that should more than cover any intro-level DE course. My test reviews consisted of working problems from this book and doing little else, and I've never felt more confident going into exams.
If you're willing to put in the time, this book is probably one of the best course-related resources you could ever spend your money on. It would also be a good reference for someone who occasionally wants help with troublesome problem types.
22 of 22 people found the following review helpful.
Excellent
By A Customer
This is an excellent supplement to any Differential Equations class. It starts out with easy and straight forward problems and progressively gets to the more advanced problems. All steps are worked out in an easy to understand way. Most importantly this book shows the algebraic steps in obtaining solutions, which is ussually where students have trouble. This book is a must have for any science major.
16 of 16 people found the following review helpful.
An Excellent Resource!
By A Customer
If you are studying DEs, get this book! It beats the usual text books that only contain solutions to selected problems, namely the ones that the professor does not assign or examine you on. This book is comprehensive and contains stratagies for attacking the various problems you will encounter in undergraduate DE courses. It even contains problems and solutions to Partial Differential Equations, Fourier Series and Boundary Value Problems, not just ODEs!
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