Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.
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180 of 184 people found the following review helpful:
5.0 out of 5 stars
Very impressive...,
By Gaurav Thakur (Rockville, MD United States) - See all my reviews
This review is from: Ordinary Differential Equations (Dover Books on Mathematics) (Paperback)
After going through this book and finishing a few weeks ago, and looking at some other comparable titles, I have to come to the conclusion that this is quite possibly overall the best introductory text on ODEs out there.The book consists of six major subtopics: first-order equations, general nth-order linear equations, systems and nonlinear equations, series solution methods, numerical solution methods and existence/uniqueness theorems. Most of the subjects tend to be divided into two or three chapters, with the first one or two containing the theoretical aspect and computational techniques and the other consisting of applications to real world problems. At some 800-odd pages the book is quite long, but the sheer amount of material covered is simply astounding; the book has several types of special ODEs and solution methods that I have not seen anywhere else, and the authors go to great lengths to make every concept fully clear to the reader while still being quite rigorous. I am personally somewhat pure-math oriented but also needed some practice with applied problems, and this text is sure to please both students of mathematics as well as those of the sciences due to the very large amounts of subject material contained in both areas. (the book is split about 55-45 in theory/application) One very nice thing is that if there is some doubt as to whether or not the reader is comfortable with something from another subject (i.e. real analysis), the book does not assume that the reader is familiar wih that topic, but rather it goes through a short review of the topic that is self-contained enough for readers who have not heard of the topic before to get a good idea of it. There are a variety of well-designed problems that provide plenty of practice along with some that expand upon the original concepts, and the average difficulty generally seems about right for the target audience. The numerical methods are also surprisingly robust considering that the book was written in 1963 and calculators/computers were not all that standard. Also, as was remarked earlier, this is one of the very few texts out there that contains the answers to all of the exercises, making it perfect for the self-study that I used it for; other authors/publishers should learn from this. All things considered, this ranks among the best textbooks on any subject that I have ever seen, and coupled with the extremely low price, it definitely lies in the "must buy" category.
68 of 69 people found the following review helpful:
5.0 out of 5 stars
Wow -- Perfect ODE book for an undergrad,
By David Diez (Boston, MA) - See all my reviews
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This review is from: Ordinary Differential Equations (Dover Books on Mathematics) (Paperback)
For math background, all that is needed for this book is a first semester in calculus. If you are looking for a book to learn ordinary differential equations (ODEs) from or for a second book for a class, buy this one. The book (which covers methods of solving/applying ordinary differential equations) are explained in just the right amount of detail--it isn't a novel, but it isn't something you should get too bogged down in. Also, there are LOTS of examples, which are all very helpful! The problem sets were put together very well--there are lots of problems and they start out easy and get harder. Also, one of the best things about this book is that it has most of the answers to problems! This makes this book more than sufficient for self-study. This is my favorite Dover Publications book!
53 of 54 people found the following review helpful:
5.0 out of 5 stars
Holy Scripture,
By
This review is from: Ordinary Differential Equations (Dover Books on Mathematics) (Paperback)
Morris Tenenbaum and Harry Pollard's 1963 first-rate introduction to _Ordinary Differential Equations_ remains the superlative text on the market.
Compendious and catholic, the book contains 65 lessons organized into 12 chapters. The student learns method after method after method with comfort and ease. A typical lesson succinctly begins with explicatory material followed with completed examples. Each lesson ends with a problem set, and to the salvation of humanity, almost all of the answers are provided, making this book great for self-study, reference, and/or supplementation. A satisfactory calculus background should be the student's only necessary qualification; the involved calculus often demands more perspiration than the differential equations themselves. Those who repent shall receive redemption! Included applications, while eating considerable space, can be found compartmentalized in separate chapters. For instance, chapter 3 contains applications involving 1st order differential equations, including topics like interest, dilution and accretion, decomposition and growth, temperature, pursuit curves, the flow of water, rotation of a liquid in a cylinder, et cetera. Chapter 6 does the same thing with second order differential equations, dealing with undamped and damped motion, electric circuits, planetary motion, suspension cables, y'get the idea. Summarizing the more strictly mathematical content also presents itself as an impossible task. The book develops ideas concerning 1st order differential equations, second order differential equations, operators, Laplace transforms, the gamma function, the Bessel equation, the Legendre equation, the Laguerre equation, Wronskians, Picard's Method, series and numerical methods, perturbation method, all topped off at the end with existence and uniqueness theorems. And I've only scratched the surface! While the scope of the content of the book might initially intimidate, the presentation and development of the ideas consistently will be found faithfully friendly. If one wants an enduring and everlasting introduction to differential equations, one has a sacred calling to purchase this +800-page bible. Amen.
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