- Hardcover: 816 pages
- Publisher: Chapman and Hall/CRC; 2 edition (28 Oct 2002)
- Language English
- ISBN-10: 1584882972
- ISBN-13: 978-1584882978
- Product Dimensions: 25.6 x 18 x 5 cm
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Amazon Bestsellers Rank:
1,549,499 in Books (See Top 100 in Books)
- #50 in Books > Science & Nature > Mathematics > Numerical Analysis
- See Complete Table of Contents
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Review
I have been reading the Polyanin books Handbook of Linear Partial Differential Equations for Engineers and Scientists and Handbook of Exact Solutions for Ordinary Differential Equations. I think these books are extraordinary, and are destined to become classics CRC Press has provided an invaluable service to science and engineering by publishing these books.
Product Description
Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handbook now contains the exact solutions to more than 6200 ordinary differential equations. The authors have made significant enhancements to this edition, including:
An introductory chapter that describes exact, asymptotic, and approximate analytical methods for solving ordinary differential equations
The addition of solutions to more than 1200 nonlinear equations
An improved format that allows for an expanded table of contents that makes locating equations of interest more quickly and easily
Expansion of the supplement on special functions
This handbook's focus on equations encountered in applications and on equations that appear simple but prove particularly difficult to integrate make it an indispensable addition to the arsenals of mathematicians, scientists, and engineers alike.
This handbook's focus on equations encountered in applications and on equations that appear simple but prove particularly difficult to integrate make it an indispensable addition to the arsenals of mathematicians, scientists, and engineers alike.
Inside This Book
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First Sentence
Particular solutions: y = Ak, where Ak are roots of the algebraic (transcendental) equation f(Ak) = 0. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Particular solutions: y = Ak, where Ak are roots of the algebraic (transcendental) equation f(Ak) = 0. Read the first page
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Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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24 of 25 people found the following review helpful
Analytic solutions are still preferable
23 Jan 2004
Format:Hardcover
An amazing tome. 6200 ordinary differential equations that are exactly solvable. Typically, when you study ODEs, your text will describe a standard pedagogical set, like systems of DEs with constant coefficients, etc. Look at Boyce and diPrima's "Elementary Differential Equations" as a good example of this.
But just as people have compiled tables of numerical values of useful functions, like Abramowitz and Stegun's "Handbook of Mathematical Functions", did anyone do likewise for ODEs? Well, Polyanin et al have done so.
These days, many who face solving an ODE might resort to doing so numerically, since computers and software packages have become so powerful. But analytic solutions are still always preferable, assuming that they exist and you can find them. The reasons are threefold. Firstly, they are more compact to encode than tables, from a computational viewpoint. Secondly, it is often easier to search for understanding in a known functional form than in a table. Thirdly, if you have a solution in the form of a function, and that function is differentiable or integrable, then you may be able to gain more insight, or apply the answer to broader usage, by doing so.
Thus analytic solutions are desirable. The problem is in finding them. That is where this book has value. It encapsulates a lot of specialised ODE solving techniques, applied to reams of equations.
As an aside, the book also shows a qualitative difference between Russia and the US. The Soviets always lagged behind the US in computing. So by necessity, Soviet scientists emphasised more the traditional pencil and paper approach to solving equations. Whereas Americans were more likely to toss it over to a nearby computer. This has lead in the US to the deprecating of courses and texts in differential equation solving. Hence if you are an American researcher facing an ODE with no obvious solution, it may be quite difficult for you, ab initio, to find a solution. So check this book first for answers.
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