Handbook of Exact Solutions for Ordinary Differential Equations [Hardcover]

Andrei D. Polyanin (Author), V. F. Zaitsev (Author)

Book Description

Publication Date: July 9, 1995 | ISBN-10: 0849394384 | ISBN-13: 978-0849394386 | Edition: 1

Exact solutions have always played and still play an important role in properly understanding the qualitative features of many phenomena. The Handbook of Exact Solutions for Ordinary Differential Equations contains a collection of more than 5,000 ordinary differential equations and their solutions. Coverage focuses on two types of equations: those that are of interest to researchers but are difficult to integrate (Abel equations, Emden-Fowler equations, Painlevé equations, etc.), and equations relevant to applications in heat and mass transfer, nonlinear mechanics, hydrodynamics, nonlinear oscillations, combustion, chemical engineering, and other related fields. The authors also pay special attention to equations containing arbitrary functions, and devote other sections to equations contain one or more arbitrary parameters that the reader can fix at will.

Product Details

• Hardcover: 720 pages
• Publisher: CRC-Press; 1 edition (July 9, 1995)
• Language: English
• ISBN-10: 0849394384
• ISBN-13: 978-0849394386
• Product Dimensions: 10.2 x 7.1 x 1.8 inches
• Shipping Weight: 3.2 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #4,817,116 in Books (See Top 100 in Books)

Customer Reviews

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24 of 25 people found the following review helpful:

5.0 out of 5 stars Analytic solutions are still preferable, January 23, 2004

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W Boudville (Terra, Sol 3) - See all my reviews
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This review is from: Handbook of Exact Solutions for Ordinary Differential Equations (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.