Special Functions & Their Applications (Dover Books on Mathematics) [Paperback]

N. N. Lebedev (Author), Mathematics (Author), Richard R. Silverman (Translator)

Book Description

Series: Dover Books on Mathematics | Publication Date: June 1, 1972

Famous Russian work covers basic theory of the more important special functions and their application to specific problems of physics and engineering. Most space devoted to the application of cylinder functions and spherical harmonics. Also explores gamma function, probability integral and related functions, Airy functions, hyper-geometric functions, more. Translated by Richard Silverman.

Editorial Reviews

Language Notes

Text: English, Russian (translation)

Product Details

• Paperback: 336 pages
• Publisher: Dover Publications; Revised edition (June 1, 1972)
• Language: English
• ISBN-10: 0486606244
• ISBN-13: 978-0486606248
• Product Dimensions: 8.5 x 5.4 x 0.6 inches
• Shipping Weight: 12 ounces (View shipping rates and policies)
• Average Customer Review: 4.8 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #340,200 in Books (See Top 100 in Books)
  • #47 in Books > Education & Reference > Foreign Language Nonfiction > Russian

Customer Reviews

Most Helpful Customer Reviews

44 of 44 people found the following review helpful:

5.0 out of 5 stars Excellent Source of Applications for Special Functions, June 2, 2000

By 

Raymond Woo - See all my reviews

This review is from: Special Functions & Their Applications (Dover Books on Mathematics) (Paperback)

This is a book which I cannot say much about except for the unusual thoroughness, accompanied by detail and depth in treatment of the underlying mathematical properties and applications of Special Functions.

Lebedev is the quintessential mathematical expert in applying Special Functions to problems in Physics and Engineering, being that he can illustrate all important concepts clearly and umambiguously with carefully prepared diagrams as well as words. I was able to cite the solution of the a problem involving a propagating electromagnetic wave along a transmission line for an important Engineering course project. For such a problem, Lebedev offers a far more detailed and precise solution with given Special Functions than anything I have ever seen in other books of the same nature with the possible exception of a specialized treatise by an MIT EE faculty member on applied electromagnetism. He also comes across as meticulous in derivations of solutions to problems worked out compared to many other authors whose works I have read. This is because he hardly ever skips an important step in deriving a solution for any given problem by leaving it out for the reader's imagination. Yet we know Lebedev as perhaps a mathematician who may not be realistically expected to come up with such complete and exhaustive solutions to practical or real-world problems, worked out with clarity as well as precision and depth. There are numerous other examples which he worked out for different applications (e.g, Legendre's and Laguerre's functions) invariably after he took pains to delineate the various mathematical properties of the Special Functions utilized to obtain the closed-form solutions. He also covers various mathematical functions which may not be as familiar to many engineering practitioners but nonetheless have an important place in applied mathematical analysis. In a sense, he saves them for occasions when we as readers may need to probe further into unfamiliar territory.

So if you are looking for depth and precision in analysis of physical problems in Engineering and Science, or are trying to cope with reaearch problems in Applied Mathematics, try out this book by Lebedev. It can initially come across as difficult to understand, but Lebedev expects the reader to follow along through diligence. It is almost one of a kind, being that it is very clear and lucid without noticeable loss in depth and mathematical rigor. I highly recommend it because I believe that few other books can even come close in offering good examples in solutions to real-world problems and, at the same time, demonstrate the power of Special Functions in applications. Of course, it is also very inexpensive.

20 of 21 people found the following review helpful:

5.0 out of 5 stars Good, August 4, 1999

By A Customer

This review is from: Special Functions & Their Applications (Dover Books on Mathematics) (Paperback)

Bessel's, harmonics, normal CDF, gamma, hypergeometrics, orthogonal polynomials, etc. The most important functions in engineering, (except for elementary stuff on our calculators, of course).

Very good coverage. No fluff. Well-organized. Conveniently sized paperback.

13 of 13 people found the following review helpful:

5.0 out of 5 stars Excellent discussion of the functions used to solve PDE, March 13, 2003

By 

Edward H. Welbon "epiphenomenalist" (Austin, Tx United States) - See all my reviews
(REAL NAME)   

This review is from: Special Functions & Their Applications (Dover Books on Mathematics) (Paperback)

Yet another excellect translation by Silverman. I've only been in possession of this book for a few days but it's already becoming a favorite mathematics text. Not a pure mathematics text but certainly a very thorough, lucid and most certainly enjoyable discussion of applied mathematics with a particularly engaging discussion of the solution of partial differential equations (Laplacian, Poisson etc.) by means of separation of variables and integral transforms. Along the way it develops the theoretical essentials of gamma functions, exponential integrals, orthogonal polynomials, Bessel functions, spherical harmonics among others. Clearly written with an emphasis on explaining the process of discovering solutions rather than merely presenting particular solutions (though it does have enlightening examples). IMO, well worth the price.