Special Functions and Their Applications (Revised English Edition)



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Special Functions and Their Applications (Revised English Edition)

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Книга: Special Functions and Their Applications (Revised English Edition)
Автор: N.N. Lebedev (Author), Richard R. Silverman (Translator)
Страниц: 308
Формат: PDF
Размер: 8,21 Мб
Качество: Отличное
Язык: Английский
Год издания: 1965
Translated by Richard Silverman. 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 application of cylinder functions and spherical harmonics. Also treated: gamma function, probability integral and related functions, Airy functions, hyper-geometric functions, more.
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.
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