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Certain dual series relations and their applications
Başlık:
Certain dual series relations and their applications
Yazar:
Srivastav, Ram Prasad, author.
ISBN:
9780438060982
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (112 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 76-08C.
Advisors: I. N. Sneddon.
Özet:
The present thesis embodies the research work done by me since October 1961 a-t the University of Glasgow, Considerable interest lies in the solution of the mixed boundary value problems in mathematical physics, A convenient approximation in this class of problems is to ignore the boundary conditions on one (or more) of the boundaries. The boundary conditions are then replaced by some sort of regularity conditions ' at infinity'. The infinity is however a mathematical idealization. In the solution of physical problems therefore it is imperative to examine the effect of the presence of a boundary with specified boundary conditions. The solutions corresponding to infinite regions are invariably simpler than those for the finite regions. The solution of a 'finite region' problem will therefore tell us about the extent of reliability of the infinite solution. The analysis is purely formal. Only a few problems admit a closed-form solution. In every other case the problem is recast so - that it is suitable for treatment by numerical methods. It should be pointed out that the word 'sum' has often been used for the integral representation of the function represented by an infinite series.
The work reported here is divided into eight chapters. In Chapter I certain circumstances are described which provide the motivation for considering this kind of problem. It was considered advisable to include some preliminary results in Chapter II; even in those sections of this chapter where seemingly new results are mentioned, there is hardly any novelty. Dual relations involving Fourier-Bessel and Dini Series form the subject matter of Chapters III and IV respectively. In Chapter V we describe two methods for solving the problems involving sine and cosine series. The reduction to Fredholm-integral equation falls within the general scheme of things. The closed form solution is due to special properties of the trigonometric functions. The comparison of two solutions is of great help in reducing the Fredholm-integral equation to a Schlomilch integral equation. One such solution has been included. It is to be hoped that this would provide a clue to solving more complicated integral equations. Making use of the theory already developed, we investigate in, Chapter VII a two dimensional crack problem for a rectangular plate. This is more in the nature of providing a check for the formal work done in solving the dual relations than as a contribution in mathematical theory of elasticity. A method is also given for solving more general problems which seem to be intractable using complex-variable tools. In the last chapter we discuss the torsion problem of a large cylinder. The iterative solutions of the integral equations are given.
Notlar:
School code: 0547
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(684866.1) | 684866-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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