In this book the analysis has been developed chiefly with the aim of obtaining exact analytical expressions for the solution of the boundary problems of mathematical physics. In many cases, however, this is impracticable, and in recent years mud attention has been devoted to methods of approximation. Since these are not described in the text with the fullness which they now deserve, a brief introduction has been written in which some of these methods are sketches and indications are given of portions of the text which will ...
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In this book the analysis has been developed chiefly with the aim of obtaining exact analytical expressions for the solution of the boundary problems of mathematical physics. In many cases, however, this is impracticable, and in recent years mud attention has been devoted to methods of approximation. Since these are not described in the text with the fullness which they now deserve, a brief introduction has been written in which some of these methods are sketches and indications are given of portions of the text which will be particularly useful to a student who is preparing to use these methods. No discussion has been given of the partial differential equations which occur in the new quantum theory of radiation because these have been well treated in several recent books, and an adequate discussion in a book of this type would have greatly increased its size. It is thought, however, that some of the analysis may prove useful to students of the new quantum theory. Some abbreviations and slight departures from the notation used in recent books have been adopted. Since the L-notation for the generalised Laguerre polynomial has been used recently by different writers with slightly different meanings, the original T-notation of Sonine has been retained as in the author's Electrical and Optical Wave Motion. It is thought, however, that a standardised L-notation will eventually be adopted by most writers in honour of the work of Lagrange and Laguerre. The abbreviations ''eit " and ''eif " used in the text might be used with advantage in the new quantum theory, together with some other abbreviations, such as ''eil" for eigenlevel and "eiv" for eigenvector. The Heaviside Calculus and the theory of integral equations are only briefly mentioned in the text; they belong rather to a separate subject which might be called the Integral Equations of Mathematical Physics. Accounts of the existence theorems of potential theory, Sturm-Liouville expansions and ellipsoidal harmonics have also been omitted. Many excellent books have however appeared recently in which these subjects are adequately treated.
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