Foundations of the classical theory
著者
書誌事項
Foundations of the classical theory
（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 30 . Partial differential equations ; 1）
Springer-Verlag, c1992
- : us
- : gw
- タイトル別名
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Partial differential equations 1
Different︠s︡ialʹnye uravnenii︠a︡ s chastnymi proizvodnymi I
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注記
Translation of: "Different︠s︡ialʹnye uravnenii︠a︡ s chastnymi proizvodnymi I," which is vol. 30 of the serial "Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalʹnye napravlenii︠a︡."
Translated from the Russian by R. Cooke
Bibliographical references: p. 242-247
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内容説明・目次
内容説明
Partial differential equations are as old as calculus itself, occurring as examples in the papers of Newton and Leibniz. Since the beginning, they have been strongly linked to physics and other sciences. This volume presents an introduction to the classical theory, emphasizing along the way physical methods and physical interpretations. The book beings with a derivation of some of the classical partial differential equations, and a discussion of the limitations of the physical models upon which the derivations are based. The second chapter discusses the classical methods for studying PDEs, including the theory of distributions and the Petrovskij classification into elliptic, parabolic and hyperbolic equations. Among the more advanced methods discussed are spectral theory, the method of planar waves and the theory of semigroups. Every topic considered is placed in its present context in mathematical research, yet the book never loses sight of the non-specialist reader with an interest in physical applications.
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