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Differential Equations, Partial, v. 1 - Foundations of the Classical Theory (Hardcover)
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Differential Equations, Partial, v. 1 - Foundations of the Classical Theory (Hardcover)
Series: Encyclopaedia of Mathematical Sciences, v. 30
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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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