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Partial Differential Equations: Basic Theory (Texts in Applied Mathematics)
Rok: 1996
ISBN: 9780387946542
OKCZID: 110064959
Citace (dle ČSN ISO 690):
TAYLOR, Michael Eugene. Partial differential equations: basic theory. Corrected 2nd print. 1999. New York: Springer, 1999, c1996, 563 s. Texts in applied mathematics, 23. ISBN 0-387-94654-3.
Anotace
This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. Companion texts, which take the theory of partial differential equations further, are AMS volume 116, treating more advanced topics in linear PDE, and AMS volume 117, treating problems in nonlinear PDE. This book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis