Qualitative Studies of Linear Equations
(Sprache: Englisch)
This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint...
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Produktinformationen zu „Qualitative Studies of Linear Equations “
This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centred about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.
Klappentext zu „Qualitative Studies of Linear Equations “
This is the second of three volumes on partial differential equations. It builds upon the basic theory of linear PDE given in Volume 1, and pursues some more advanced topics in linear PDE. Analytical tools introduced in Volume 2 for these studies include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. There is also a development of basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion. The 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.
Inhaltsverzeichnis zu „Qualitative Studies of Linear Equations “
Contents: Contents of Volumes I and III.- Introduction.
- Pseudodifferential Operators.
- Spectral Theory.
- Scattering by Obstacles.
- Dirac Operators and Index Theory.
- Brownian Motion and Potential Theory.
- The Partial-Neumann Problem.
- Connections and Curvature.
- Index.
Autoren-Porträt von Michael E. Taylor
Michael E. Taylor is a Professor at University of North Carolina in the Department of Mathematics.
Bibliographische Angaben
- Autor: Michael E. Taylor
- 2011, 2nd ed., XXII, 614 Seiten, Maße: 16,6 x 24,2 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1441970517
- ISBN-13: 9781441970510
Sprache:
Englisch
Rezension zu „Qualitative Studies of Linear Equations “
From the reviews of the second edition:"This substantial three-volume work is an upgraded version of the comprehensive qualitative analysis of partial differential equations presented in the earlier edition. ... Graduate students ... will find these three volumes to be not just a fine and rigorous treatment of the subject, but also a source of inspiration to apply their knowledge and ability to the solution of other challenging problems in the field of partial differential equations. ... an excellent text for all devotees of the charming and thought-provoking byways of higher mathematics." (Christian Constanda, The Mathematical Association of America, June, 2011)
Pressezitat
From the reviews of the second edition:"This substantial three-volume work is an upgraded version of the comprehensive qualitative analysis of partial differential equations presented in the earlier edition. ... Graduate students ... will find these three volumes to be not just a fine and rigorous treatment of the subject, but also a source of inspiration to apply their knowledge and ability to the solution of other challenging problems in the field of partial differential equations. ... an excellent text for all devotees of the charming and thought-provoking byways of higher mathematics." (Christian Constanda, The Mathematical Association of America, June, 2011)
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