Partial Differential Equations II
Qualitative Studies of Linear Equations
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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 ...
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.
Table of contents:
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.
Table of contents:
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.