Partial Differential Equations II: Qualitative Studies of Linear Equations ( Applied Mathematical Sciences) 〈Vol. 116〉

Taylor, Michael E.

Springer（2006/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 528 p.
• 商品コード 9780387946511

Full Description

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.

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.