Partial Differential Equations

Builds upon the basic theory of linear Partial Differential Equations (PDE). This title introduces analytical tools that include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. It develops basic differential geometrical concepts, centred about curvature.

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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.