Series Overview

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

Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure.

Geometrical Concepts

The book also develops basic differential geometrical concepts, centred about curvature.

Topics Covered

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.