This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.

In this first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are treated:

integration and differentiation on manifolds

foundations of functional analysis

Brouwer's mapping degree

generalized analytic functions

potential theory and spherical harmonics

linear partial differential equations

This new second...

This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.

In this second volume, special emphasis is placed on functional analytic methods and applications to differential geometry. The following topics are treated: solvability of operator equations in Banach spaceslinear operators in Hilbert spaces and spectral theory Schauder's theory of linear elliptic differential equations weak solutions of differential equationsnonlinear partial differential equations and...