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 edition of this volume has been thoroughly revised and a new section
on the boundary behavior of Cauchy's integral has been added. The second volume will present
functional analytic methods and applications to problems in differential geometry. This
textbook will be of particular use to graduate and postgraduate students interested in this
field and will be of interest to advanced undergraduate students. It may also be used for
independent study.
