Krantz Differential Equations

by Daniel J. Arrigo (Author), Steven G. Krantz (Editor)
This is an introduction to methods for solving nonlinear partial differential equations (NLPDEs).

Blank and Krantz's Calculus 2e brings together time-tested methods and innovative thinking to address the needs of today's students, who come from a wide range of backgrounds and look ahead to a variety of futures.

This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians.