Overview

This comprehensive two-volume textbook presents the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is put on the connection of PDEs and complex variable methods.

In this first volume the following topics are treated: Integration and differentiation on manifolds, Functional analytic foundations, Brouwer's degree of mapping, Generalized analytic functions, Potential theory and spherical harmonics, Linear partial differential equations. While we solve the partial differential equations via integral representations in this volume, we shall present functional analytic solution methods in the second volume.

This textbook can be chosen for a course over several semesters on a medium level. Advanced readers may study each chapter independently from the others.

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9783540824503

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Reviews

From the reviews: <p> Friedrich Sauvignya (TM)s remarkable two-volume opus a ] constitutes the authora (TM)s attempt to treat the beautiful and difficult subject of PDEs in a thorough and instructive way a ] . is a fine place to learn PDEs with the goal of doing serious work in the field. a ] Friedrich Sauvignya (TM)s scholarship is exemplary and thorough; at the same time his book is both broad and deep and is a pleasure to read. (Michael Berg, MathDL, February, 2007)

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