Partial Differential Equations 2: v. 1 (Universitext) - Tapa blanda

From the reviews: "Friedrich Sauvigny’s remarkable two-volume opus ... constitutes the author’s attempt to treat the beautiful and difficult subject of PDEs in a thorough and instructive way ... . is a fine place to learn PDEs with the goal of doing serious work in the field. ... Friedrich Sauvigny’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) “The aim of the author is to present the entire domain of Partial Differential Equations (PDE’s) - so reach in theories and applications - to students at the intermediate level. ... the present textbook can be used for a course extending over several semesters. For advanced readers, each chapter may be studied independently from the others.­­­­­”­­­ (Lubomira Softova, Zentralblatt MATH, Vol. 1198, 2010)

This comprehensive two-volume textbook covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is placed 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. We solve partial differential equations via integral representations in this volume, reserving functional analytic solution methods for Volume Two.