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This first volume discusses 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 here, reserving functional analytic solution methods for Volume Two.
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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)
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