Partial Differential Equations 1 [electronic resource] : Foundations and Integral Representations / by Friedrich Sauvigny.Material type: TextSeries: UniversitextPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006Description: XIV, 437 p. 14 illus., 1 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540344599Subject(s): Differential equations, partial | Mathematical physics | Partial Differential Equations | Mathematical Methods in PhysicsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 515.353 LOC classification: QA370-380Online resources: Click here to access online
Differentiation and Integration on Manifolds -- Foundations of Functional Analysis -- Brouwer’s Degree of Mapping with Geometric Applications -- Generalized Analytic Functions -- Potential Theory and Spherical Harmonics -- Linear Partial Differential Equations in ?n.
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.