An examination of approaches to easy-to-understand but difficult-to-solve mathematical problems, this classic text balances the individuality of objects with the generality of mathematical methods. Beginning with a discussion of Dirichlet's principle and the boundary value problem of potential theor[...]

The new Chapter 1 contains all the fundamental properties of linear differential forms and their integrals. These prepare the reader for the introduction to higher-order exterior differential forms added to Chapter 3. Also found now in Chapter 3 are a new proof of the implicit function theorem by su[...]

VIII uber den Inhalt im einzelnen unterrichtet das ausfuhrliche Ver zeichnis. Zur Form ist etwas Grundsatzliches zu sagen: Das klassische Ideal einer gewissermassen atomistischen Auffassung der Mathematik ver langt, den Stoff in Form von Voraussetzungen, Satzen und Beweisen zu kondensieren. Dabei is[...]