In this second English edition of Caratheodory's work (originally published in German), the two volumes of the first edition have been combined into one (with a combination of the two indexes into a single index). There is a deep and fundamental relationship between the differential equations that occur in the calculus of variations and partial differential equations of the first order: in particular, to each such partial differential equation there correspond variational problems. This basic fact forms the rationale for Caratheodory's work.
In this second English edition of Caratheodory's work (originally published in German), the two volumes of the first edition have been combined into o...
