Calculus of Variations I (Grundlehren der mathematischen Wissenschaften)

This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems―such as those of geometric optics―of parts of the theory. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.