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 problemssuch as those of geometric opticsof 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.
Table of Contentsof Calculus of Variations I.- 1. The First Variation.- 2. Variational Problems with Subsidiary Conditions.- 3. General Variational Formulas.- 4. Second Variation, Excess Function, Convexity.- 5. Weak Minimizers and Jacobi Theory.- 6. Weierstrass Field Theory for One-Dimensional Integrals and Strong Minimizers.- Supplement. Some Facts from Differential Geometry and Analysis.- 1. Euclidean Spaces.- 2. Some Function Classes.- 3. Vector and Covector Fields. Transformation Rules.- 4. Differential Forms.- 6. Mean Curvature and Gauss Curvature.