Calculus of Variations II

Focusing on the classical variational calculus, this book serves as a comprehensive resource for analysts, geometers, and physicists. Volume 1 introduces the foundational concepts and nonparametric field theory, while Volume 2 explores parametric variational problems, Hamilton-Jacobi theory, and first-order partial differential equations. Unique emphasis is placed on inner variations, leading to insights on conservation laws and symmetries, particularly through Emmy Noether's principles. Additionally, it covers Legendre-Jacobi theory, one-dimensional field theory, and the application of convexity in variational calculus.