This text is basically divided into two parts. Chapters 1-4 include background material, basic theorems and isoperimetric problems. Chapters 5-12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics and other topics. Exercises in each chapter. 1952 edition.
Here's a sample of other books in this Dover category
Introduction to the Calculus of Variations by Hans Sagan Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.
Calculus of Variations by Lev D. Elsgolc This text offers an introduction to the fundamentals and standard methods of the calculus of variations, covering fixed and movable boundaries, plus solutions of variational problems. 1961 edition.