From the Preface to the First Russian Edition IntroductionI. The Method of Variation in Problems with Fixed Boundaries 1. The Variation and Its Properties 2. Euler Equation 3. Functionals of the Form: x1∫x0 F(x,Y1,Y2,...,Yn,Y'1,Y'2,...,Y'n)dx 4. Functionals Involving Derivatives of Higher Order 5. Functionals Depending on Functions of Several Independent Variables 6. Parametric Representation of Variational Problems 7. Some Applications ProblemsII. Variational Problems with Movable Boundaries and Some Other Problems 1. Simplest Problem with Movable Boundaries 2. Problems with Movable Boundaries for Functionals of the Form x1∫x0 F(x,y,z,y',z')dx 3. Problems with Movable Boundaries for Functionals of the Form x1∫x0 F(x,y, y',y'')dx 4. Extremals with Cusps 5. One-Sided Variations 6. Mixed Problems Problems