Calculus of Variations
Published on 10. July 2014
178 pages
978-1-4831-3756-8 (ISBN)
Description
Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter is illustrated by a large number of problems some of which are taken from existing textbooks. The solutions to the problems in each chapter are provided at the end of the book.
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Content
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
