![]() Bruce van Brunt is Senior Lecturer at Massey University, New Zealand. The book can be used as a textbook for a one semester course on the calculus of variations, or as a book to supplement a course on applied mathematics or classical mechanics. The text contains numerous examples to illustrate key concepts along with problems to help the student consolidate the material. In addition, more advanced topics such as the inverse problem, eigenvalue problems, separability conditions for the Hamilton-Jacobi equation, and Noether's theorem are discussed. The fixed endpoint problem and problems with constraints are discussed in detail. (I understand that its one way to derive the Euler-Lagrange equations.) For the computational approach I would say Goldstein has a pretty clear explanation. although I havent looked at it in 20 years. AxiomOfChoice said: I first encountered calculus of variations in my graduate mechanics class, and we did a few problems with it, but I never really understood it completely. Boundary and Eigenvalue Problems in Mathematical Physics (Dover Books on Physics): Sagan, Hans: 9780486661322: : Books. ![]() The book focuses on variational problems that involve one independent variable. When I was in graduate school I remember this book being pretty useful. ![]() The mathematical background assumed of the reader is a course in multivariable calculus, and some familiarity with the elements of real analysis and ordinary differential equations. This book is an introductory account of the calculus of variations suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering. Based on a series of lectures given by I.M.Gelfand at Moscow State University, this book actually goes considerably beyond the material presented in the. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. The calculus of variations has a long history of interaction with other branches of mathematics, such as geometry and differential equations, and with physics, particularly mechanics. Preface - Introduction - The First Variation - Some Generalizations - Isoperimetric Problems - Applications to Eigenvalue Problems - Holonomic and Nonholonomic Constraints - Problems with Variable Endpoints - The Hamiltonian Formulation - Noether's Theorem - The Second Variation - Appendix A: Some Results from Analysis and Differential Equations - Appendix B: Function Spaces - References - Index The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.Includes bibliographical references (pages 283-285) and index While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field.
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