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Mathematical analysis --- Calculus of variations --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Calcul des variations

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"This comprehensive introduction to the calculus of variations and its main principles also presents their real-life applications in various contexts: mathematical physics, differential geometry, and optimization in economics. Based on the authors' original work, it provides an overview of the field, with examples and exercises suitable for graduate students entering research. The method of presentation will appeal to readers with diverse backgrounds in functional analysis, differential geometry and partial differential equations. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. Since much of the material has a strong geometric flavor, the authors have supplemented the text with figures to illustrate the abstract concepts. Its extensive reference list and index also make this a valuable resource for researchers working in a variety of fields who are interested in partial differential equations and functional analysis"--

Calculus of variations --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima

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Variational methods in optimum control theory

Calculus of variations. --- Control theory. --- Linear control theory. --- Nonlinear control theory. --- Stability. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Dynamics --- Machine theory

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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. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations. This book is an introduction to the calculus of variations for mathematicians and scientists. The reader interested primarily in mathematics will find results of interest in geometry and differential equations. I have paused at times to develop the proofs of some of these results, and discuss briefly various topics not normally found in an introductory book on this subject such as the existence and uniqueness of solutions to boundary-value problems, the inverse problem, and Morse theory. I have made “passive use” of functional analysis (in particular normed vector spaces) to place certain results in context and reassure the mathematician that a suitable framework is available for a more rigorous study. For the reader interested mainly in techniques and applications of the calculus of variations, I leavened the book with numerous examples mostly from physics. In addition, topics such as Hamilton’s Principle, eigenvalue approximations, conservation laws, and nonholonomic constraints in mechanics are discussed. More importantly, the book is written on two levels. The technical details for many of the results can be skipped on the initial reading. The student can thus learn the main results in each chapter and return as needed to the proofs for a deeper understanding.

Calculus of variations. --- Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematical optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima

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The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of

Calculus of variations. --- Variational inequalities (Mathematics) --- Mathematical physics. --- Physical mathematics --- Physics --- Inequalities, Variational (Mathematics) --- Calculus of variations --- Differential inequalities --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Mathematics