12/14/2023 0 Comments Best book on calculus of variationsIt covers the preliminaries, variational problems with fixed. This textbook is intended for graduate and higher-level college and university students, introducing them to the basic concepts and calculation methods used in the calculus of variations. Substantially revised and corrected by the translator, this inexpensive ne edition will be welcomed by advanced undergraduate and graduate students of mathematics and physics. This book focuses on the calculus of variations, including fundamental theories and applications. Two appendices and suggestions for supplementary reading round out the text. The problems following each chapter were made specially for this English-language edition, and many of them comment further on corresponding parts of the text. Chapter seven considers the application of variational methods to the study of systems with infinite degrees of freedom, and Chapter eight deals with direct methods in the calculus of variations. Students wishing a more extensive treatment, however, will find the first six chapters comprise a complete university-level course in the subject, including the theory of fields and sufficient conditions for weak and strong extrema. The reader who merely wishes to become familiar with the most basic concepts and methods of the calculus of variations need only study the first chapter. and Leibnitz's work on extremum problems and the calculus of variations. Considerable attention is devoted to physical applications of variational methods, e.g., canonical equations, variational principles of mechanics, and conservation laws. Thousands of books covering various aspects of optimization and operations. The aim is to give treatment of the elements of the calculus of variations in a form both easily understandable and sufficiently modern. Bruce van Brunt is Senior Lecturer at Massey University, New Zealand.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 lectures. 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. The book focuses on variational problems that involve one independent variable. 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. Which one will become your favorite text (among all. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations. The book is less formal than Sagan's book Introduction to the Calculus of Variations (Dover Books on Mathematics) and Gelfand and Fomin's Calculus of Variations (Dover Books on Mathematics) but more rigorous than Weinstock's Calculus of Variations: with Applications to Physics and Engineering. 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 Includes bibliographical references (pages 283-285) and index
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