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Fundamental Theories and Their Applications of the Calculus of Variations / by Dazhong Lao, Shanshan Zhao

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Publisher: Singapore : Springer Singapore, 2021Publisher: Singapore : Imprint: Springer, 2021Edition: 1st ed. 2021Description: 1 Online-Ressource(XX, 992 p. 77 illus., 35 illus. in color.)ISBN:
  • 9789811560705
Subject(s): Additional physical formats: 9789811560699 | 9789811560712 | 9789811560729 | Erscheint auch als: 9789811560699 Druck-Ausgabe | Erscheint auch als: 9789811560712 Druck-Ausgabe | Erscheint auch als: 9789811560729 Druck-AusgabeDOI: DOI: 10.1007/978-981-15-6070-5Online resources: Summary: Preliminaries -- Variational Problems with Fixed Boundaries -- Sufficient Conditions of Extrema of Functionals -- Problems with Variable Boundaries -- Variational Problems of Conditional Extrema -- Variational Problems in Parametric Forms -- Variational Principles -- Methods of Variational Problems -- Variational Principles in Mechanics and Their Applications -- Variational Problems of Functionals with Vector, Tensor and Hamiltonian Operators. .Summary: This book focuses on the calculus of variations, including fundamental theories and applications. 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. It covers the preliminaries, variational problems with fixed boundaries, sufficient conditions of extrema of functionals, problems with undetermined boundaries, variational problems of conditional extrema, variational problems in parametric forms, variational principles, direct methods for variational problems, variational principles in mechanics and their applications, and variational problems of functionals with vector, tensor and Hamiltonian operators. Many of the contributions are based on the authors’ research, addressing topics such as the extension of the connotation of the Hilbert adjoint operator, definitions of the other three kinds of adjoint operators, the extremum function theorem of the complete functional, unified Euler equations in variational methods, variational theories of functionals with vectors, modulus of vectors, arbitrary order tensors, Hamiltonian operators and Hamiltonian operator strings, reconciling the Euler equations and the natural boundary conditions, and the application range of variational methods. The book is also a valuable reference resource for teachers as well as science and technology professionals. .PPN: PPN: 1734640979Package identifier: Produktsigel: ZDB-2-ENG | ZDB-2-SEB | ZDB-2-SXE
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