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Fundamental Theories and Their Applications of the Calculus of Variations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Fundamental Theories and Their Applications of the Calculus of Variations/ by Dazhong Lao, Shanshan Zhao.
Author:	Lao, Dazhong.
other author:	Zhao, Shanshan.
Description:	XX, 992 p. 77 illus., 35 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Applied mathematics. -
Online resource:	https://doi.org/10.1007/978-981-15-6070-5
ISBN:	9789811560705

Fundamental Theories and Their Applications of the Calculus of Variations
Lao, Dazhong.

Fundamental Theories and Their Applications of the Calculus of Variations[electronic resource] /by Dazhong Lao, Shanshan Zhao. - 1st ed. 2021. - XX, 992 p. 77 illus., 35 illus. in color.online resource.

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. .

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. .

ISBN: 9789811560705

Standard No.: 10.1007/978-981-15-6070-5doiSubjects--Topical Terms:

1069907
Applied mathematics.

LC Class. No.: TA329-348

Dewey Class. No.: 519

Fundamental Theories and Their Applications of the Calculus of Variations
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520 $a 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. .
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