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Fundamental theories and their appli...

Lao, Dazhong.

Fundamental theories and their applications of the calculus of variations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Fundamental theories and their applications of the calculus of variationsby Dazhong Lao, Shanshan Zhao.
作者:	Lao, Dazhong.
其他作者:	Zhao, Shanshan.
出版者:	Singapore :Springer Singapore :2021.
面頁冊數:	xx, 992 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Calculus of variations.
電子資源:	https://doi.org/10.1007/978-981-15-6070-5
ISBN:	9789811560705$q(electronic bk.)

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. - Singapore :Springer Singapore :2021. - xx, 992 p. :ill., digital ;24 cm.

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$q(electronic bk.)

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

191127
Calculus of variations.

LC Class. No.: QA315 / .L36 2021

Dewey Class. No.: 515.64

Fundamental theories and their applications of the calculus of variations
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505 0 $a 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.
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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