| 書目名稱 | Fundamental Theories and Their Applications of the Calculus of Variations | | 編輯 | Dazhong Lao,Shanshan Zhao | | 視頻video | http://file.papertrans.cn/351/350055/350055.mp4 | | 概述 | Proposes a new concept of the complete functional.Presents the fundamental lemma of the variation of functionals with nth-order tensors.Extends the connotation of the Hilbert adjoint operator and offe | | 圖書封面 |  | | 描述 | .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 Hamiltonia | | 出版日期 | Book 2021 | | 關(guān)鍵詞 | Calculus Of Variations; Variational Problem; Euler Equation; Lagrange Multiplier; Total Variation; Variat | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-15-6070-5 | | isbn_softcover | 978-981-15-6072-9 | | isbn_ebook | 978-981-15-6070-5 | | copyright | Beijing Institute of Technology Press and Springer Nature Singapore Pte Ltd. 2021 |
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