Fundamental Theories and Their Applications of the Calculus of Variations
(Sprache: Englisch)
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...
This textbook is intended for graduate and higher-level college and university students, introducing them to the basic concepts and calculation...
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Klappentext zu „Fundamental Theories and Their Applications of the Calculus of Variations “
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.
Inhaltsverzeichnis zu „Fundamental Theories and Their Applications of the Calculus of Variations “
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.
Autoren-Porträt von Dazhong Lao, Shanshan Zhao
Dazhong Lao is an Associate Professor at the School of Aerospace Engineering, Beijing Institute of Technology, and a Distinguished Professor of Yinchuan University of Energy. As an Associate Professor from 1998 to 2017, his research focused on combustion flow theory and testing technologies for rocket motors. During this time, he published more than 100 academic papers and presided over or participated in over 20 scientific research projects. Since August 2017, he has served as a Senior Engineer involved in thermal system modeling at Beijing Dafeng Tianli Technology Co., Ltd. He was appointed as a Distinguished Professor and Academic Leader of Energy and Power Engineering at Yinchuan University of Energy in 2018.
Bibliographische Angaben
- Autoren: Dazhong Lao , Shanshan Zhao
- 2021, 1st ed. 2021, XX, 992 Seiten, 35 farbige Abbildungen, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 9811560722
- ISBN-13: 9789811560729
Sprache:
Englisch
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