Visionneuse

Date_TXT

Singapore: Springer, 2021

Auteur

Lao Dazhong, Zhao Shanshan

Sujet

Calculus Of Variations; Variational Problem; Euler Equation; Lagrange Multiplier; Total Variation; Variational Principles; Generalized Variational Principle; Hamiltonian Operator String; Gradient Type Functional; Divergence Type Functional; Rotation Type; Functional; Modulus Of Vector; Tensor Of Order; Parallel Type Inner Product Tensors; Series Type Inner Product Tensor; Transposed Tensor; Trace Of Tensor; Self-adjoint Operator; Conjugate Operator; Self-conjugate Operator

Type de document

Livre

Description :

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