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Fundamental Theories and Their Applications of the Calculus of Variations (Hardcover, 1st ed. 2021)
Loot Price: R7,784
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Fundamental Theories and Their Applications of the Calculus of Variations (Hardcover, 1st ed. 2021)
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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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