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Tensor Calculus With Applications (Paperback)
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Tensor Calculus With Applications (Paperback)
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This textbook presents the foundations of tensor calculus and the
elements of tensor analysis, in addition to considering numerous
applications of tensors to geometry, mechanics and physics. While
developing tensor calculus, the authors emphasize its relationship
with linear algebra. Necessary notions and theorems of linear
algebra are introduced and proved in connection with the
construction of the apparatus of tensor calculus; prior knowledge
is not assumed. For simplicity and to enable the reader to
visualize concepts more clearly, all exposition is conducted in
three-dimensional space. The principal feature of the book is that
the authors use mainly orthogonal tensors, since such tensors are
important in applications to physics and engineering. All notions
introduced in the book, and also the obtained results, are
illustrated with numerous examples discussed in the text. Each
section of the book presents problems (a total over 300 problems
are given). Examples and problems are intended to illustrate,
reinforce textbook presents the foundations of tensor calculus and
the elements of tensor analysis, in addition to considering
numerous applications of tensors to geometry, mechanics and
physics. While developing tensor calculus, the authors emphasize
its relationship with linear algebra. Necessary notions and
theorems of linear algebra are introduced and proved in connection
with the construction of the apparatus of tensor calculus; prior
knowledge is not assumed. For simplicity and to enable the reader
to visualize concepts more clearly, all exposition is conducted in
three-dimensional space. The principal feature of the book is that
the authors use mainly orthogonal tensors, sincesuch tensors are
important in applications to physics and engineering. All notions
introduced in the book, and also the obtained results, are
illustrated with numerous examples discussed in the text. Each
section of the book presents problems (a total over 300 problems
are given). Examples and problems are intended to illustrate,
reinforce and deepen the presented material. There are answers to
most of (he problems, as well as hints and solutions to selected
problems at the end of the book.
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