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The early chapters have many words and few equations.
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A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation, and the discussion of the interplay between algebra and geometry. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. Yet, as the author shows, it remains remarkably vital and relevant. The tensor technique, invented at the turn of the 20 th century, is now considered classical. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak.
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If calculus and linear algebra are central to the reader’s scientific endeavors, tensor calculus is indispensable. The tensor approach can be of benefit to members of all technical sciences including mathematics and all engineering disciplines.
#Tensor calculus full#
Tensor calculus is a powerful tool that combines the geometric and analytical perspectives and enables us to take full advantage of the computational utility of coordinate systems. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation, and dynamic fluid film equations. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. This text is meant to deepen its readers’ understanding of vector calculus, differential geometry and related subjects in applied mathematics.