Introduction to Tensor Analysis and the Calculus of Moving Surfaces

種類:

電子ブック

責任表示:

by Pavel Grinfeld

出版情報:

New York, NY : Springer New York : Imprint: Springer, 2013

著者名:

• Grinfeld, Pavel
• SpringerLink (Online service)

ISBN:

9781461478676 [1461478677]    

注記:

This text is meant to deepen its readers’ understanding of vector calculus, differential geometry and related subjects in applied mathematics. 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. 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. 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. The tensor approach can be of benefit to members of all technical sciences including mathematics and all engineering disciplines. If calculus and linear algebra are central to the reader’s scientific endeavors, tensor calculus is indispensable. The language of tensors, originally championed by Einstein, is as fundame

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