Author: Bewley
Publisher:
ISBN: 9780471073444
Category :
Languages : en
Pages :

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Author: Loyal Vivian Bewley
Publisher:
ISBN:
Category :
Languages : en
Pages : 540

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Author: Loyal Vivian Bewley
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 330

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Author: Gabriel Kron
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 276

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Author: William John Gibbs
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 104

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Author: Pavel Grinfeld
Publisher: Springer Science & Business Media
ISBN: 1461478677
Category : Mathematics
Languages : en
Pages : 303

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Book Description
This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. 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. 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. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. 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 early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.

Author: John G. Papastavridis
Publisher: Routledge
ISBN: 1351411616
Category : Mathematics
Languages : en
Pages : 444

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Book Description
Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.

Author: Gabriel Kron
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 250

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Author:
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 224

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Book Description

Author: Gabriel Kron
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 292

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Book Description