Introduction To Tensor Analysis And The Calculus Of Moving Surfaces
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Introduction To Tensor Analysis And The Calculus Of Moving Surfaces
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Author : Pavel Grinfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-24
Introduction To Tensor Analysis And The Calculus Of Moving Surfaces written by Pavel Grinfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-24 with Mathematics categories.
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.
Introduction To Tensor Analysis And The Calculus Of Moving Surfaces
DOWNLOAD
Author : Pavel Grinfeld
language : en
Publisher: Springer
Release Date : 2013-09-24
Introduction To Tensor Analysis And The Calculus Of Moving Surfaces written by Pavel Grinfeld and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-24 with Mathematics categories.
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.
Tensor Calculus For Physics
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Author : Dwight E. Neuenschwander
language : en
Publisher: JHU Press
Release Date : 2015
Tensor Calculus For Physics written by Dwight E. Neuenschwander and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.--Gary White, editor of The Physics Teacher "American Journal of Physics"
Tensor Algebra And Tensor Analysis For Engineers
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Author : Mikhail Itskov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-04
Tensor Algebra And Tensor Analysis For Engineers written by Mikhail Itskov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-04 with Technology & Engineering categories.
There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.
Tensor Analysis And Continuum Mechanics
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Author : Wilhelm Flügge
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Tensor Analysis And Continuum Mechanics written by Wilhelm Flügge and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
Through several centuries there has been a lively interaction between mathematics and mechanics. On the one side, mechanics has used mathemat ics to formulate the basic laws and to apply them to a host of problems that call for the quantitative prediction of the consequences of some action. On the other side, the needs of mechanics have stimulated the development of mathematical concepts. Differential calculus grew out of the needs of Newtonian dynamics; vector algebra was developed as a means . to describe force systems; vector analysis, to study velocity fields and force fields; and the calcul~s of variations has evolved from the energy principles of mechan ics. In recent times the theory of tensors has attracted the attention of the mechanics people. Its very name indicates its origin in the theory of elasticity. For a long time little use has been made of it in this area, but in the last decade its usefulness in the mechanics of continuous media has been widely recognized. While the undergraduate textbook literature in this country was becoming "vectorized" (lagging almost half a century behind the development in Europe), books dealing with various aspects of continuum mechanics took to tensors like fish to water. Since many authors were not sure whether their readers were sufficiently familiar with tensors~ they either added' a chapter on tensors or wrote a separate book on the subject.
Manifolds Tensors And Forms
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Author : Paul Renteln
language : en
Publisher: Cambridge University Press
Release Date : 2014
Manifolds Tensors And Forms written by Paul Renteln and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.
Tensor Analysis And Elementary Differential Geometry For Physicists And Engineers
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Author : Hung Nguyen-Schafer
language : en
Publisher:
Release Date : 2014-07-31
Tensor Analysis And Elementary Differential Geometry For Physicists And Engineers written by Hung Nguyen-Schafer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-31 with categories.
Mathematical Methods For Physicists
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Author : Tai L. Chow
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-27
Mathematical Methods For Physicists written by Tai L. Chow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-27 with Science categories.
This text is designed for an intermediate-level, two-semester undergraduate course in mathematical physics. It provides an accessible account of most of the current, important mathematical tools required in physics these days. It is assumed that the reader has an adequate preparation in general physics and calculus. The book bridges the gap between an introductory physics course and more advanced courses in classical mechanics, electricity and magnetism, quantum mechanics, and thermal and statistical physics. The text contains a large number of worked examples to illustrate the mathematical techniques developed and to show their relevance to physics. The book is designed primarily for undergraduate physics majors, but could also be used by students in other subjects, such as engineering, astronomy and mathematics.
Introduction To Vector And Tensor Analysis
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Author : Robert C. Wrede
language : en
Publisher: Courier Corporation
Release Date : 2013-01-30
Introduction To Vector And Tensor Analysis written by Robert C. Wrede and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-30 with Mathematics categories.
Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.