An Introduction To Differential Geometrywith Use Of The Tensor Calculus
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An Introduction To Differential Geometry With The Use Of Tensor Calculus
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Author : Luther Pfahler Eisenhart
language : en
Publisher: Read Books Ltd
Release Date : 2011-03-23
An Introduction To Differential Geometry With The Use Of Tensor Calculus written by Luther Pfahler Eisenhart and has been published by Read Books Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-23 with Mathematics categories.
Since 1909, when my Differential Geometry of Curves and Surfaces was published, the tensor calculus, which had previously been invented by Ricci, was adopted by Einstein in his General Theory of Relativity, and has been developed further in the study of Riemannian Geometry and various generalizations of the latter. In the present book the tensor calculus of cuclidean 3-space is developed and then generalized so as to apply to a Riemannian space of any number of dimensions. The tensor calculus as here developed is applied in Chapters III and IV to the study of differential geometry of surfaces in 3-space, the material treated being equivalent to what appears in general in the first eight chapters of my former book with such additions as follow from the introduction of the concept of parallelism of Levi-Civita and the content of the tensor calculus. Of the many exercises in the book some involve merely direct application of the text, but most of them constitute an extension of it. In the writing of the book I have received valuable assistance and criticism from Professor H. P. Robertson and from my students, Messrs. Isaac Battin, Albert J. Coleman, Douglas R. Crosby, John Giese, Donald C. May, and in particular, Wayne Johnson. The excellent line drawings and half-tone illustrations were conceived and executed by Mr. John H. Lewis.
Introduction To Differential Geometry
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Author : Luther Pfahler Eisenhart
language : en
Publisher: Princeton University Press
Release Date : 2015-12-08
Introduction To Differential Geometry written by Luther Pfahler Eisenhart and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.
Book 3 in the Princeton Mathematical Series. Originally published in 1950. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
An Introduction To Differential Geometry
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Author : Luther Pfahler Eisenhart
language : en
Publisher:
Release Date : 1940
An Introduction To Differential Geometry written by Luther Pfahler Eisenhart and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1940 with Calculus of tensors categories.
Tensor And Vector Analysis
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Author : C. E. Springer
language : en
Publisher: Courier Corporation
Release Date : 2013-09-26
Tensor And Vector Analysis written by C. E. Springer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Mathematics categories.
Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.
An Introduction To Differential Geometrywith Use Of The Tensor Calculus
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Author : Luther Pfahler Eisenhart
language : en
Publisher: Legare Street Press
Release Date : 2023-07-18
An Introduction To Differential Geometrywith Use Of The Tensor Calculus written by Luther Pfahler Eisenhart and has been published by Legare Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-18 with categories.
A classic text on differential geometry, this book offers a comprehensive introduction to the subject for advanced undergraduate and graduate students. It covers topics such as tangent spaces, vector fields, and the curvature tensor, and provides numerous examples and exercises to aid understanding. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Introduction To Differential Geometry With The Use Of Tensor Calculus
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Author : Luther Pfahler Eisenhart
language : en
Publisher: Maugham Press
Release Date : 2008-11
An Introduction To Differential Geometry With The Use Of Tensor Calculus written by Luther Pfahler Eisenhart and has been published by Maugham Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11 with Mathematics categories.
AN INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH USE OF THE TENSOR CALCULUS By LUTHER PFAHLER EISENHART. Preface: Since 1909, when my Differential Geometry of Curves and Surfaces was published, the tensor calculus, which had previously been invented by Ricci, was adopted by Einstein in his General Theory of Relativity, and has been developed further in the study of Riemannian Geometry and various generalizations of the latter. In the present book the tensor calculus of cuclidean 3-space is developed and then generalized so as to apply to a Riemannian space of any number of dimensions. The tensor calculus as here developed is applied in Chapters III and IV to the study of differential geometry of surfaces in 3-space, the material treated being equivalent to what appears in general in the first eight chapters of my former book with such additions as follow from the introduction of the concept of parallelism of Levi-Civita and the content of the tensor calculus. LUTHER PFAHLER EISENHART. Contents include: CHAPTER I CURVES IN SPACE SECTION PAGE 1. Curves ami surfaces. The summation convention 1 2. Length of a curve. Linear element, 8 3. Tangent to a curve. Order of contact. Osculating plane 11 4. Curvature. Principal normal. Circle of curvature 16 5. TBi normal. Torsion 19 6r The Frenet Formulas. The form of a curve in the neighborhood of a point 25 7. Intrinsic equations of a curve 31 8. Involutes and evolutes of a curve 34 9. The tangent surface of a curve. The polar surface. Osculating sphere. . 38 10. Parametric equations of a surface. Coordinates and coordinate curves trT a surface 44 11. 1 Tangent plane to a surface 50 tSffDovelopable surfaces. Envelope of a one-parameter family of surfaces. . 53 CHAPTER II TRANSFORMATION OF COORDINATES. TENSOR CALCULUS 13. Transformation of coordinates. Curvilinear coordinates 63 14. The fundamental quadratic form of space 70 15. Contravariant vectors. Scalars 74 16. Length of a contravariant vector. Angle between two vectors 80 17. Covariant vectors. Contravariant and covariant components of a vector 83 18. Tensors. Symmetric and skew symmetric tensors 89 19. Addition, subtraction and multiplication of tensors. Contraction.... 94 20. The Christoffel symbols. The Riemann tensor 98 21. The Frenet formulas in general coordinates 103 22. Covariant differentiation 107 23. Systems of partial differential equations of the first order. Mixed systems 114 CHAPTER III INTRINSIC GEOMETRY OF A SURFACE 24. Linear element of a surface. First fundamental quadratic form of a surface. Vectors in a surface 123 25. Angle of two intersecting curves in a surface. Element of area 129 26. Families of curves in a surface. Principal directions 138 27. The intrinsic geometry of a surface. Isometric surfaces 146 28. The Christoffel symbols for a surface. The Riemannian curvature tensor. The Gaussian curvature of a surface 149 29. Differential parameters 155 30. Isometric orthogonal nets. Isometric coordinates 161 31...
An Introduction To Differential Geometry With Use Of The Tensor Calculus By Luther Pfahler Eisenhart
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Author : Luther Pfahler Eisenhart
language : en
Publisher:
Release Date : 1947
An Introduction To Differential Geometry With Use Of The Tensor Calculus By Luther Pfahler Eisenhart written by Luther Pfahler Eisenhart and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1947 with categories.
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.
Textbook Of Tensor Calculus And Differential Geometry
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Author : Prasun Kumar Nayak
language : en
Publisher:
Release Date : 2012
Textbook Of Tensor Calculus And Differential Geometry written by Prasun Kumar Nayak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Calculus of tensors categories.
An Introduction To Differential Geometry
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Author : T. J. Willmore
language : en
Publisher: Courier Corporation
Release Date : 2013-05-13
An Introduction To Differential Geometry written by T. J. Willmore and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-13 with Mathematics categories.
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.