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Author: Luther Pfahler Eisenhart
Publisher: Princeton University Press
ISBN: 1400877865
Category : Mathematics
Languages : en
Pages : 315
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Book Description
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.
Author: Luther Pfahler Eisenhart
Publisher: Princeton University Press
ISBN: 1400877865
Category : Mathematics
Languages : en
Pages : 315
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Book Description
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.
Author: PRASUN KUMAR NAYAK
Publisher: PHI Learning Pvt. Ltd.
ISBN: 812034507X
Category : Mathematics
Languages : en
Pages : 551
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Book Description
Primarily intended for the undergraduate and postgraduate students of mathematics, this textbook covers both geometry and tensor in a single volume. This book aims to provide a conceptual exposition of the fundamental results in the theory of tensors. It also illustrates the applications of tensors to differential geometry, mechanics and relativity. Organized in ten chapters, it provides the origin and nature of the tensor along with the scope of the tensor calculus. Besides this, it also discusses N-dimensional Riemannian space, characteristic peculiarity of Riemannian space, intrinsic property of surfaces, and properties and transformation of Christoffel’s symbols. Besides the students of mathematics, this book will be equally useful for the postgraduate students of physics. KEY FEATURES : Contains 250 worked out examples Includes more than 350 unsolved problems Gives thorough foundation in Tensors
Author: Luther Pfahler Eisenhart
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 304
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Book Description
Author: Luther Pfahler Eisenhart
Publisher: Maugham Press
ISBN: 1443722936
Category : Mathematics
Languages : en
Pages : 320
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Book Description
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...
Author: Luther Pfahler Eisenhart
Publisher: Legare Street Press
ISBN: 9781019425824
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Luther Pfahler Eisenhart
Publisher:
ISBN:
Category :
Languages : en
Pages : 312
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Book Description
Author: Shahab Sahraee
Publisher: Springer Nature
ISBN: 3031339533
Category : Technology & Engineering
Languages : en
Pages : 684
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Book Description
The book contains the basics of tensor algebra as well as a comprehensive description of tensor calculus, both in Cartesian and curvilinear coordinates. Some recent developments in representation theorems and differential forms are included. The last part of the book presents a detailed introduction to differential geometry of surfaces and curves which is based on tensor calculus. By solving numerous exercises, the reader is equipped to properly understand the theoretical background and derivations. Many solved problems are provided at the end of each chapter for in-depth learning. All derivations in this text are carried out line by line which will help the reader to understand the basic ideas. Each figure in the book includes descriptive text that corresponds with the theoretical derivations to facilitate rapid learning.
Author: Luther Pfahler Eisenhart
Publisher:
ISBN: 9780486780597
Category : Calculus of tensors
Languages : en
Pages : 320
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Book Description
Having introduced a generation of students to the serious mathematics of relativity theory and Riemannian geometry, this volume remains a valuable guide to today's advanced undergraduates and graduate students. Topics include curves in space, transformation of coordinates, tensor calculus, intrinsic geometry of a surface, and surfaces in space. 1947 edition.
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: Charles Ernest Weatherburn
Publisher: CUP Archive
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 214
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Book Description
