An Introduction To Differential Geometry With The Use Of Tensor Calculus

Author : Luther Pfahler Eisenhart
Publisher : Princeton University Press
Page : 315 pages
File Size : 52,6 Mb
Release : 2015-12-08
Category : Mathematics
ISBN : 9781400877867

Get Book

Introduction to Differential Geometry by Luther Pfahler Eisenhart Pdf

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 : Unknown
Page : 304 pages
File Size : 50,8 Mb
Release : 1940
Category : Calculus of tensors
ISBN : OCLC:13417368

Get Book

An Introduction to Differential Geometry by Luther Pfahler Eisenhart Pdf

Author : Luther Pfahler Eisenhart
Publisher : Maugham Press
Page : 320 pages
File Size : 40,5 Mb
Release : 2008-11
Category : Mathematics
ISBN : 9781443722933

Get Book

An Introduction to Differential Geometry - With the Use of Tensor Calculus by Luther Pfahler Eisenhart Pdf

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
Page : 0 pages
File Size : 49,7 Mb
Release : 2023-07-18
Category : Electronic
ISBN : 1021206423

Get Book

An Introduction To Differential GeometryWith Use Of The Tensor Calculus by Luther Pfahler Eisenhart Pdf

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 : Dipankar De
Publisher : John Wiley & Sons
Page : 516 pages
File Size : 52,9 Mb
Release : 2022-05-24
Category : Mathematics
ISBN : 9781119795629

Get Book

Introduction to Differential Geometry with Tensor Applications by Dipankar De Pdf

INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH TENSOR APPLICATIONS This is the only volume of its kind to explain, in precise and easy-to-understand language, the fundamentals of tensors and their applications in differential geometry and analytical mechanics with examples for practical applications and questions for use in a course setting. Introduction to Differential Geometry with Tensor Applications discusses the theory of tensors, curves and surfaces and their applications in Newtonian mechanics. Since tensor analysis deals with entities and properties that are independent of the choice of reference frames, it forms an ideal tool for the study of differential geometry and also of classical and celestial mechanics. This book provides a profound introduction to the basic theory of differential geometry: curves and surfaces and analytical mechanics with tensor applications. The author has tried to keep the treatment of the advanced material as lucid and comprehensive as possible, mainly by including utmost detailed calculations, numerous illustrative examples, and a wealth of complementing exercises with complete solutions making the book easily accessible even to beginners in the field. Groundbreaking and thought-provoking, this volume is an outstanding primer for modern differential geometry and is a basic source for a profound introductory course or as a valuable reference. It can even be used for self-study, by students or by practicing engineers interested in the subject. Whether for the student or the veteran engineer or scientist, Introduction to Differential Geometry with Tensor Applications is a must-have for any library. This outstanding new volume: Presents a unique perspective on the theories in the field not available anywhere else Explains the basic concepts of tensors and matrices and their applications in differential geometry and analytical mechanics Is filled with hundreds of examples and unworked problems, useful not just for the student, but also for the engineer in the field Is a valuable reference for the professional engineer or a textbook for the engineering student

Author : T. J. Willmore
Publisher : Courier Corporation
Page : 336 pages
File Size : 46,6 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486282107

Get Book

An Introduction to Differential Geometry by T. J. Willmore Pdf

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.

Author : Shahab Sahraee,Peter Wriggers
Publisher : Springer Nature
Page : 684 pages
File Size : 46,5 Mb
Release : 2023-12-12
Category : Technology & Engineering
ISBN : 9783031339530

Get Book

Tensor Calculus and Differential Geometry for Engineers by Shahab Sahraee,Peter Wriggers Pdf

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 : Pavel Grinfeld
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 48,8 Mb
Release : 2013-09-24
Category : Mathematics
ISBN : 9781461478676

Get Book

Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Pavel Grinfeld Pdf

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
Page : 214 pages
File Size : 54,7 Mb
Release : 1938
Category : Calculus of tensors
ISBN : 8210379456XXX

Get Book

An Introduction to Riemannian Geometry and the Tensor Calculus by Charles Ernest Weatherburn Pdf

Author : Luther Pfahler Eisenhart
Publisher : Unknown
Page : 320 pages
File Size : 44,7 Mb
Release : 2014-07
Category : Calculus of tensors
ISBN : 0486780597

Get Book

An Introduction to Differential Geometry by Luther Pfahler Eisenhart Pdf

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 : PRASUN KUMAR NAYAK
Publisher : PHI Learning Pvt. Ltd.
Page : 551 pages
File Size : 48,8 Mb
Release : 2011-12-23
Category : Mathematics
ISBN : 9788120345072

Get Book

TEXTBOOK OF TENSOR CALCULUS AND DIFFERENTIAL GEOMETRY by PRASUN KUMAR NAYAK Pdf

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 : K.K. Dube
Publisher : I. K. International Pvt Ltd
Page : 377 pages
File Size : 41,7 Mb
Release : 2013-12-30
Category : Mathematics
ISBN : 9789380026589

Get Book

Differential Geometry and Tensors by K.K. Dube Pdf

The purpose of this book is to give a simple, lucid, rigorous and comprehensive account of fundamental notions of Differential Geometry and Tensors. The book is self-contained and divided in two parts. Section A deals with Differential Geometry and Section B is devoted to the study of Tensors. Section A deals with: " Theory of curves, envelopes and developables. " Curves on surfaces and fundamental magnitudes, curvature of surfaces and lines of curvature. " Fundamental equations of surface theory. " Geodesics. Section B deals with: " Tensor algebra. " Tensor calculus. " Christoffel symbols and their properties. " Riemann symbols and Einstein space, and their properties. " Physical components of contravariant and covariant vectors. " Geodesics and Parallelism of vectors. " Differentiable manifolds, charts, atlases.

Author : Thomas J. Willmore
Publisher : Unknown
Page : 317 pages
File Size : 49,8 Mb
Release : 1961
Category : Geometry, Differential
ISBN : OCLC:490250721

Get Book

An Introduction to Differential Geometry by Thomas J. Willmore Pdf

Author : Tracy Y. Thomas
Publisher : Elsevier
Page : 128 pages
File Size : 50,9 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483263717

Get Book

Concepts from Tensor Analysis and Differential Geometry by Tracy Y. Thomas Pdf

Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.

Author : Taha Sochi
Publisher : Taha Sochi
Page : 252 pages
File Size : 48,7 Mb
Release : 2022-09-14
Category : Mathematics
ISBN : 8210379456XXX

Get Book

Introduction to Differential Geometry of Space Curves and Surfaces by Taha Sochi Pdf

This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.