Introduction to Differential Geometry with Tensor Applications PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Introduction to Differential Geometry with Tensor Applications PDF full book. Access full book title Introduction to Differential Geometry with Tensor Applications by Dipankar De. Download full books in PDF and EPUB format.
Author: Dipankar De Publisher: John Wiley & Sons ISBN: 1119795621 Category : Mathematics Languages : en Pages : 516
Book Description
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: Dipankar De Publisher: John Wiley & Sons ISBN: 1119795621 Category : Mathematics Languages : en Pages : 516
Book Description
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: Luther Pfahler Eisenhart Publisher: Princeton University Press ISBN: 1400877865 Category : Mathematics Languages : en Pages : 315
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: C. E. Springer Publisher: Courier Corporation ISBN: 048632091X Category : Mathematics Languages : en Pages : 256
Book Description
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.
Author: K.K. Dube Publisher: I. K. International Pvt Ltd ISBN: 9380026587 Category : Mathematics Languages : en Pages : 377
Book Description
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: T. J. Willmore Publisher: Courier Corporation ISBN: 0486282104 Category : Mathematics Languages : en Pages : 336
Book Description
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: Nail H. Ibragimov Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110379503 Category : Mathematics Languages : en Pages : 197
Book Description
This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.
Author: Philippe G. Ciarlet Publisher: Springer Science & Business Media ISBN: 1402042485 Category : Technology & Engineering Languages : en Pages : 212
Book Description
curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, begins by a detailed description of the nonlinear and linear equations proposed by W.T. Koiter for modeling thin elastic shells. These equations are “two-dimensional”, in the sense that they are expressed in terms of two curvilinear coordinates used for de?ning the middle surface of the shell. The existence, uniqueness, and regularity of solutions to the linear Koiter equations is then established, thanks this time to a fundamental “Korn inequality on a surface” and to an “in?nit- imal rigid displacement lemma on a surface”. This chapter also includes a brief introduction to other two-dimensional shell equations. Interestingly, notions that pertain to di?erential geometry per se,suchas covariant derivatives of tensor ?elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory. Occasionally, portions of the material covered here are adapted from - cerpts from my book “Mathematical Elasticity, Volume III: Theory of Shells”, published in 2000by North-Holland, Amsterdam; in this respect, I am indebted to Arjen Sevenster for his kind permission to rely on such excerpts. Oth- wise, the bulk of this work was substantially supported by two grants from the Research Grants Council of Hong Kong Special Administrative Region, China [Project No. 9040869, CityU 100803 and Project No. 9040966, CityU 100604].
Author: PRASUN KUMAR NAYAK Publisher: PHI Learning Pvt. Ltd. ISBN: 812034507X Category : Mathematics Languages : en Pages : 551
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: Read Books Ltd ISBN: 1446545458 Category : Mathematics Languages : en Pages : 379
Book Description
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.
Author: Dipankar De
Author: Dipankar De
Author: Luther Pfahler Eisenhart
Author: C. E. Springer
Author: K.K. Dube
Author: Richard L. Bishop
Author: T. J. Willmore
Author: Nail H. Ibragimov
Author: Philippe G. Ciarlet
Author: PRASUN KUMAR NAYAK
Author: Luther Pfahler Eisenhart