Introduction To Differential Geometry With Tensor Applications
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Introduction To Differential Geometry With Tensor Applications
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Author : Dipankar De
language : en
Publisher: John Wiley & Sons
Release Date : 2022-05-24
Introduction To Differential Geometry With Tensor Applications written by Dipankar De and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-24 with Mathematics categories.
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
An Introduction To Differential Geometry With Applications To Elasticity
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Author : Philippe G. Ciarlet
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-28
An Introduction To Differential Geometry With Applications To Elasticity written by Philippe G. Ciarlet 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 2006-06-28 with Technology & Engineering categories.
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].
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 : T. J. Willmore
language : en
Publisher: Courier Corporation
Release Date : 2012-01-01
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 2012-01-01 with Mathematics categories.
A solid introduction to the methods of differential geometry and tensor calculus, this volume is suitable for advanced undergraduate and graduate students of mathematics, physics, and engineering. Rather than a comprehensive account, it offers an introduction to the essential ideas and methods of differential geometry. Part 1 begins by employing vector methods to explore the classical theory of curves and surfaces. An introduction to the differential geometry of surfaces in the large provides students with ideas and techniques involved in global research. Part 2 introduces the concept of a tensor, first in algebra, then in calculus. It covers the basic theory of the absolute calculus and the fundamentals of Riemannian geometry. Worked examples and exercises appear throughout the text.
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.
An Introduction To Differential Geometry
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Author : Luther Pfahler Eisenhart
language : en
Publisher:
Release Date : 1947
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 1947 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.
Introduction To Differential Geometry
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Author : Joel W. Robbin
language : en
Publisher: Springer Nature
Release Date : 2022-01-12
Introduction To Differential Geometry written by Joel W. Robbin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-12 with Mathematics categories.
This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
Introductory Differential Geometry For Physicists
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Author : A Visconti
language : en
Publisher: World Scientific Publishing Company
Release Date : 1992-10-09
Introductory Differential Geometry For Physicists written by A Visconti and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-10-09 with categories.
This book develops the mathematics of differential geometry in a way more intelligible to physicists and other scientists interested in this field. This book is basically divided into 3 levels; level 0, the nearest to intuition and geometrical experience, is a short summary of the theory of curves and surfaces; level 1 repeats, comments and develops upon the traditional methods of tensor algebra analysis and level 2 is an introduction to the language of modern differential geometry. A final chapter (chapter IV) is devoted to fibre bundles and their applications to physics. Exercises are provided to amplify the text material.
Introduction To Differential Geometry With Applications To Navier Stokes Dynamics
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Author : Troy L Story
language : en
Publisher: iUniverse
Release Date : 2005
Introduction To Differential Geometry With Applications To Navier Stokes Dynamics written by Troy L Story and has been published by iUniverse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Geometry, Differential categories.
Introduction to Differential Geometry with applications to Navier-Stokes Dynamics is an invaluable manuscript for anyone who wants to understand and use exterior calculus and differential geometry, the modern approach to calculus and geometry. Author Troy Story makes use of over thirty years of research experience to provide a smooth transition from conventional calculus to exterior calculus and differential geometry, assuming only a knowledge of conventional calculus. Introduction to Differential Geometry with applications to Navier-Stokes Dynamics includes the topics: Geometry, Exterior calculus, Homology and co-homology, Applications of differential geometry and exterior calculus to: Hamiltonian mechanics, geometric optics, irreversible thermodynamics, black hole dynamics, electromagnetism, classical string fields, and Navier-Stokes dynamics.