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
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 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].
Differential Geometry
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Author : Ta-tsien Li
language : en
Publisher: World Scientific
Release Date : 2008
Differential Geometry written by Ta-tsien Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a self-contained and accessible manner. Although the field is often considered a OC classicalOCO one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role.The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and mesh generation in finite element methods.This volume will be very useful to graduate students and researchers in pure and applied mathematics."
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.
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.
Tensor Analysis On Manifolds
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Author : Richard L. Bishop
language : en
Publisher: Courier Corporation
Release Date : 1980-12-01
Tensor Analysis On Manifolds written by Richard L. Bishop and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-12-01 with Mathematics categories.
Striking just the right balance between formal and abstract approaches, this text proceeds from generalities to specifics. Topics include function-theoretical and algebraic aspects, manifolds and integration theory, several important structures, and adaptation to classical mechanics. "First-rate. . . deserves to be widely read." — American Mathematical Monthly. 1980 edition.
Tensor Analysis
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Author : Ivan Stephen Sokolnikoff
language : en
Publisher: Malabar, Fla. : R.E. Krieger Publishing Company
Release Date : 1990
Tensor Analysis written by Ivan Stephen Sokolnikoff and has been published by Malabar, Fla. : R.E. Krieger Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Calculus of tensors categories.
Introduction To Numerical Linear Algebra And Optimisation
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Author : Philippe G. Ciarlet
language : en
Publisher: Cambridge University Press
Release Date : 1989-08-25
Introduction To Numerical Linear Algebra And Optimisation written by Philippe G. Ciarlet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-25 with Computers categories.
The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation. The prerequisites are some familiarity with the basic properties of matrices, finite-dimensional vector spaces, advanced calculus, and some elementary notations from functional analysis. The book is in two parts. The first deals with numerical linear algebra (review of matrix theory, direct and iterative methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimisation (general algorithms, linear and nonlinear programming). The author has based the book on courses taught for advanced undergraduate and beginning graduate students and the result is a well-organised and lucid exposition. Summaries of basic mathematics are provided, proofs of theorems are complete yet kept as simple as possible, and applications from physics and mechanics are discussed. Professor Ciarlet has also helpfully provided over 40 line diagrams, a great many applications, and a useful guide to further reading. This excellent textbook, which is translated and revised from the very successful French edition, will be of great value to students of numerical analysis, applied mathematics and engineering.
Manifolds Tensors And Forms
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Author : Paul Renteln
language : en
Publisher: Cambridge University Press
Release Date : 2014
Manifolds Tensors And Forms written by Paul Renteln and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.