Introduction To Differential Geometry
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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.
Introduction To Differential Geometry For Engineers
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Author : Brian F. Doolin
language : en
Publisher: Courier Corporation
Release Date : 2012-01-01
Introduction To Differential Geometry For Engineers written by Brian F. Doolin 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.
This outstanding guide supplies important mathematical tools for diverse engineering applications, offering engineers the basic concepts and terminology of modern global differential geometry. Suitable for independent study as well as a supplementary text for advanced undergraduate and graduate courses, this volume also constitutes a valuable reference for control, systems, aeronautical, electrical, and mechanical engineers. The treatment's ideas are applied mainly as an introduction to the Lie theory of differential equations and to examine the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, vector fields, exterior algebra, and Lie algebras. An appendix reviews concepts related to vector calculus, including open and closed sets, compactness, continuity, and derivative.
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 And Topology In Mathematical Physics
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Author : Wang Rong
language : en
Publisher: World Scientific
Release Date : 1999-01-18
An Introduction To Differential Geometry And Topology In Mathematical Physics written by Wang Rong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-18 with Mathematics categories.
This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics.
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].
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.
Introduction To Differential Geometry Of Space Curves And Surfaces
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Author : Taha Sochi
language : en
Publisher: Taha Sochi
Release Date : 2022-09-14
Introduction To Differential Geometry Of Space Curves And Surfaces written by Taha Sochi and has been published by Taha Sochi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-14 with Mathematics categories.
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.
Introduction To Differential Geometry
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Author : Abraham Goetz
language : en
Publisher:
Release Date : 1970
Introduction To Differential Geometry written by Abraham Goetz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
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.
An Introduction To Differential Geometry
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Author : Thomas James Willmore
language : en
Publisher:
Release Date : 1966
An Introduction To Differential Geometry written by Thomas James Willmore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.