Applied Differential Geometry A Modern Introduction
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Applied Differential Geometry A Modern Introduction
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Author : Vladimir G Ivancevic
language : en
Publisher: World Scientific
Release Date : 2007-05-21
Applied Differential Geometry A Modern Introduction written by Vladimir G Ivancevic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-21 with Mathematics categories.
This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator — “Human Biodynamics Engine”, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools — this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.
Applied Differential Geometry
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Author : William L. Burke
language : en
Publisher: Cambridge University Press
Release Date : 1985-05-31
Applied Differential Geometry written by William L. Burke 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 1985-05-31 with Mathematics categories.
This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.
Modern Differential Geometry For Physicists
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Author : Chris J. Isham
language : en
Publisher: Allied Publishers
Release Date : 2002
Modern Differential Geometry For Physicists written by Chris J. Isham and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Geometry, Differential categories.
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.
Introduction To Differential Geometry For Engineers
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Author : Brian F. Doolin
language : en
Publisher: Courier Corporation
Release Date : 2013-05-13
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 2013-05-13 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.
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."
Differential Geometry And Its Applications
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Author : John Oprea
language : en
Publisher: MAA
Release Date : 2007-09-06
Differential Geometry And Its Applications written by John Oprea and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-06 with Mathematics categories.
This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.
Differential Geometry
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Author : Heinrich W. Guggenheimer
language : en
Publisher: Courier Corporation
Release Date : 2012-04-27
Differential Geometry written by Heinrich W. Guggenheimer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-27 with Mathematics categories.
This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.
Modern Differential Geometry Of Curves And Surfaces With Mathematica
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Author : Elsa Abbena
language : en
Publisher: CRC Press
Release Date : 2017-09-06
Modern Differential Geometry Of Curves And Surfaces With Mathematica written by Elsa Abbena and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.
Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions. The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.
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.