Introduction To Differential Geometry For Engineers

Author : Brian F. Doolin,Clyde F. Martin
Publisher : Courier Corporation
Page : 178 pages
File Size : 44,8 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486281940

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Introduction to Differential Geometry for Engineers by Brian F. Doolin,Clyde F. Martin Pdf

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.

Author : Brian F. Doolin,Clyde F. Martin
Publisher : Courier Corporation
Page : 178 pages
File Size : 40,6 Mb
Release : 2012-01-01
Category : Mathematics
ISBN : 9780486488165

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Introduction to Differential Geometry for Engineers by Brian F. Doolin,Clyde F. Martin Pdf

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.

Author : Brian F. Doolin,Clyde F. Martin
Publisher : Unknown
Page : 183 pages
File Size : 44,6 Mb
Release : 2024-05-13
Category : Electronic
ISBN : 060808929X

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Introduction to Differential Geometry for Engineers by Brian F. Doolin,Clyde F. Martin Pdf

Author : William L. Burke
Publisher : Cambridge University Press
Page : 440 pages
File Size : 51,7 Mb
Release : 1985-05-31
Category : Mathematics
ISBN : 0521269296

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Applied Differential Geometry by William L. Burke Pdf

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.

Author : B. F. Doolin
Publisher : Unknown
Page : 76 pages
File Size : 44,6 Mb
Release : 1982
Category : Electronic
ISBN : NASA:31769000525603

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Global Differential Geometry: An Introduction for Control Engineers by B. F. Doolin Pdf

Author : Chris J. Isham
Publisher : Allied Publishers
Page : 308 pages
File Size : 44,7 Mb
Release : 2002
Category : Geometry, Differential
ISBN : 8177643169

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Modern Differential Geometry for Physicists by Chris J. Isham Pdf

Author : Joel W. Robbin,Dietmar A. Salamon
Publisher : Springer Nature
Page : 426 pages
File Size : 46,7 Mb
Release : 2022-01-12
Category : Mathematics
ISBN : 9783662643402

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Introduction to Differential Geometry by Joel W. Robbin,Dietmar A. Salamon Pdf

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.

Author : William Munger Boothby
Publisher : Gulf Professional Publishing
Page : 444 pages
File Size : 49,6 Mb
Release : 2003
Category : Mathematics
ISBN : 0121160513

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An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised by William Munger Boothby Pdf

The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields

Author : Walter A. Poor
Publisher : Courier Corporation
Page : 352 pages
File Size : 52,5 Mb
Release : 2015-04-27
Category : Mathematics
ISBN : 9780486151915

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Differential Geometric Structures by Walter A. Poor Pdf

This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.

Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 646 pages
File Size : 55,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9780387217529

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Introduction to Smooth Manifolds by John M. Lee Pdf

Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why

Author : T. J. Willmore
Publisher : Courier Corporation
Page : 336 pages
File Size : 40,5 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486282107

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An Introduction to Differential Geometry by T. J. Willmore Pdf

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 : John Oprea
Publisher : MAA
Page : 508 pages
File Size : 42,6 Mb
Release : 2007-09-06
Category : Mathematics
ISBN : 0883857480

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Differential Geometry and Its Applications by John Oprea Pdf

This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.

Author : Loring W. Tu
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 52,7 Mb
Release : 2010-10-05
Category : Mathematics
ISBN : 9781441974006

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An Introduction to Manifolds by Loring W. Tu Pdf

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Author : Dipankar De
Publisher : John Wiley & Sons
Page : 516 pages
File Size : 53,5 Mb
Release : 2022-05-24
Category : Mathematics
ISBN : 9781119795629

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Introduction to Differential Geometry with Tensor Applications by Dipankar De Pdf

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 : Leonor Godinho,José Natário
Publisher : Springer
Page : 467 pages
File Size : 51,5 Mb
Release : 2014-07-26
Category : Mathematics
ISBN : 9783319086668

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An Introduction to Riemannian Geometry by Leonor Godinho,José Natário Pdf

Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.