Differential Topology With A View To Applications
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Differential Topology With A View To Applications
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Author : David Chillingworth
language : en
Publisher: Fearon Publishers
Release Date : 1976
Differential Topology With A View To Applications written by David Chillingworth and has been published by Fearon Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
Differential Geometry And Topology
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Author : Keith Burns
language : en
Publisher: CRC Press
Release Date : 2005-05-27
Differential Geometry And Topology written by Keith Burns and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-27 with Mathematics categories.
Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field.
Algebraic And Differential Topology Of Robust Stability
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Author : Edmond A. Jonckheere
language : en
Publisher: Oxford University Press
Release Date : 1997-05-29
Algebraic And Differential Topology Of Robust Stability written by Edmond A. Jonckheere and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-29 with Mathematics categories.
In this book, two seemingly unrelated fields -- algebraic topology and robust control -- are brought together. The book develops algebraic/differential topology from an application-oriented point of view. The book takes the reader on a path starting from a well-motivated robust stability problem, showing the relevance of the simplicial approximation theorem and how it can be efficiently implemented using computational geometry. The simplicial approximation theorem serves as a primer to more serious topological issues such as the obstruction to extending the Nyquist map, K-theory of robust stabilization, and eventually the differential topology of the Nyquist map, culminating in the explanation of the lack of continuity of the stability margin relative to rounding errors. The book is suitable for graduate students in engineering and/or applied mathematics, academic researchers and governmental laboratories.
Topology From The Differentiable Viewpoint
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Author : John Willard Milnor
language : en
Publisher: Princeton University Press
Release Date : 1997-12-14
Topology From The Differentiable Viewpoint written by John Willard Milnor 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 1997-12-14 with Mathematics categories.
This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.
Differential Topology And Geometry With Applications To Physics
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Author : Eduardo Nahmad-Achar
language : en
Publisher:
Release Date : 2018
Differential Topology And Geometry With Applications To Physics written by Eduardo Nahmad-Achar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Geometry, Differential categories.
"Differential geometry has encountered numerous applications in physics. More and more physical concepts can be understood as a direct consequence of geometric principles. The mathematical structure of Maxwell's electrodynamics, of the general theory of relativity, of string theory, and of gauge theories, to name but a few, are of a geometric nature. All of these disciplines require a curved space for the description of a system, and we require a mathematical formalism that can handle the dynamics in such spaces if we wish to go beyond a simple and superficial discussion of physical relationships. This formalism is precisely differential geometry. Even areas like thermodynamics and fluid mechanics greatly benefit from a differential geometric treatment. Not only in physics, but in important branches of mathematics has differential geometry effected important changes. Aimed at graduate students and requiring only linear algebra and differential and integral calculus, this book presents, in a concise and direct manner, the appropriate mathematical formalism and fundamentals of differential topology and differential geometry together with essential applications in many branches of physics." -- Prové de l'editor.
Differential Topology
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Author : David B. Gauld
language : en
Publisher:
Release Date : 1982
Differential Topology written by David B. Gauld and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Originally published: New York: M. Dekker, 1982.
Differential Topology
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Author : Victor Guillemin
language : en
Publisher: Prentice Hall
Release Date : 1974
Differential Topology written by Victor Guillemin and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
This text fits any course with the word "Manifold" in the title. It is a graduate level book.
Introduction To Differential Topology
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Author : Theodor Bröcker
language : en
Publisher:
Release Date : 2007
Introduction To Differential Topology written by Theodor Bröcker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Differential topology categories.
Differential Forms In Algebraic Topology
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Author : Raoul Bott
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Differential Forms In Algebraic Topology written by Raoul Bott 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 2013-04-17 with Mathematics categories.
Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
Introduction To Differential Topology
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Author : Theodor Bröcker
language : en
Publisher: Cambridge University Press
Release Date : 1982-09-16
Introduction To Differential Topology written by Theodor Bröcker 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 1982-09-16 with Mathematics categories.
This book is intended as an elementary introduction to differential manifolds. The authors concentrate on the intuitive geometric aspects and explain not only the basic properties but also teach how to do the basic geometrical constructions. An integral part of the work are the many diagrams which illustrate the proofs. The text is liberally supplied with exercises and will be welcomed by students with some basic knowledge of analysis and topology.