An Introductory Course On Differentiable Manifolds
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An Introductory Course On Differentiable Manifolds
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Author : Siavash Shahshahani
language : en
Publisher: Courier Dover Publications
Release Date : 2017-03-23
An Introductory Course On Differentiable Manifolds written by Siavash Shahshahani and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-23 with Mathematics categories.
Based on author Siavash Shahshahani's extensive teaching experience, this volume presents a thorough, rigorous course on the theory of differentiable manifolds. Geared toward advanced undergraduates and graduate students in mathematics, the treatment's prerequisites include a strong background in undergraduate mathematics, including multivariable calculus, linear algebra, elementary abstract algebra, and point set topology. More than 200 exercises offer students ample opportunity to gauge their skills and gain additional insights. The four-part treatment begins with a single chapter devoted to the tensor algebra of linear spaces and their mappings. Part II brings in neighboring points to explore integrating vector fields, Lie bracket, exterior derivative, and Lie derivative. Part III, involving manifolds and vector bundles, develops the main body of the course. The final chapter provides a glimpse into geometric structures by introducing connections on the tangent bundle as a tool to implant the second derivative and the derivative of vector fields on the base manifold. Relevant historical and philosophical asides enhance the mathematical text, and helpful Appendixes offer supplementary material.
Differentiable Manifolds
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Author : Lawrence Conlon
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Differentiable Manifolds written by Lawrence Conlon 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.
This book is based on the full year Ph.D. qualifying course on differentiable manifolds, global calculus, differential geometry, and related topics, given by the author at Washington University several times over a twenty year period. It is addressed primarily to second year graduate students and well prepared first year students. Presupposed is a good grounding in general topology and modern algebra, especially linear algebra and the analogous theory of modules over a commutative, unitary ring. Although billed as a "first course" , the book is not intended to be an overly sketchy introduction. Mastery of this material should prepare the student for advanced topics courses and seminars in differen tial topology and geometry. There are certain basic themes of which the reader should be aware. The first concerns the role of differentiation as a process of linear approximation of non linear problems. The well understood methods of linear algebra are then applied to the resulting linear problem and, where possible, the results are reinterpreted in terms of the original nonlinear problem. The process of solving differential equations (i. e., integration) is the reverse of differentiation. It reassembles an infinite array of linear approximations, result ing from differentiation, into the original nonlinear data. This is the principal tool for the reinterpretation of the linear algebra results referred to above.
Differentiable Manifolds
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Author : Karo Maestro
language : en
Publisher:
Release Date : 2019-07-30
Differentiable Manifolds written by Karo Maestro and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-30 with categories.
The study of the basic elements of smooth manifolds is one of the most important courses for mathematics and physics graduate students. Inexpensively priced and quality textbooks on the subject are currently particularly scarce. Matshushima's book is a welcome addition to the literature in a very low priced edition. The prerequisites for the course are solid undergraduate courses in real analysis of several variables, linear and abstract algebra and point-set topology. A previous classical differential geometry course on curve and surface theory isn't really necessary, but will greatly enhance a first course in manifolds by supplying many low-dimensional examples in ℝn . The standard topics for such a course are all covered masterfully and concisely: Differentiable manifolds and their atlases, smooth mappings, immersions and embeddings, submanifolds, multilinear algebra, Lie groups and algebras, integration of differential forms and much more. This book is remarkable in it's clarity and range, more so then most other introductions of the subject. Not only does it cover more material then most introductions to manifolds in a concise but readable manner, but it covers in detail several topics most introductions do not, such as homogeneous spaces and Lie subgroups. Most significantly, it covers a major topic that most books at this level avoid: complex and almost complex manifolds. Despite the fact complex and almost complex manifolds are incredibly important in both pure mathematics and mathematical physics-they play important roles in both differential and algebraic geometry, as well as in the modern formulation of geometry in general relativity, particularly in modeling spacetime curvature near conditions of extreme gravitational force such as neutron stars and black holes -almost all introductory textbooks on differentiable manifolds vehemently avoid both. Part of the reason is the subject's difficulty once one gets past the most basic elements, which is considerable and requires sophisticated machinery from algebra and topology such as sheaves and cohomology. Another reason is that complex manifolds are important in both differential geometry and its' sister subject, algebraic geometry-and it's difficult sometimes to separate these aspects. By discussing only the barest essentials of complex manifolds, Mashushima avoids both these problems. This unique content usually absent in introductory texts and presented by a master makes the book far more valuable as a supplementary and reference text. Blue Collar Scholar is now proud to republish this lost classic in an inexpensive new edition for strong undergraduates and first year graduate students of both mathematics and the physical sciences.BCS founder Karo Maestro has added his usual personal touch with a preface introducing the student to smooth manifolds and a recommended reading list for further study. Matsushima's book is a wonderful, self contained and inexpensive basis for a first course on the subject that will provide a strong foundation for either subsequent courses in differential geometry or advanced courses on smooth manifold theor
A First Course In Differential Geometry
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Author : Izu Vaisman
language : en
Publisher: CRC Press
Release Date : 2020-11-26
A First Course In Differential Geometry written by Izu Vaisman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.
This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.
Introduction To Differentiable Manifolds
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Author : Louis Auslander
language : en
Publisher: Courier Corporation
Release Date : 2012-10-30
Introduction To Differentiable Manifolds written by Louis Auslander and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Mathematics categories.
This text presents basic concepts in the modern approach to differential geometry. Topics include Euclidean spaces, submanifolds, and abstract manifolds; fundamental concepts of Lie theory; fiber bundles; and multilinear algebra. 1963 edition.
An Introduction To Differentiable Manifolds And Riemannian Geometry
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Author :
language : en
Publisher: Academic Press
Release Date : 1986-04-21
An Introduction To Differentiable Manifolds And Riemannian Geometry written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-04-21 with Mathematics categories.
An Introduction to Differentiable Manifolds and Riemannian Geometry
Differentiable Manifolds
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Author : Yozō Matsushima
language : en
Publisher:
Release Date : 1972
Differentiable Manifolds written by Yozō Matsushima and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
"The intention of this book is to provide an introduction to the theory of differential manifolds and Lie groups. The book is designed as an advanced undergraduate course or an introductory graduate course and assumes a knowledge of the elements of algebra (vector spaces, groups), point set topology, and some amount of basic analysis."--from the Preface.
An Introduction To Differential Manifolds
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Author : Barden Dennis
language : en
Publisher: World Scientific
Release Date : 2003-03-12
An Introduction To Differential Manifolds written by Barden Dennis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-12 with Mathematics categories.
This invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology. Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincaré-Hopf theorem relating the Euler number of a manifold and the index of a vector field. Each chapter contains exercises of varying difficulty for which solutions are provided. Special features include examples drawn from geometric manifolds in dimension 3 and Brieskorn varieties in dimensions 5 and 7, as well as detailed calculations for the cohomology groups of spheres and tori.
Manifolds And Differential Geometry
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Author : Jeffrey M. Lee
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-08
Manifolds And Differential Geometry written by Jeffrey M. Lee and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-08 with Mathematics categories.
Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.
An Introduction To Differentiable Manifolds And Riemannian Geometry
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Author : William Munger Boothby
language : en
Publisher:
Release Date : 1975
An Introduction To Differentiable Manifolds And Riemannian Geometry written by William Munger Boothby and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.