Differentiable Manifolds PDF Download
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Author | : Lawrence Conlon |
Publisher | : Springer Science & Business Media |
Total Pages | : 402 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475722842 |
Download Differentiable Manifolds Book in PDF, ePub and Kindle
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.
Author | : Frank W. Warner |
Publisher | : Springer Science & Business Media |
Total Pages | : 283 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 1475717997 |
Download Foundations of Differentiable Manifolds and Lie Groups Book in PDF, ePub and Kindle
Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.
Author | : Antoni A. Kosinski |
Publisher | : Courier Corporation |
Total Pages | : 290 |
Release | : 2013-07-02 |
Genre | : Mathematics |
ISBN | : 048631815X |
Download Differential Manifolds Book in PDF, ePub and Kindle
Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.
Author | : William Munger Boothby |
Publisher | : Gulf Professional Publishing |
Total Pages | : 444 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9780121160517 |
Download An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised Book in PDF, ePub and Kindle
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 | : P.M. Gadea |
Publisher | : Springer Science & Business Media |
Total Pages | : 446 |
Release | : 2009-12-12 |
Genre | : Mathematics |
ISBN | : 9048135648 |
Download Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers Book in PDF, ePub and Kindle
A famous Swiss professor gave a student’s course in Basel on Riemann surfaces. After a couple of lectures, a student asked him, “Professor, you have as yet not given an exact de nition of a Riemann surface.” The professor answered, “With Riemann surfaces, the main thing is to UNDERSTAND them, not to de ne them.” The student’s objection was reasonable. From a formal viewpoint, it is of course necessary to start as soon as possible with strict de nitions, but the professor’s - swer also has a substantial background. The pure de nition of a Riemann surface— as a complex 1-dimensional complex analytic manifold—contributes little to a true understanding. It takes a long time to really be familiar with what a Riemann s- face is. This example is typical for the objects of global analysis—manifolds with str- tures. There are complex concrete de nitions but these do not automatically explain what they really are, what we can do with them, which operations they really admit, how rigid they are. Hence, there arises the natural question—how to attain a deeper understanding? One well-known way to gain an understanding is through underpinning the d- nitions, theorems and constructions with hierarchies of examples, counterexamples and exercises. Their choice, construction and logical order is for any teacher in global analysis an interesting, important and fun creating task.
Author | : Loring W. Tu |
Publisher | : Springer Science & Business Media |
Total Pages | : 426 |
Release | : 2010-10-05 |
Genre | : Mathematics |
ISBN | : 1441974008 |
Download An Introduction to Manifolds Book in PDF, ePub and Kindle
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 | : Jacques Lafontaine |
Publisher | : Springer |
Total Pages | : 408 |
Release | : 2015-07-29 |
Genre | : Mathematics |
ISBN | : 3319207350 |
Download An Introduction to Differential Manifolds Book in PDF, ePub and Kindle
This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory. The original French text Introduction aux variétés différentielles has been a best-seller in its category in France for many years. Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.
Author | : Gerardo F. Torres del Castillo |
Publisher | : Springer Nature |
Total Pages | : 447 |
Release | : 2020-06-23 |
Genre | : Mathematics |
ISBN | : 3030451933 |
Download Differentiable Manifolds Book in PDF, ePub and Kindle
This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. Included throughout the book are a collection of exercises of varying degrees of difficulty. Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, and differential equations and a basic knowledge of analytical mechanics.
Author | : Michael Spivak |
Publisher | : Westview Press |
Total Pages | : 164 |
Release | : 1965 |
Genre | : Science |
ISBN | : 9780805390216 |
Download Calculus on Manifolds Book in PDF, ePub and Kindle
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
Author | : John M. Lee |
Publisher | : Springer Science & Business Media |
Total Pages | : 646 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 0387217525 |
Download Introduction to Smooth Manifolds Book in PDF, ePub and Kindle
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