Download or read book Differential Manifolds and Theoretical Physics written by and published by Academic Press. This book was released on 1985-05-24 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Manifolds and Theoretical Physics
Download or read book Differentiable Manifolds written by Gerardo F. Torres del Castillo and published by Springer Nature. This book was released on 2020-06-23 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Geometry and Mathematical Physics written by Gerd Rudolph and published by Springer Science & Business Media. This book was released on 2012-11-09 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
Download or read book Differential Geometry For Physicists written by Bo-yu Hou and published by World Scientific Publishing Company. This book was released on 1997-10-31 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.
Download or read book An Introduction to Differential Manifolds written by Jacques Lafontaine and published by Springer. This book was released on 2015-07-29 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Manifolds A Basic Approach For Experimental Physicists written by Paul Baillon and published by World Scientific Publishing Company. This book was released on 2013-11-22 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Manifold is the framework of particle physics and astrophysics nowadays. It is important for all research physicists to be well accustomed to it and even experimental physicists should be able to manipulate equations and expressions in that framework.This book gives a comprehensive description of the basics of differential manifold with a full proof of any element. A large part of the book is devoted to the basic mathematical concepts in which all necessary for the development of the differential manifold is expounded and fully proved.This book is self-consistent: it starts from first principles. The mathematical framework is the set theory with its axioms and its formal logic. No special knowledge is needed.
Download or read book Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics written by Steinar Johannesen and published by CRC Press. This book was released on 2016-12-08 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics provides complete and rigorous proofs of all the results presented within. Among the themes illustrated in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. It can be used as a textbook for a pure mathematics course in differential geometry, assuming the reader has a good understanding of basic analysis, linear algebra and point set topology. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories.
Download or read book Analysis and Algebra on Differentiable Manifolds A Workbook for Students and Teachers written by P.M. Gadea and published by Springer Science & Business Media. This book was released on 2009-12-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modern Differential Geometry for Physicists written by Chris J. Isham and published by Allied Publishers. This book was released on 2002 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometrical Methods of Mathematical Physics written by Bernard F. Schutz and published by Cambridge University Press. This book was released on 1980-01-28 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
Download or read book Differential Geometry Gauge Theories and Gravity written by M. Göckeler and published by Cambridge University Press. This book was released on 1989-07-28 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.
Download or read book A Course in Modern Mathematical Physics written by Peter Szekeres and published by Cambridge University Press. This book was released on 2004-12-16 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.
Download or read book Differential Geometry and Lie Groups for Physicists written by Marián Fecko and published by Cambridge University Press. This book was released on 2006-10-12 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.
Download or read book Differentiable Manifolds written by Lawrence Conlon and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Geometry written by Clifford Taubes and published by Oxford University Press. This book was released on 2011-10-13 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bundles, connections, metrics and curvature are the lingua franca of modern differential geometry and theoretical physics. Supplying graduate students in mathematics or theoretical physics with the fundamentals of these objects, this book would suit a one-semester course on the subject of bundles and the associated geometry.
Download or read book Introduction to Topological Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Download or read book Topology and Geometry for Physicists written by Charles Nash and published by Courier Corporation. This book was released on 2013-08-16 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.
