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Author : Paul Renteln
Publisher : Cambridge University Press
Page : 343 pages
File Size : 55,6 Mb
Release : 2014
Category : Mathematics
ISBN : 9781107042193
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.
Author : Ralph Abraham,Jerrold E. Marsden,Tudor Ratiu
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210290
The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.
Author : David Lovelock,Hanno Rund
Publisher : Courier Corporation
Page : 400 pages
File Size : 48,8 Mb
Release : 2012-04-20
Category : Mathematics
ISBN : 9780486131986
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
Author : Richard L. Bishop,Samuel I. Goldberg
Publisher : Courier Corporation
Page : 288 pages
File Size : 55,5 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486139234
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Author : Jon Pierre Fortney
Publisher : Springer
Page : 468 pages
File Size : 42,6 Mb
Release : 2018-11-03
Category : Mathematics
ISBN : 9783319969923
This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.
Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 646 pages
File Size : 43,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9780387217529
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 : Frank W. Warner
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 45,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475717990
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 : Robert Wasserman
Publisher : Oxford University Press, USA
Page : 468 pages
File Size : 54,9 Mb
Release : 2004
Category : Language Arts & Disciplines
ISBN : 0198510594
This book sets forth the basic principles of tensors and manifolds and describes how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics.
Author : Loring W. Tu
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 46,5 Mb
Release : 2010-10-05
Category : Mathematics
ISBN : 9781441974006
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 : Joaquim M. Domingos
Publisher : World Scientific
Page : 82 pages
File Size : 42,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812700445
This is a brief introduction to some geometrical topics including topological spaces, the metric tensor, Euclidean space, manifolds, tensors, r-forms, the orientation of a manifold and the Hodge star operator. It provides the reader who is approaching the subject for the first time with a deeper understanding of the geometrical properties of vectors and covectors. The material prepares the reader for discussions on basic concepts such as the differential of a function as a covector, metric dual, inner product, wedge product and cross product.J M Domingos received his D Phil from the University of Oxford and has now retired from the post of Professor of Physics at the University of Coimbra, Portugal.
Author : David Bachman
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 54,6 Mb
Release : 2012-02-02
Category : Mathematics
ISBN : 9780817683047
This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.
Author : J. M. Landsberg
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 48,8 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780821869079
Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.
Author : James R. Munkres
Publisher : CRC Press
Page : 381 pages
File Size : 44,8 Mb
Release : 2018-02-19
Category : Mathematics
ISBN : 9780429962691
A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.
Author : Anadi Jiban Das
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 42,6 Mb
Release : 2007-10-05
Category : Science
ISBN : 9780387694696
Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.
Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 43,7 Mb
Release : 2015
Category : Mathematics
ISBN : 9781421415642
It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.--Gary White, editor of The Physics Teacher "American Journal of Physics"