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Author : Paul Renteln
Publisher : Cambridge University Press
Page : 343 pages
File Size : 49,96 MB
Release : 2014
Category : Mathematics
ISBN : 1107042194
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.
Author : Robert Wasserman
Publisher : Oxford University Press, USA
Page : 468 pages
File Size : 45,7 MB
Release : 2004
Category : Language Arts & Disciplines
ISBN : 9780198510598
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 : Richard L. Bishop
Publisher : Courier Corporation
Page : 290 pages
File Size : 39,99 MB
Release : 2012-04-26
Category : Mathematics
ISBN : 0486139239
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Author : Ralph Abraham
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 36,11 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461210291
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 : Robert Wasserman
Publisher : Oxford University Press, USA
Page : 409 pages
File Size : 35,89 MB
Release : 1992
Category : Science
ISBN : 9780195065619
This book is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics at Michigan State University. The courses were intended to present an introduction to the expanse of modern mathematics and its applications in modern mathematics and its application in modern physics. This book gives an introduction perspective to young students intending to go into a field of pure mathematics, and who, with the usual 'pigeon-hold' graduate curriculum, will not get an overall perspective for several years, much less any idea of application.
Author : Anadi Jiban Das
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 19,49 MB
Release : 2007-10-05
Category : Science
ISBN : 0387694692
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 : David Lovelock
Publisher : Courier Corporation
Page : 402 pages
File Size : 49,27 MB
Release : 2012-04-20
Category : Mathematics
ISBN : 048613198X
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 : Uwe Mühlich
Publisher : Springer
Page : 134 pages
File Size : 27,71 MB
Release : 2017-04-18
Category : Science
ISBN : 3319562649
This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out.
Author : A. I. Borisenko
Publisher : Courier Corporation
Page : 292 pages
File Size : 39,25 MB
Release : 2012-08-28
Category : Mathematics
ISBN : 0486131904
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
Author : C. E. Springer
Publisher : Courier Corporation
Page : 258 pages
File Size : 29,79 MB
Release : 2013-09-26
Category : Mathematics
ISBN : 048632091X
Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.