Manifolds Tensor Analysis And Applications

Author : Ralph Abraham,Jerrold E. Marsden,Tudor Ratiu
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210290

Get Book

Manifolds, Tensor Analysis, and Applications by Ralph Abraham,Jerrold E. Marsden,Tudor Ratiu Pdf

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 : Ralph Abraham
Publisher : Unknown
Page : 654 pages
File Size : 54,5 Mb
Release : 1988
Category : Calculus of tensors
ISBN : 7506205475

Get Book

Manifolds, Tensor Analysis, and Applications by Ralph Abraham Pdf

Author : Richard L. Bishop,Samuel I. Goldberg
Publisher : Courier Corporation
Page : 288 pages
File Size : 46,9 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486139234

Get Book

Tensor Analysis on Manifolds by Richard L. Bishop,Samuel I. Goldberg Pdf

DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div

Author : Paul Renteln
Publisher : Cambridge University Press
Page : 343 pages
File Size : 43,7 Mb
Release : 2014
Category : Mathematics
ISBN : 9781107042193

Get Book

Manifolds, Tensors and Forms by Paul Renteln Pdf

Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.

Author : A. I. Borisenko,I. E. Tarapov
Publisher : Courier Corporation
Page : 288 pages
File Size : 40,5 Mb
Release : 2012-08-28
Category : Mathematics
ISBN : 9780486131900

Get Book

Vector and Tensor Analysis with Applications by A. I. Borisenko,I. E. Tarapov Pdf

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 : Pavel Grinfeld
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 54,8 Mb
Release : 2013-09-24
Category : Mathematics
ISBN : 9781461478676

Get Book

Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Pavel Grinfeld Pdf

This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.

Author : David Lovelock,Hanno Rund
Publisher : Courier Corporation
Page : 400 pages
File Size : 49,7 Mb
Release : 2012-04-20
Category : Mathematics
ISBN : 9780486131986

Get Book

Tensors, Differential Forms, and Variational Principles by David Lovelock,Hanno Rund Pdf

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 : Zafar Ahsan
Publisher : Anshan Pub
Page : 0 pages
File Size : 50,7 Mb
Release : 2008
Category : Calculus of tensors
ISBN : 1905740867

Get Book

Tensor Analysis with Applications by Zafar Ahsan Pdf

The principal aim of tensor analysis is to investigate the relations which remain valid when we change from one coordinate system to another. Albert Einstein found it to be an excellent tool for the presentation of his general theory of relativity and consequently tensor analysis came to prominence in mathematics. It has applications in most branches of theoretical physics and engineering. This present book is intended as a text for postgraduate students of mathematics, physics and engineering. It is self-contained and requires prior knowledge of elementary calculus, differential equations and classical mechanics. It consists of five chapters, each containing a large number of solved examples, unsolved problems and links to the solution of these problems. "Tensor Analysis with Applications" can be used on a selection of university courses, and will be a welcome addition to the library of maths, physics and engineering departments.

Author : Uwe Mühlich
Publisher : Springer
Page : 125 pages
File Size : 43,7 Mb
Release : 2017-04-18
Category : Science
ISBN : 9783319562643

Get Book

Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds by Uwe Mühlich Pdf

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 : Jan Arnoldus Schouten
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 43,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662129272

Get Book

Ricci-Calculus by Jan Arnoldus Schouten Pdf

This is an entirely new book. The first edition appeared in 1923 and at that time it was up to date. But in 193 5 and 1938 the author and Prof. D. J. STRUIK published a new book, their Einführung I and li, and this book not only gave the first systematic introduction to the kernel index method but also contained many notions that had come into prominence since 1923. For instance densities, quantities of the second kind, pseudo-quantities, normal Coordinates, the symbolism of exterior forms, the LIE derivative, the theory of variation and deformation and the theory of subprojective connexions were included. Now since 1938 there have been many new developments and so a book on RICCI cal culus and its applications has to cover quite different ground from the book of 1923. Though the purpose remains to make the reader acquainted with RICCI's famous instrument in its modern form, the book must have quite a different methodical structure and quite different applica tions have to be chosen. The first chapter contains algebraical preliminaries but the whole text is modernized and there is a section on hybrid quantities (quantities with indices of the first and of the second kind) and one on the many abridged notations that have been developed by several authors. In the second chapter the most important analytical notions that come before the introduction of a connexion aredealt with in full.

Author : John G. Papastavridis
Publisher : Routledge
Page : 435 pages
File Size : 42,7 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781351411622

Get Book

Tensor Calculus and Analytical Dynamics by John G. Papastavridis Pdf

Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.

Author : J. L. Synge,A. Schild
Publisher : Courier Corporation
Page : 336 pages
File Size : 44,8 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486141398

Get Book

Tensor Calculus by J. L. Synge,A. Schild Pdf

Fundamental introduction of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, more.

Author : Robert Wasserman
Publisher : Oxford University Press, USA
Page : 468 pages
File Size : 51,6 Mb
Release : 2004
Category : Language Arts & Disciplines
ISBN : 0198510594

Get Book

Tensors and Manifolds by Robert Wasserman Pdf

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 : Robert Wasserman
Publisher : Oxford University Press, USA
Page : 464 pages
File Size : 50,8 Mb
Release : 2004
Category : Language Arts & Disciplines
ISBN : 9780198510598

Get Book

Tensors and Manifolds by Robert Wasserman Pdf

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 : James R. Munkres
Publisher : CRC Press
Page : 381 pages
File Size : 54,5 Mb
Release : 2018-02-19
Category : Mathematics
ISBN : 9780429962691

Get Book

Analysis On Manifolds by James R. Munkres Pdf

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.