Tensor Analysis on Manifolds PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Tensor Analysis on Manifolds PDF full book. Access full book title Tensor Analysis on Manifolds by Richard L. Bishop. Download full books in PDF and EPUB format.
Author: Richard L. Bishop
Publisher: Courier Corporation
ISBN: 0486139239
Category : Mathematics
Languages : en
Pages : 290
Get Book Here
Book Description
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Author: Richard L. Bishop
Publisher: Courier Corporation
ISBN: 0486139239
Category : Mathematics
Languages : en
Pages : 290
Get Book Here
Book Description
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Author: Richard L. Bishop
Publisher: Courier Corporation
ISBN: 0486640396
Category : Mathematics
Languages : en
Pages : 290
Get Book Here
Book Description
Striking just the right balance between formal and abstract approaches, this text proceeds from generalities to specifics. Topics include function-theoretical and algebraic aspects, manifolds and integration theory, several important structures, and adaptation to classical mechanics. "First-rate. . . deserves to be widely read." — American Mathematical Monthly. 1980 edition.
Author: Richard Lawrence Bishop
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 0
Get Book Here
Book Description
Author: Ralph Abraham
Publisher: Springer Science & Business Media
ISBN: 1461210291
Category : Mathematics
Languages : en
Pages : 666
Get Book Here
Book Description
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: C. E. Springer
Publisher: Courier Corporation
ISBN: 048632091X
Category : Mathematics
Languages : en
Pages : 258
Get Book Here
Book Description
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.
Author: A. I. Borisenko
Publisher: Courier Corporation
ISBN: 0486131904
Category : Mathematics
Languages : en
Pages : 292
Get Book Here
Book Description
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
ISBN: 1461478677
Category : Mathematics
Languages : en
Pages : 303
Get Book Here
Book Description
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
Publisher: Courier Corporation
ISBN: 048613198X
Category : Mathematics
Languages : en
Pages : 402
Get Book Here
Book Description
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: Tracy Y. Thomas
Publisher: Elsevier
ISBN: 1483263711
Category : Mathematics
Languages : en
Pages : 128
Get Book Here
Book Description
Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.
Author: Michael Spivak
Publisher: Westview Press
ISBN: 9780805390216
Category : Science
Languages : en
Pages : 164
Get Book Here
Book Description
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.
