Tensor Analysis on Manifolds

Author: Richard L. Bishop
Publisher: Courier Corporation
ISBN: 9780486139234
Release Date: 2012-04-26
Genre: Mathematics

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

Tensors Differential Forms and Variational Principles

Author: David Lovelock
Publisher: Courier Corporation
ISBN: 9780486131986
Release Date: 2012-04-20
Genre: Mathematics

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.

Vector and Tensor Analysis with Applications

Author: A. I. Borisenko
Publisher: Courier Corporation
ISBN: 9780486131900
Release Date: 2012-08-28
Genre: Mathematics

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.

Manifolds Tensor Analysis and Applications

Author: Ralph Abraham
Publisher: Springer Science & Business Media
ISBN: 9781461210290
Release Date: 2012-12-06
Genre: Mathematics

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.

Tensor Calculus

Author: J. L. Synge
Publisher: Courier Corporation
ISBN: 9780486141398
Release Date: 2012-04-26
Genre: Mathematics

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.

Manifolds Tensors and Forms

Author: Paul Renteln
Publisher: Cambridge University Press
ISBN: 9781107042193
Release Date: 2013-11-21
Genre: Science

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

Applications of Tensor Analysis

Author: A J McConnell
Publisher:
ISBN: 1614276897
Release Date: 2014-09-02
Genre: Mathematics

2014 Reprint of 1957 Edition. Full facsimile of the original edition. Not reproduced with Optical Recognition Software. Formerly entitled "Applications of the Absolute Differential Calculus," this work applies tensorial methods to subjects within the realm of advanced college mathematics. In four major divisions, it explains the fundamental ideas and notation of tensor theory; covers the geometrical treatment of tensor algebra; introduces the theory of the differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics.

Analysis and Algebra on Differentiable Manifolds

Author: Pedro M. Gadea
Publisher: Springer Science & Business Media
ISBN: 9789400759527
Release Date: 2012-12-30
Genre: Mathematics

This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear. A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics. In this 2nd edition: • 76 new problems • a section devoted to a generalization of Gauss’ Lemma • a short novel section dealing with some properties of the energy of Hopf vector fields • an expanded collection of formulae and tables • an extended bibliography Audience This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.

Introduction to Vector and Tensor Analysis

Author: Robert C. Wrede
Publisher: Courier Corporation
ISBN: 9780486137117
Release Date: 2013-01-30
Genre: Mathematics

Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.

Curvature in Mathematics and Physics

Author: Shlomo Sternberg
Publisher: Courier Corporation
ISBN: 9780486292717
Release Date: 2013-04-17
Genre: Mathematics

Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

Differential Geometry

Author: Erwin Kreyszig
Publisher: Courier Corporation
ISBN: 9780486318622
Release Date: 2013-04-26
Genre: Mathematics

An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.

Applied Exterior Calculus

Author: Dominic G. B. Edelen
Publisher: Courier Corporation
ISBN: 9780486438719
Release Date: 1985
Genre: Mathematics

This text begins with the essentials, advancing to applications and studies of physical disciplines, including classical and irreversible thermodynamics, electrodynamics, and the theory of gauge fields. Geared toward advanced undergraduates and graduate students, it develops most of the theory and requires only a familiarity with upper-division algebra and mathematical analysis. "Essential." — SciTech Book News. 1985 edition.

Curvature and Homology

Author:
Publisher: Academic Press
ISBN: 0080873235
Release Date: 2011-08-29
Genre: Mathematics

Curvature and Homology

Differential Geometry

Author: Heinrich W. Guggenheimer
Publisher: Courier Corporation
ISBN: 9780486157207
Release Date: 2012-04-27
Genre: Mathematics

This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.

Introduction to Tensor Analysis and the Calculus of Moving Surfaces

Author: Pavel Grinfeld
Publisher: Springer Science & Business Media
ISBN: 9781461478676
Release Date: 2013-09-24
Genre: Mathematics

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.