Vector and Tensor Analysis with Applications

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Author: A. I. Borisenko,I. E. Tarapov

Publisher: Courier Corporation

ISBN: 0486131904

Category: Mathematics

Page: 288

View: 6098

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.

Tensor and Vector Analysis

With Applications to Differential Geometry

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Author: C. E. Springer

Publisher: Courier Corporation

ISBN: 048632091X

Category: Mathematics

Page: 256

View: 3839

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.

Tensoranalysis

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Author: Heinz Schade,Klaus Neemann

Publisher: Walter de Gruyter

ISBN: 3110213214

Category: Science

Page: 462

View: 6143

Dieses Lehrbuch stellt eine umfassende und leicht verständliche Einführung in die Tensoranalysis dar, die hier als Oberbegriff von klassischer Tensoranalysis und Tensoralgebra zu verstehen ist und die in vielen Anwendungen der Physik und der Ingenieurwissenschaften benötigt wird. Es vermittelt die nötigen algebraischen Hilfsmittel und enthält zahlreiche Übungsaufgaben mit Lösungen, so dass es sich auch für ein Selbststudium eignet.

Vector and Tensor Analysis

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Author: George E. Hay

Publisher: Courier Corporation

ISBN: 0486601099

Category: Mathematics

Page: 193

View: 339

"Remarkably comprehensive, concise and clear." — Industrial Laboratories "Considered as a condensed text in the classical manner, the book can well be recommended." — Nature Here is a clear introduction to classic vector and tensor analysis for students of engineering and mathematical physics. Chapters range from elementary operations and applications of geometry, to application of vectors to mechanics, partial differentiation, integration, and tensor analysis. More than 200 problems are included throughout the book.

Tensor Analysis for Physicists

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Author: Jan Arnoldus Schouten

Publisher: Courier Corporation

ISBN: 0486655822

Category: Science

Page: 277

View: 7545

This rigorous and advanced mathematical explanation of classic tensor analysis was written by one of the founders of tensor calculus. Its concise exposition of the mathematical basis of the discipline is integrated with well-chosen physical examples of the theory, including those involving elasticity, classical dynamics, relativity, and Dirac's matrix calculus. 1954 edition.

Applications of Tensor Analysis

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Author: A. J. McConnell

Publisher: Courier Corporation

ISBN: 0486603733

Category: Mathematics

Page: 318

View: 7311

Standard work applies tensorial methods to subjects within realm of advanced college mathematics. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor algebra; introduces theory of differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics. 685 exercises, most with answers.

Elements of Tensor Calculus

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Author: A. Lichnerowicz

Publisher: Courier Dover Publications

ISBN: 0486811867

Category: Mathematics

Page: 176

View: 8755

This classic introductory text, geared toward undergraduate students of mathematics, is the work of an internationally renowned authority on tensor calculus. The two-part treatment offers a rigorous presentation of tensor calculus as a development of vector analysis as well as discussions of the most important applications of tensor calculus. Starting with a chapter on vector spaces, Part I explores affine Euclidean point spaces, tensor algebra, curvilinear coordinates in Euclidean space, and Riemannian spaces. Part II examines the use of tensors in classical analytical dynamics and details the role of tensors in special relativity theory. The book concludes with a brief presentation of the field equations of general relativity theory.

Finite-Elemente-Methoden

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Author: Klaus-Jürgen Bathe

Publisher: Springer Verlag

ISBN: 9783540668060

Category: Technology & Engineering

Page: 1253

View: 5388

Dieses Lehr- und Handbuch behandelt sowohl die elementaren Konzepte als auch die fortgeschrittenen und zukunftsweisenden linearen und nichtlinearen FE-Methoden in Statik, Dynamik, Festkörper- und Fluidmechanik. Es wird sowohl der physikalische als auch der mathematische Hintergrund der Prozeduren ausführlich und verständlich beschrieben. Das Werk enthält eine Vielzahl von ausgearbeiteten Beispielen, Rechnerübungen und Programmlisten. Als Übersetzung eines erfolgreichen amerikanischen Lehrbuchs hat es sich in zwei Auflagen auch bei den deutschsprachigen Ingenieuren etabliert. Die umfangreichen Änderungen gegenüber der Vorauflage innerhalb aller Kapitel - vor allem aber der fortgeschrittenen - spiegeln die rasche Entwicklung innerhalb des letzten Jahrzehnts auf diesem Gebiet wieder.

Differentialgeometrie von Kurven und Flächen

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Author: Manfredo P. do Carmo

Publisher: Springer-Verlag

ISBN: 3322850722

Category: Technology & Engineering

Page: 263

View: 7487

Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang

Tensor Calculus

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Author: J. L. Synge,A. Schild

Publisher: Courier Corporation

ISBN: 048614139X

Category: Mathematics

Page: 336

View: 9335

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.

Tensor Analysis on Manifolds

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Author: Richard L. Bishop,Samuel I. Goldberg

Publisher: Courier Corporation

ISBN: 0486139239

Category: Mathematics

Page: 288

View: 2307

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

Special Relativity

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Author: Nicholas M.J. Woodhouse

Publisher: Springer-Verlag

ISBN: 3540466762

Category: Science

Page: 88

View: 5401

Tensor Calculus

A Concise Course

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Author: Barry Spain

Publisher: Courier Corporation

ISBN: 0486428311

Category: Mathematics

Page: 125

View: 5947

A compact exposition of the theory of tensors, this text also illustrates the power of the tensor technique by its applications to differential geometry, elasticity, and relativity. Explores tensor algebra, the line element, covariant differentiation, geodesics and parallelism, and curvature tensor. Also covers Euclidean 3-dimensional differential geometry, Cartesian tensors and elasticity, and the theory of relativity. 1960 edition.

Introduction to Tensor Analysis and the Calculus of Moving Surfaces

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Author: Pavel Grinfeld

Publisher: Springer Science & Business Media

ISBN: 1461478677

Category: Mathematics

Page: 302

View: 4708

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.

Naive Mengenlehre

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Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 4872

Introduction to Vector and Tensor Analysis

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Author: Robert C. Wrede

Publisher: Courier Corporation

ISBN: 0486137112

Category: Mathematics

Page: 418

View: 7143

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.

Non Linear Mathematics Vol. I

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Author: Thomas L., Saaty ,Joseph, Bram

Publisher: RWS Publications

ISBN: 1888603380

Category: Business & Economics

Page: 396

View: 8844

"We are surrounded and deeply involved, in the natural world, with non- linear events which are not necessarily mathematical," the authors write. "For example . . . the nonlinear problem of pedalling a bicycle up and down a hillside. On a grand scale . . . the struggle for existence between two species, one of which preys exclusively on the other." This book is' for mathematicians and researchers who believe that "nonlinear mathematics is' the mathematics of today"; it is also for economists, engineers, operations analysts, "the reader who has been thus bemused into an artificially linear conception of the universe." Nonlinear Mathematics is the first attempt to consider the widest range of nonlinear topics found in the -scattered literature. Accessible to non- mathematics professionals as well as college seniors and graduates, it offers a discussion both particular and broad enough to stimulate research towards a unifying theory of nonlinear mathematics. Ideas are presented "according to existence and uniqueness theorems, characterization (e.g., stability and asymptotic behavior), construction of solutions, convergence, approximation and errors."

...und Einstein hatte doch recht

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Author: Clifford M. Will

Publisher: Springer-Verlag

ISBN: 3642743145

Category: Science

Page: 275

View: 1081

Keine wissenschaftliche Theorie ist auf solche Faszination auch außerhalb der Wissenschaft gestoßen wie die Allgemeine Relativitätstheorie von Albert Einstein, und keine wurde so nachdrücklich mit den Mitteln der modernen Physik überprüft. Wie hat sie diesen Test mit Raumsonden, Radioastronomie, Atomuhren und Supercomputern standgehalten? Hatte Einstein recht? Mit der Autorität des Fachmanns und dem Flair des unvoreingenommenen Erzählers schildert Clifford Will die Menschen, Ideen und Maschinen hinter den Tests der allgemeinen Relativitätstheorie. Ohne Formeln und Fachjargon wird der leser mit Einsteins Gedanken vertraut und erfährt von der Bestätigung seiner Vorhersagen, angefangen bei der Lichtablenkung im Schwerefeld der Sonne 1919 bis zu den ausgefeilten Kreiselexperimenten auf dem Space Shuttle. Die Allgemeine Relativitätstheorie hat nich nur alle diese Tests bestanden, sie hat darüber hinaus wesentlich beigetragen zu unserem Verständnis von Phänomenen wie Pulsaren, Quasaren, Schwarzen Löchern und Gravitationslinsen. Dieses Buch erzählt lebendig und spannend die Geschichte einer der größten geistigen Leistungen unserer Zeit.

The Mathematics of Games

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Author: John D. Beasley

Publisher: Courier Corporation

ISBN: 048615162X

Category: Mathematics

Page: 176

View: 6576

Lucid, instructive, and full of surprises, this book examines how simple mathematical analysis can throw unexpected light on games of every type, from poker to golf to the Rubik's cube. 1989 edition.