The Absolute Differential Calculus (Calculus of Tensors)


Author: Tullio Levi-Civita
Publisher: Courier Corporation
ISBN: 0486316254
Category: Mathematics
Page: 452
View: 9219

Continue Reading →

Written by a distinguished mathematician, this classic examines the mathematical material necessary for a grasp of relativity theory. Covers introductory theories, fundamental quadratic forms, absolute differential calculus, and physical applications. 1926 edition.

The Absolute Differential Calculus

Calculus of Tensors
Author: Tullio Levi-Civita
Publisher: Dover Publications
ISBN: 9780486446370
Category: Mathematics
Page: 452
View: 7383

Continue Reading →

A chief requirement in the study of relativity is knowledge of the absolute differential calculus, the subject that Einstein found necessary for developing his ideas mathematically. Tullio Levi-Civita was one of the founders of this field of mathematics, and he presents a clear, detailed exposition of the subject in this classic book. The first section of the three-part treatment examines functional determinants and matrices; systems of total differential equations; linear partial differential equations in complete systems; and algebraic foundations of the absolute differential calculus, concluding with a geometrical introduction to the theory of differential quadratic forms. Part two, a study of the fundamental quadratic form and the absolute differential calculus, focuses on covariant differentiation, invariants and differential parameters, and locally geodesic coordinates; Riemann's symbols and properties relating to curvature, Ricci's and Einstein's symbols, and geodesic deviation; relations between two different metrics referred to the same parameters, manifolds of constant curvature; and differential quadratic forms of class zero and class one; and some applications of intrinsic geometry. The third and final section explores physical applications, including the evolution of mechanics and geometrical optics and their relation to a four-dimensional world according to Einstein; and gravitational equations and general relativity.

Tensor Calculus


Author: J. L. Synge,A. Schild
Publisher: Courier Corporation
ISBN: 048614139X
Category: Mathematics
Page: 336
View: 4739

Continue Reading →

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.

Elements of Tensor Calculus


Author: A. Lichnerowicz
Publisher: Courier Dover Publications
ISBN: 0486805174
Category: Mathematics
Page: 176
View: 5448

Continue Reading →

Part I: rigorous presentation of tensor calculus as a develoment of vector analysis. Part II: important applications of tensor calculus. Concluding section: field equations of general relativity theory. 1962 edition.

Differential Geometry


Author: Erwin Kreyszig
Publisher: Courier Corporation
ISBN: 0486318621
Category: Mathematics
Page: 384
View: 9343

Continue Reading →

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.

Tensors, Differential Forms, and Variational Principles


Author: David Lovelock,Hanno Rund
Publisher: Courier Corporation
ISBN: 048613198X
Category: Mathematics
Page: 400
View: 9684

Continue Reading →

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.

The World of Mathematics


Author: James Roy Newman
Publisher: Courier Corporation
ISBN: 9780486411521
Category: Mathematics
Page: 464
View: 6601

Continue Reading →

Presents 33 essays on such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the mathematical way of thinking, the unreasonableness of mathematics, and mathematics as an art. A reprint of volume 3 of the four-volume edition originally published by Simon and Schuster in 1956. Annotation c. Book News, Inc., Portland, OR (booknews.com).

Cartesian Tensors

An Introduction
Author: George Frederick James Temple
Publisher: Courier Corporation
ISBN: 9780486439082
Category: Mathematics
Page: 92
View: 5246

Continue Reading →

An introduction to the theory of Cartesian tensors, this text notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. Covers isotropic tensors and spinor analysis within the confines of Euclidean space; and tensors in orthogonal curvilinear coordinates. Examples. 1960 edition.

Fourier Series and Orthogonal Polynomials


Author: Dunham Jackson
Publisher: Courier Corporation
ISBN: 9780486438085
Category: Mathematics
Page: 234
View: 5151

Continue Reading →

This text illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Begins with a definition and explanation of the elements of Fourier series, and examines Legendre polynomials and Bessel functions. Also includes Pearson frequency functions and chapters on orthogonal, Jacobi, Hermite, and Laguerre polynomials, more. 1941 edition.

An Introduction to Differential Geometry


Author: T. J. Willmore
Publisher: Courier Corporation
ISBN: 0486282104
Category: Mathematics
Page: 336
View: 7492

Continue Reading →

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

Tensor Analysis for Physicists


Author: Jan Arnoldus Schouten
Publisher: Courier Corporation
ISBN: 0486655822
Category: Science
Page: 277
View: 5353

Continue Reading →

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.

Absolute Analysis


Author: Frithjof Nevanlinna,Rolf Nevanlinna
Publisher: Springer-Verlag
ISBN: 3662215934
Category: Mathematics
Page: 259
View: 4064

Continue Reading →

Das vorliegende Werk ist als Ergebnis von Vorlesungen entstanden, welche die Verfasser seit 1953 im Laufe von mehreren Jahren an den Universitäten Helsinki und Zürich gehalten haben. Die nachfolgende Einleitung gibt über die Tendenzen Aufschluß, die für unsere Darstellung der Grundlagen einer absoluten, koordinaten- und dimensionsfreien Infinitesimalrechnung maßgebend gewesen sind. Die Lektüre setzt an Vorkenntnissen nur wenig voraus; sie kann jedem Studierenden emp fohlen werden, der mit dem üblichen, auf die Benutzung von Koordi naten fußenden Aufbau der Elemente der analytischen Geometrie, der Differential- und Integralrechnung und der Theorie der Differential gleichungen vertraut ist. Unsere Arbeit ist durch die Hilfe wesentlich erleichtert worden, die uns von mehreren Seiten zuteil geworden ist. Herr Ilppo Simo Louhi vaara hat von Anfang bis zu Ende an der Herstellung dieses Werkes mit unermüdlichem Interesse und minutiöser Sorgfalt teilgenommen und durch zahlreiche sachliche und formelle Bemerkungen und Vor schläge unsere Arbeit wesentlich gefördert. Für seine wertvolle, auf opfernde Unterstützung sprechen wir hier unseren herzlichen Dank aus. Den Herren H. Keller, T. Klemola, T. Nieminen, Ph. Tondeur und K. 1. Virtanen, die unsere Darstellung im Manuskript gelesen haben, verdanken wir verschiedene wichtige kritische Bemerkungen. Unser Dank gilt auch Herrn Professor Dr. F. K. Schmidt für die Aufnahme dieses Werkes in die Reihe der Grundlehren der mathema tischen Wissenschaften, und dem Springer-Verlag, der unseren Wünschen mit freundlicher Bereitwilligkeit entgegengekommen ist.

Applications of Tensor Analysis


Author: A. J. McConnell
Publisher: Courier Corporation
ISBN: 0486603733
Category: Mathematics
Page: 318
View: 8568

Continue Reading →

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.

Lineare Algebra


Author: Gilbert Strang
Publisher: Springer-Verlag
ISBN: 3642556310
Category: Mathematics
Page: 656
View: 7024

Continue Reading →

Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

A short course in discrete mathematics


Author: Edward A. Bender,Stanley Gill Williamson
Publisher: Dover Pubns
ISBN: N.A
Category: Mathematics
Page: 240
View: 1333

Continue Reading →

What sort of mathematics do I need for computer science? In response, a pair of professors at the University of California at San Diego created this text. Explores Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Assumes some familiarity with calculus. Original 2005 edition.

A Collection of Problems on Complex Analysis


Author: Lev Izrailevich Volkovyskiĭ
Publisher: Courier Dover Publications
ISBN: N.A
Category: Mathematics
Page: 426
View: 4812

Continue Reading →

Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. Topics include conformal mappings, integrals and power series, Laurent series, parametric integrals, integrals of the Cauchy type, analytic continuation, Riemann surfaces, much more. Answers and solutions at end of text. Bibliographical references. 1965 edition.

The Theory of Remainders


Author: Andrea Rothbart
Publisher: Courier Dover Publications
ISBN: N.A
Category: Mathematics
Page: 178
View: 3488

Continue Reading →

An imaginative introduction to number theory, this unique approach employs a pair of fictional characters, Ant and Gnam. Ant leads Gnam through a variety of theories, and together, they put the theories into action—applying linear diophantine equations to football scoring, using a black-magic device to simplify problems in modular structures, and developing intriguing modifications to the rules of chess. Appropriate for anyone familiar with algebra at the high-school level, The Theory of Remainders offers a captivating introduction to both number theory and abstract algebra. Both elementary and challenging, it provides a view of mathematics as a conceptual net and illustrates the differences between conceptual and paraconceptual claims—an excellent start to expanding students' perspectives on mathematics. Exercises throughout the book form an integral part of the text, extending students' experience with the concepts under discussion and presenting opportunities to observe patterns. In addition to the exercises, a series of optional problems allows more advanced readers to further develop the concepts.