Ricci Calculus

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.

Ricci Calculus

Author: Jan Arnoldus Schouten

Publisher: Springer Science & Business Media

ISBN: 3662129272

Page: 514

View: 410

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.

Encyclopaedia of Mathematics

Tensor calculus is an important constituent part of the apparatus of differential
geometry. In this connection it was first systematically developed by G. Ricci and
T. Levi-Civita (see [I]): it has often been called the 'Ricci calculus". The term '
tensor* ...

Encyclopaedia of Mathematics

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

ISBN: 9781556080081

Page: 536

View: 255

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

The Attraction of Gravitation

to call attention to "Ricci's generally neglected absolute calculus and to its
suggestiveness as an implement of research in developing the theory of surfaces
of two dimensions in Euclidean space of n dimensions" (Wilson 1916). During
this ...

The Attraction of Gravitation

Author: John Earman

Publisher: Springer Science & Business Media

ISBN: 9780817636241

Page: 432

View: 169

Devoted to the history of general relativity, this text provides reviews from scholars all over the world. Many of the papers originated at the Third International Conference on the History of General Relativity, held at the University of Pittsburgh in the summer of 1991. Topics covered include: disputes with Einstein; the empirical basis of general relativity; variational principles in general relativity; the reception and development of general relativity; and cosmology and general relativity.

Vector Analysis

13.3 Three Principles of the Ricci Calculus on Manifolds without a Metric We now
use these objects—k-forms and dual k-forms, and 1-forms and vector fields in
particular—to illustrate three general principles of the Ricci calculus: (1) the ...

Vector Analysis

Author: Klaus Jänich

Publisher: Springer Science & Business Media

ISBN: 1475734786

Page: 284

View: 696

This book presents modern vector analysis and carefully describes the classical notation and understanding of the theory. It covers all of the classical vector analysis in Euclidean space, as well as on manifolds, and goes on to introduce de Rham Cohomology, Hodge theory, elementary differential geometry, and basic duality. The material is accessible to readers and students with only calculus and linear algebra as prerequisites. A large number of illustrations, exercises, and tests with answers make this book an invaluable self-study source.

Tensor Calculus

BIBLIOGRAPHY. 1. G. RICCI and T. LEVI−CIVITA, Méthodes de calcul
differentiel absolu et leurs applications (Paris, 1923). (Reprinted from
Mathematische Annalen, tome 54, 1900.) 2. J. A. SCHOUTEN, Ricci Calculus (
2nd ed., Berlin, 1954).

Tensor Calculus

Author: J. L. Synge

Publisher: Courier Corporation

ISBN: 048614139X

Page: 336

View: 252

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.

The Development of Mathematics

The method of calculation is the absolute differential calculus, or tensor analysis,
of M. M. G. Ricci (1853–1925, Italian), which was noted earlier in connection with
the general progress of recent mathematics toward structure. The Ricci calculus ...

The Development of Mathematics

Author: E. T. Bell

Publisher: Courier Corporation

ISBN: 0486152286

Page: 656

View: 605

Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.

Academic Press Dictionary of Science and Technology

Also, Ricci calculus. calculus of variations Mathematics, the study of problems
concerned with determining maxima or minima of a given functional or definite
integral, relative to a class of functions or to the dependent variables of the
integrand ...

Academic Press Dictionary of Science and Technology

Author: Christopher G. Morris

Publisher: Gulf Professional Publishing

ISBN: 9780122004001

Page: 2432

View: 111

Over 125,000 entries cover 124 scientific and technological fields, including acoustical engineering, cartography graphic arts, microbiology, organic chemistry, radiology, and zoology

An Introduction to RIEMANNIAN GEOMETRY AND THE TENSOR CALCULUS

Ricci ' s labours and his new method attracted comparatively little attention for
many years . ... his pupil Levi - Civita collaborated in a memoir on the Methods of
the Absolute Differential Calculus and their applications , which appeared in vol .

An Introduction to RIEMANNIAN GEOMETRY AND THE TENSOR CALCULUS

Author:

Publisher: CUP Archive

ISBN:

Page:

View: 760

The Symbolic Universe

In recent times , important historical studies have been devoted to both the
origins and early development of tensor calculus and Ricci ' s part in it . Therefore
, in this paper I will not discuss this matter again . Instead , it is of interest to try to
look ...

The Symbolic Universe

Author: Jeremy Gray

Publisher: Oxford University Press on Demand

ISBN: 9780198500889

Page: 289

View: 760

The Symbolic Universe considers the ways in which many leading mathematicians between 1890 and 1930 attempted to apply geometry to physics. It concentrates on responses to Einstein's theories of special and general relativity, but also considers the philosophical implications of these ideas.

Dynamical Spacetimes and Numerical Relativity

This structure , we suggest , will show more clearly when examined in the
language of geometry rather than in the language of differential equations , more
readily in Regge calculus than in Ricci calculus , and more directly from a
geometry ...

Dynamical Spacetimes and Numerical Relativity

Author: Joan M. Centrella

Publisher: CUP Archive

ISBN: 9780521328609

Page: 465

View: 107

Body Tensor Fields in Continuum Mechanics

It is well known that the natural tool for such a situation is general tensor analysis
(also called the absolute differential calculus or Ricci calculus). Tensor equations
automatically possess the desired invariance properties with respect to ...

Body Tensor Fields in Continuum Mechanics

Author: Arthur S. Lodge

Publisher: Academic Press

ISBN: 1483262995

Page: 336

View: 805

Body Tensor Fields in Continuum Mechanics: With Applications to Polymer Rheology aims to define body tensor fields and to show how they can be used to advantage in continuum mechanics, which has hitherto been treated with space tensor fields. General tensor analysis is developed from first principles, using a novel approach that also lays the foundations for other applications, e.g., to differential geometry and relativity theory. The applications given lie in the field of polymer rheology, treated on the macroscopic level, in which relations between stress and finite-strain histories are of central interest. The book begins with a review of mathematical prerequisites, namely primitive concepts, linear spaces, matrices and determinants, and functionals. This is followed by separate chapters on body tensor and general space tensor fields; the kinematics of shear flow and shear-free flow; Cartesian vector and tensor fields; and relative tensors, field transfer, and the body stress tensor field. Subsequent chapters deal with constitutive equations for viscoelastic materials; reduced constitutive equations for shear flow and shear-free flow; covariant differentiation and the stress equations of motion; and stress measurements in unidirectional shear flow.

Twistors in Mathematics and Physics

Ricci-Calculus. Springer Verlag 1954. [52] P. Szekeres. Conformal tensors. Proc.
Roy. Soc. A304 (1968), 113-122. [53] T.Y. Thomas. On conformal geometry. Proc.
Nat. Acad. Sci. 11 (1925), 352—359. [54] T.Y. Thomas. Conformal tensors I.

Twistors in Mathematics and Physics

Author: T. N. Bailey

Publisher: Cambridge University Press

ISBN: 0521397839

Page: 384

View: 549

Twistor theory has become a diverse subject as it has spread from its origins in theoretical physics to applications in pure mathematics. This 1990 collection of review articles covers the considerable progress made in a wide range of applications such as relativity, integrable systems, differential and integral geometry and representation theory. The articles explore the wealth of geometric ideas which provide the unifying themes in twistor theory, from Penrose's quasi-local mass construction in relativity, to the study of conformally invariant differential operators, using techniques of representation theory.

Philosophical Problems of Space and Time

Schouten, J. A., Tensor Analysis for Physicists, Oxford University Press, London
1951. Schouten, J. A., Ricci-Calculus, 2nd edition, Springer-Verlag, Berlin 1954.
Stachel, J., Space-Time Problems', a review of the Synge Festschrift entitled ...

Philosophical Problems of Space and Time

Author: Adolf Grünbaum

Publisher: Springer Science & Business Media

ISBN: 940102622X

Page: 884

View: 683

It is ten years since Adolf Griinbaum published the first edition of this book. It was promptly recognized to be one of the few major works in the philosophy of the natural sciences of this generation. In part, this is so because Griinbaum has chosen a problem basic both to philosophy and to the natural sciences - the nature of space and time; and in part, this is so because he so admirably exemplifies that Aristotelian devotion to the intimate and mutual dependence of actual science and philosophical understanding. More than this, however, the quality of his work derives from his achievement in combining detail with scope. The problems of space and time have been among the most difficult in contemporary and classical thought, and Griinbaum has been responsible to the full depth and complexity of these difficulties. This revised and enlarged second edition is a work in progress, in the tradition of reflective analysis of modern science of such figures as Ehrenfest and Reichenbach. In publishing this work among the Boston Studies in the Philosophy of Science, we hope to contribute to and encourage that broad tradition of natural philosophy which is marked by the close collaboration of philoso phers and scientists. To this end, we have published the proceedings of our Colloquia, of meetings and conferences here and abroad, as well as the works of single authors.

Tensor Calculus

TENSOR THEORY J . A . SCHOUTEN , Der Ricci - Kalkül , ( 1924 ) . L . P .
EISENHART , Riemannian Geometry , ( 1926 ) . T . LEVI - CIVITA , The Absolute
Differential Calculus , ( 1927 ) . O . VEBLEN , Invariants of Quadratic Differential
Forms ...

Tensor Calculus

Author: Barry Spain

Publisher:

ISBN:

Page: 125

View: 366

Tensor Calculus

G . Ricci and T . LEVI - CIVITA , Méthodes de calcul differentiel absolu et leurs
applications ( Paris , 1923 ) . ( Reprinted from Mathematische Annalen , tome 54 ,
1900 . ) 2 . J . A . SCHOUTEN , Ricci Calculus ( 2nd ed . , Berlin , 1954 ) . 3 .

Tensor Calculus

Author: John Lighton Synge

Publisher:

ISBN:

Page: 324

View: 821

An Introduction to Differential Geometry

Géométrie des groupes de transformations, Dunod, Paris (1958). NomzU, K., Lie
Groups and Diflerential Geometry, Tokyo (1956). DE RHAM, G., Variétés
différeritiablea, Hermann (1955). SCHOUTEN, J. A., Ricci-Calculus, Springer (
1954).

An Introduction to Differential Geometry

Author: T. J. Willmore

Publisher: Courier Corporation

ISBN: 0486282104

Page: 336

View: 837

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.