The Absolute Differential Calculus (Calculus of Tensors)

Tullio Levi-Civita

468 pages, parution le 01/01/1990

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Résumé

A chief requirement in the study of relativity is knowledge of the absolute differential calculus, the subject which 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 contents are divided into three parts: introductory theories; the fundamental quadratic form and the absolute differential calculus; and physical applications. Twelve chapters cover; functional determinants and matrices; systems of total differential equations; linear partial differential equations complete systems; algebraic foundations of the absolute differential calculus; geometrical introduction to the theory of differential quadratic forms; covariant geodesic co-ordinates; Riemann's symbols and properties relating to curvature, Ricci's and Einstein's symbols, geodesic deviation; relations between two different metrics referred to the same parameters, manifolds of constant curvature; differential quadratic forms of class zero and class one; some applications of intrinsic geometry; evolution of mechanics and geometrical optics, their relation to a tour-dimensional world according to Einstein; and the gravitational equations and general relativity.

Originally published in Rome in 1925 as Lezioni di calcolo diffrenziale assoluto, this book appeared in an authorized English translation in 1926 with two new chapters by Levi-Civita on the general theory of relativity. The Dover edition is a reprint of this 1926 English translation.

Unabridged, unaltered re-publication of the original (1926) English edition, with authorized translation by Marjorie Long. Index of names, general index. 4 illustrations, xvi -f- 452pp. 5 _5/8 x 8 _l/4.
Paperbound.

Contents

Introductory Theories

Functional Determinants and Matrices
Systems of Total Differential Equations
Linear Partial Differential Equations Complete Systems
Algebraic Foundations of the Absolute Differential Calculus
Geometrical Introduction to the Theory 01 Differential Quadratic Forms

The Fundamental Quadratic Form and the Absolute Differential Calculus

Covariant Differentiation; Invariants and Differential Parameters; Locally Geodesic Co-ordinates
Riemann's Symbols and Properties Relating to Curvature; Ricci's and Einstein's Symbols; Geodesic Deviation
Relations Between Two Different Metrics Referred to the Same Parameters; Manifolds of Constant Curvature
Differential Quadratic Forms of Class Zero and Class One
Some Applications of Intrinsic Geometry

Physical Applications

Evolution of Mechanics and Geometrical Optics; Their Relation to a Four-Dimensional World According to Einstein
The Gravitational Equations and General Relativity

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Dover
Auteur(s)	Tullio Levi-Civita
Parution	01/01/1990
Nb. de pages	468
Format	14,3 x 20,7
Couverture	Broché
Poids	485g
Intérieur	Noir et Blanc
EAN13	9780486634012