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Wednesday, July 22, 2020 | History

1 edition of Tensor Geometry found in the catalog.

Tensor Geometry

The Geometric Viewpoint and its Uses

by Christopher Terence John Dodson

  • 90 Want to read
  • 35 Currently reading

Published by Springer Berlin Heidelberg in Berlin, Heidelberg .
Written in English

    Subjects:
  • Global differential geometry,
  • Mathematics,
  • Matrix theory

  • About the Edition

    This treatment of differential geometry and the mathematics required for general relativity makes the subject of this book accessible for the first time to anyone familiar with elementary calculus in one variable and with a knowledge of some vector algebra. The emphasis throughout is on the geometry of the mathematics, which is greatly enhanced by the many illustrations presenting figures of three and more dimensions as closely as book form will allow. The imaginative text is a major contribution to expounding the subject of differential geometry as applied to studies in relativity, and will prove of interest to a large number of mathematicians and physicists. Review from L"Enseignement Mathématique.

    Edition Notes

    Statementby Christopher Terence John Dodson, Timothy Poston
    SeriesGraduate Texts in Mathematics -- 130, Graduate texts in mathematics -- 130.
    ContributionsPoston, T.
    Classifications
    LC ClassificationsQA641-670
    The Physical Object
    Format[electronic resource] :
    Pagination1 online resource (xiv, 434 p.)
    Number of Pages434
    ID Numbers
    Open LibraryOL27091322M
    ISBN 10366213117X, 3642105149
    ISBN 109783662131176, 9783642105142
    OCLC/WorldCa851746181

    -tensor=scalar=number 26 1 0-tensor=contravariant1-tensor=vector 27 0 1-tensor=covariant1-tensor=covector 27 0 2-tensor=covariant2-tensor = lineartransformation:V!V 28 2 0-tensor=contravariant2-tensor = lineartransformation:V!V 32 1 1-tensor=mixed2-tensor = lineartransformation:V!V andV!V 35 0 3-tensor.   Tensor Geometry: The Geometric Viewpoint and its Uses Author: Christopher Terence John Dodson, Timothy Poston Published by Springer Berlin Heidelberg ISBN: DOI: /

    1 The index notation Before we start with the main topic of this booklet, tensors, we will first introduce a new notation for vectors and matrices, and their algebraic manipulations: the indexFile Size: KB. Tensor analysis, branch of mathematics concerned with relations or laws that remain valid regardless of the system of coordinates used to specify the quantities. Such relations are called covariant. Tensors were invented as an extension of vectors to formalize the manipulation of geometric entities arising in the study of mathematical manifolds.. A vector is an entity that has both magnitude.

    Lectures on Geodesics Riemannian Geometry. Aim of this book is to give a fairly complete treatment of the foundations of Riemannian geometry through the tangent bundle and the geodesic flow on it. Topics covered includes: Sprays, Linear connections, Riemannian manifolds, Geodesics, Canonical connection, Sectional Curvature and metric structure. Primarily intended for the undergraduate and postgraduate students of mathematics, this textbook covers both geometry and tensor in a single volume. This book aims to provide a conceptual exposition of the fundamental results in the theory of tensors. It also illustrates the applications of tensors to differential geometry, mechanics and s: 2.


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Tensor Geometry by Christopher Terence John Dodson Download PDF EPUB FB2

'Tensor Analysis' suggests to a mathematician an ungeometric, manipulative debauch of indices, with tensors ill-defined as 'quantities that transform according to' unspeakable formulae. 'Differential Geometry' would leave many a physicist unaware that the book is about matters with which he is very much by: The applications of tensors to the fields of differential geometry, relativity, cosmology and electromagnetism is another attraction of the present book.

This book is intended to serve as text for postgraduate students of mathematics, physics and engineering. It is ideally suited for both students and teachers who are Tensor Geometry book in /5(6).

The geometry of tensors is Tensor Geometry book a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in by:   Tensor Geometry book.

Read reviews from world’s largest community for readers. We have been very encouraged by the reactions of students and teachers usi /5(9). Tensor Geometry The Geometric Viewpoint and its Uses. Authors: Dodson, Christopher T.

J., Poston, Timothy Free Preview. The authors present a thorough development of TENSOR CALCULUS, from basic principals, such as ordinary three dimensional vector space. Tensors are generalizations of vectors to any number of dimensions (vectors are type (1,0) tensors, diff.

forms are type (0,1) tensors).Cited by: This book includes both tensor calculus and differential geometry in a single volume.

This book provides a conceptual exposition of the fundamental results in the theory of tensors. It also illustrates the applications of tensors to differential geometry, mechanics and relativity. Tensor calculus is a powerful tool that combines the geometric and analytical perspectives and enables us to take full advantage of the computational utility of coordinate systems.

The tensor approach can be of benefit to members of all technical sciences including mathematics and all engineering by: that they provide a useful way to organize data.

Geometry is a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: as a classroom textbook, a reference work for researchers, and.

Tensor which depends on two directions one normal to the area and other that of the force on it. Tensors have their applications to Riemannian Geometry, Mechanics, Elasticity, Theory of Relativity, Electromagnetic Theory and many other disciplines of Science and Size: 1MB.

geometry—I’ll save those for a separate set of notes. The title, The Poor Man’s Introduction to Tensors, is a reference to Gravitation by Misner, Thorne and Wheeler, which characterizes simplified approaches to a problem as “the poor man’s way to do X.” Originally, these notes were.

Renteln’s book makes it clear what the meaning of the word is, whereas other books leave it undefined and somewhat mystical. We have the mathematical object of a differentiable manifold, and it is imbued with a topology and a metric.

The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to.

Tensor Calculus and Differential Geometry 2WAH0 Luc Florack March 9, Cover illustration: papyrus fragment from Euclid’s Elements of Geometry, Book II [8]. Contents Preface iii Notation 1 1 Prerequisites from Linear Algebra 3 2 Tensor Calculus 7File Size: 1MB.

Tensor analysis is the type of subject that can make even the best of students shudder. My own post-graduate instructor in the subject took away much of the fear by speaking of an implicit rhythm in the peculiar notation traditionally used, and helped me to see how this rhythm plays its way throughout the various Size: KB.

Tensor Geometry: The Geometric Viewpoint and its Uses - Christopher T. Dodson, Timothy Poston - Google Books We have been very encouraged by the reactions of. Algebraic Geometry Theory ear Oscillations, and S.

LEFSCI WOLFE vol. IV McCARTHY tems 1. TUCKER vol. UCKER, and les, vol. IV A. TUŒa (near Oscillatior hysics aces -entia] 1. ANNALS OF MATHEMATICS STUDIES Edited by Robert C. Gunning, John C. Moc Algebraic Theory of Numbers By HERMANN WEYLFile Size: 3MB. Sharipov. Quick Introduction to Tensor Analysis: lecture notes.

Freely distributed on-line. Is free for individual use and educational purposes. Any commercial use without written consent from the author is prohibited. This book was written as lecture notes for classes that I taught to undergraduate.

In mathematics, a tensor is an algebraic object related to a vector space and its dual space that can take several different forms, for example, a scalar, a tangent vector at a point, a cotangent vector (dual vector) at a point, or a multi-linear map between vector spaces.

KEY WORDS: Curve, Frenet frame, curvature, torsion, hypersurface, funda-mental forms, principal curvature, Gaussian curvature, Minkowski curvature, manifold, tensor eld, connection, geodesic curve SUMMARY: The aim of this textbook is to give an introduction to di er-ential geometry.

It is based on the lectures given by the author at E otv os. The book deals with integral geometry of symmetric tensor flelds. This section of integral geometry can be viewed as mathematical basis for tomography of anisotropic media whose interaction with sounding radiation depends essentially on the direction in which the latter propagates.Differential Geometry Lecture Notes.

This book covers the following topics: Smooth Manifolds, Plain curves, Submanifolds, Differentiable maps, immersions, submersions and embeddings, Basic results from Differential Topology, Tangent spaces and tensor calculus, Riemannian geometry.Tensor Geometry The Geometric Viewpoint and its Uses.

Authors (view affiliations) Christopher Terence John Dodson; Timothy Poston; Book. 41 Citations; We have been very encouraged by the reactions of students and teachers using our book over the past ten years and so this is a complete retype in TEX, with corrections of known errors and the.