Last edited by Kigaktilar

Sunday, April 26, 2020 | History

8 edition of **Tensor Geometry** found in the catalog.

- 369 Want to read
- 3 Currently reading

Published
**July 1979** by Pitman Publishing (UK) .

Written in English

- Calculus,
- Mathematics

The Physical Object | |
---|---|

Format | Paperback |

Number of Pages | 620 |

ID Numbers | |

Open Library | OL10284684M |

ISBN 10 | 0273010409 |

ISBN 10 | 9780273010401 |

"This is a first-rate book and deserves to be widely read." — American Mathematical Monthly Despite its success as a mathematical tool in the general theory of relativity and its adaptability to a wide range of mathematical and physical problems, tensor analysis has always had a rather restricted level of use, with an emphasis on notation and the manipulation of indices/5(40). Assuming only a knowledge of basic calculus, this text presents an elementary and gradual development of tensor theory. From this treatment, the traditional material of courses on vector analysis is deduced as a particular case. In addition, the book forms an introduction to metric differential geometry. Tensor geometry: the geometric viewpoint and its uses. [Christopher T J Dodson; Timothy Poston] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Contacts Search for a Library. Create Book\/a>, schema:CreativeWork\/a> ;.

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'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 engaged in /5(6).

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 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 Tensor Geometry book. 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 Tensor Geometry book 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.

Tensors: Geometry and Applications is about what happens in the general case: given an element φ of a tensor product A ⊗ B ⊗ C ⊗ ⊗ Z, it can be represented as a sum of rank one tensors a ⊗ b ⊗ c ⊗ ⊗ z.

Define the rank of φ to be the minimal number of terms in a representation. may denote a tensor of rank (2,0) by T(P,˜ Q˜); one of rank (2,1) by T(P,˜ Q,˜ A~), etc.

Our notation will not distinguish a (2,0) tensor T from a (2,1) tensor T, although a notational distinction could be made by placing marrows and ntildes over the symbol, or by appropriate use of dummy indices (Wald ).File Size: KB.

-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. Math Books Tensor Analysis and Differential Geometry free download. contain houndreds of Free Math e-Books.

Which cover almost all topics of mathematics. To see an extisive list of Tensor Analysis and Differential Geometry. We hope mathematician or person who’s interested in mathematics like these books. A carefully selected set of unsolved problems is also given at the end of each chapter, and the answers and hints for the solution of these problems are given at the end of the book.

The applications of tensors to the fields of differential geometry, relativity, cosmology and electromagnetism is another attraction of the present book.3/5(2). Plus, Tensor Calculus is really just a corollary to Differential Geometry. EDIT: I usually don't do DG, I typically stick to Algebraic Geometry (which are both structurally similar thanks to Grothendieck), so I can't recommend the best introductory book.

Tensor Analysis book. Read reviews from world’s largest community for readers. Tensor Analysis book. Read reviews from world’s largest community for readers. Start your review of Tensor Analysis: Theory And Applications To Geometry And Mechanics Of Continua.

Write a review. Abdullah Chami marked it as to-read Books: The lectures are intended to go with the official textbook: T. Frankel, The Geometry of Physics: An Introduction. The exact order of topics in the lectures may be different from the book, but I encourage you to read the book, and not necessarily only the sections that correspond to.

introduction to tensor calculus and continuum mechanics In Part One I have included introductory topics in tensors, differential geometry and relativity. Part Two presents basics from the areas of continuum mechanics (dynamics, elasticity, fluids, electricity, magnetism).

The first chapters of the book focus on the basic concepts and facts of analytic geometry, the theory of space curves, and the foundations of the theory of surfaces, including problems closely related to the first and second fundamental forms.

The treatment of the theory of surfaces makes full use of the tensor calculus.5/5(2). Leonhardt & Philbin: Geometry & Light - This book starts by developing variational principles and tensor calculus from scratch and uses them to explain the (real) science of cloaking.

Media with varying refractivity are treated mathematically as curved spaces and formal paralles are drwn with phenomena in general relativity. Let’s begin with a useful textbook from the Schaum’s Outline series, containing chapters with course notes, many solved problems, and supplementary exercises: Schaum's Outline of Differential Geometry, by Martin Lipschutz.

After starting with conc. Tensor and Vector Analysis: With Applications to Differential Geometry - Ebook written by C. E. Springer. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Tensor and Vector Analysis: With Applications to Differential Geometry.4/5(2).

Believe it or not, I made it all the way to a PhD in math at Rice University without studying anything called "tensor" in math or physics. I think many things I studied were some of the same ideas by different names - differential geometry, lots.In mathematics and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold).Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in materials, and in numerous applications in the physical sciences.

As a tensor is a generalization of a scalar (a pure number.