Cartesian Tensors

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Vector Analysis and Cartesian Tensors

Author : D. E. Bourne
Publisher : Academic Press
ISBN 13 : 1483260704
Total Pages : 271 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Vector Analysis and Cartesian Tensors by : D. E. Bourne

Download or read book Vector Analysis and Cartesian Tensors written by D. E. Bourne and published by Academic Press. This book was released on 2014-05-10 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector Analysis and Cartesian Tensors, Second Edition focuses on the processes, methodologies, and approaches involved in vector analysis and Cartesian tensors, including volume integrals, coordinates, curves, and vector functions. The publication first elaborates on rectangular Cartesian coordinates and rotation of axes, scalar and vector algebra, and differential geometry of curves. Discussions focus on differentiation rules, vector functions and their geometrical representation, scalar and vector products, multiplication of a vector by a scalar, and angles between lines through the origin. The text then elaborates on scalar and vector fields and line, surface, and volume integrals, including surface, volume, and repeated integrals, general orthogonal curvilinear coordinates, and vector components in orthogonal curvilinear coordinates. The manuscript ponders on representation theorems for isotropic tensor functions, Cartesian tensors, applications in potential theory, and integral theorems. Topics include geometrical and physical significance of divergence and curl, Poisson's equation in vector form, isotropic scalar functions of symmetrical second order tensors, and diagonalization of second-order symmetrical tensors. The publication is a valuable reference for mathematicians and researchers interested in vector analysis and Cartesian tensors.

Cartesian Tensors

Author : G. Temple
Publisher : Courier Corporation
ISBN 13 : 0486154548
Total Pages : 108 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Cartesian Tensors by : G. Temple

Download or read book Cartesian Tensors written by G. Temple and published by Courier Corporation. This book was released on 2012-05-04 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate-level text provides an introduction to isotropic tensors and spinor analysis, with numerous examples that illustrate the general theory and indicate certain extensions and applications. 1960 edition.

Cartesian Tensors

Author : Harold Jeffreys
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Cartesian Tensors by : Harold Jeffreys

Download or read book Cartesian Tensors written by Harold Jeffreys and published by . This book was released on 1969 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Irreducible Cartesian Tensors

Author : Robert F. Snider
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110564866
Total Pages : 268 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Irreducible Cartesian Tensors by : Robert F. Snider

Download or read book Irreducible Cartesian Tensors written by Robert F. Snider and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-12-04 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers the concept of cartesian tensors with the needs and interests of physicists, chemists and other physical scientists in mind. After introducing elementary tensor operations and rotations, spherical tensors, combinations of tensors are introduced, also covering Clebsch-Gordan coefficients. After this, readers from the physical sciences will find generalizations of the results to spinors and applications to quantum mechanics.

Linear Vector Spaces and Cartesian Tensors

Author : James Kenyon Knowles
Publisher : Oxford University Press on Demand
ISBN 13 : 9780195112542
Total Pages : 120 pages
Book Rating : 4.1/5 (125 download)

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Book Synopsis Linear Vector Spaces and Cartesian Tensors by : James Kenyon Knowles

Download or read book Linear Vector Spaces and Cartesian Tensors written by James Kenyon Knowles and published by Oxford University Press on Demand. This book was released on 1998 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Vector Spaces and Cartesian Tensors is primarily concerned with the theory of finite dimensional Euclidian spaces. It makes a careful distinction between real and complex spaces, with an emphasis on real spaces, and focuses on those elements of the theory that are especially important in applications to continuum mechanics. The geometric content of the theory and the distinction between matrices and tensors are emphasized, and absolute- and component-notation are both employed. While the mathematics is rigorous, the style is casual. Chapter 1 deals with the basic notion of a linear vector space; many examples of such spaces are given, including infinite-dimensional ones. The idea of a linear transformation of a vector space into itself is introduced and explored in Chapter 2. Chapter 3 deals with linear transformations on finite dimensional real Euclidean spaces (i.e., Cartesian tensors), focusing on symmetric tensors, orthogonal tensors, and the interaction of both in the kinetically important polar decomposition theorem. Chapter 4 exploits the ideas introduced in the first three chapters in order to construct the theory of tensors of rank four, which are important in continuum mechanics. Finally, Chapter 5 concentrates on applications of the earlier material to the kinematics of continua, to the notion of isotropic materials, to the concept of scalar invariant functions of tensors, and to linear dynamical systems. Exercises and problems of varying degrees of difficulty are included at the end of each chapter. Two appendices further enhance the text: the first is a short list of mathematical results that students should already be familiar with, and the second contains worked out solutions to almost all of the problems. Offering many unusual examples and applications, Linear Vector Spaces and Cartesian Tensors serves as an excellent text for advanced undergraduate or first year graduate courses in engineering mathematics and mechanics. Its clear writing style also makes this work useful as a self-study guide.

Cartesian Tensors

Author : George Frederick James Temple
Publisher : Courier Corporation
ISBN 13 : 9780486439082
Total Pages : 114 pages
Book Rating : 4.4/5 (39 download)

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Book Synopsis Cartesian Tensors by : George Frederick James Temple

Download or read book Cartesian Tensors written by George Frederick James Temple and published by Courier Corporation. This book was released on 2004-09-01 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Vectors, Tensors and the Basic Equations of Fluid Mechanics

Author : Rutherford Aris
Publisher : Courier Corporation
ISBN 13 : 048613489X
Total Pages : 322 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Vectors, Tensors and the Basic Equations of Fluid Mechanics by : Rutherford Aris

Download or read book Vectors, Tensors and the Basic Equations of Fluid Mechanics written by Rutherford Aris and published by Courier Corporation. This book was released on 2012-08-28 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.

Irreducible Cartesian Tensors

Author : Robert F. Snider
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110563738
Total Pages : 266 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Irreducible Cartesian Tensors by : Robert F. Snider

Download or read book Irreducible Cartesian Tensors written by Robert F. Snider and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-12-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers the concept of cartesian tensors with the needs and interests of physicists, chemists and other physical scientists in mind. After introducing elementary tensor operations and rotations, spherical tensors, combinations of tensors are introduced, also covering Clebsch-Gordan coefficients. After this, readers from the physical sciences will find generalizations of the results to spinors and applications to quantum mechanics.

Vector Analysis and Cartesian Tensors

Author : Donald Edward Bourne
Publisher : CRC Press
ISBN 13 : 1351094424
Total Pages : 274 pages
Book Rating : 4.3/5 (51 download)

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Book Synopsis Vector Analysis and Cartesian Tensors by : Donald Edward Bourne

Download or read book Vector Analysis and Cartesian Tensors written by Donald Edward Bourne and published by CRC Press. This book was released on 2018-05-04 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive self-contained text suitable for use by undergraduate mathematics, science and engineering students following courses in vector analysis. The earlier editions have been used extensively in the design and teaching of may undergraduate courses. Vectors are introduced in terms of Cartesian components, an approach which is found to appeal to many students because of the basic algebraic rules of composition of vectors and the definitions of gradient divergence and curl are thus made particularly simple. The theory is complete, and intended to be as rigorous as possible at the level at which it is aimed.

Cartesian Tensors in Engineering Science

Author : L. G. Jaeger
Publisher : Elsevier
ISBN 13 : 1483138720
Total Pages : 125 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Cartesian Tensors in Engineering Science by : L. G. Jaeger

Download or read book Cartesian Tensors in Engineering Science written by L. G. Jaeger and published by Elsevier. This book was released on 2016-06-06 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cartesian Tensors in Engineering Science provides a comprehensive discussion of Cartesian tensors. The engineer, when working in three dimensions, often comes across quantities which have nine components. Variation of the components in a given plane may be shown graphically by a familiar construction called Mohr's circle. For such quantities it is always possible to find three mutually perpendicular axes, called principal axes, with respect to which the six ""paired up"" components are all zero. Such quantities are called symmetric tensors of the second order. The student may at this stage be struck by the fact that the physical quantities with which he normally deals have either one component, three components or nine components, being respectively scalars, vectors, and what have just been called second order tensors. The family of quantities having 1, 3, 9, 27, ... components does exist. It is the tensor family in three dimensions. The book discusses the ""tests"" a given quantity must pass in order to qualify as a member of the family. The products of tensors, elasticity, and second moment of area and moment of inertia are also covered. Although written primarily for engineers, it is hoped that students of various branches of physical science may find this book useful.

Vector Analysis and Cartesian Tensors, Third edition

Author : P C Kendall
Publisher : Routledge
ISBN 13 : 1351405616
Total Pages : 324 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Vector Analysis and Cartesian Tensors, Third edition by : P C Kendall

Download or read book Vector Analysis and Cartesian Tensors, Third edition written by P C Kendall and published by Routledge. This book was released on 2017-09-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive and self-contained text suitable for use by undergraduate mathematics, science and engineering students. Vectors are introduced in terms of cartesian components, making the concepts of gradient, divergent and curl particularly simple. The text is supported by copious examples and progress can be checked by completing the many problems at the end of each section. Answers are provided at the back of the book.

All Things Flow

Author : William Smyth
Publisher :
ISBN 13 : 9781794807525
Total Pages : 186 pages
Book Rating : 4.8/5 (75 download)

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Book Synopsis All Things Flow by : William Smyth

Download or read book All Things Flow written by William Smyth and published by . This book was released on 2019-09-10 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate-level textbook for students in the natural sciences. After reviewing the necessary math, it describes the logical path from Newton's laws of motion to our modern understanding of fluid mechanics. It does not describe engineering applications but instead focuses on phenomena found in nature. Once developed, the theory is applied to three familiar examples of flows that can be observed easily in Earth's atmosphere, oceans, rivers and lakes: vortices, interfacial waves, and hydraulic transitions. The student will then have both (1) the tools to analyze a wide range of naturally-occurring flows and (2) a solid foundation for more advanced studies in atmospheric dynamics and physical oceanography. Appendices give more detailed explanations and optional topics.

Applied Cartesian Tensors for Aerospace Simulations

Author : David Melvin Henderson
Publisher : AIAA (American Institute of Aeronautics & Astronautics)
ISBN 13 :
Total Pages : 234 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Applied Cartesian Tensors for Aerospace Simulations by : David Melvin Henderson

Download or read book Applied Cartesian Tensors for Aerospace Simulations written by David Melvin Henderson and published by AIAA (American Institute of Aeronautics & Astronautics). This book was released on 2006 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new approach to aerospace flight vehicle equations of motion based on a unifying tensorbased formulation. Covering the fundamental concepts of the geometry of space, applied mechanics, and aerospace engineering analysis, the author builds on these flight mechanics essentials to describe the motion of aircraft and space vehicles. Concepts are amplified by the presentation of aerospace applications in use today and that are tied directly to the material presented. The basic concepts of Cartesian analysis are developed along with the application of tensor notation to engineering analysis. Tensor notation (the Einstein summation convention) is introduced to give the reader exact component equations and to demonstrate its value in multi-variable analysis. By applying the summation notation in the analysis, the author believes that a more complete description of the dynamic problems of aerospace vehicle motion can be offered, and that this approach is already finding applications in aerospace engineering technologies.

Tensors for Physics

Author : Siegfried Hess
Publisher : Springer
ISBN 13 : 331912787X
Total Pages : 449 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Tensors for Physics by : Siegfried Hess

Download or read book Tensors for Physics written by Siegfried Hess and published by Springer. This book was released on 2015-04-25 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with. The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic by external orienting fields. The dynamics of tensors deals with phenomena of current research. In the last section, the 3D Maxwell equations are reformulated in their 4D version, in accord with special relativity.

Vector Analysis and Cartesian Tensors

Author : Krishnamurty Karamcheti
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Vector Analysis and Cartesian Tensors by : Krishnamurty Karamcheti

Download or read book Vector Analysis and Cartesian Tensors written by Krishnamurty Karamcheti and published by . This book was released on 1967 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Cartesian Tensors

Author : Harold Jeffreys
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Cartesian Tensors by : Harold Jeffreys

Download or read book Cartesian Tensors written by Harold Jeffreys and published by . This book was released on 1961 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Tensor Analysis

Author : Bipin Singh Koranga
Publisher : CRC Press
ISBN 13 : 1000795918
Total Pages : 127 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis An Introduction to Tensor Analysis by : Bipin Singh Koranga

Download or read book An Introduction to Tensor Analysis written by Bipin Singh Koranga and published by CRC Press. This book was released on 2022-09-01 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of Tensor Analysis deals with the problem of the formulation of the relation between various entities in forms which remain invariant when we pass from one system of coordinates to another. The invariant form of equation is necessarily related to the possible system of coordinates with reference to which the equation remains invariant. The primary purpose of this book is the study of the invariance form of equation relative to the totally of the rectangular co-ordinate system in the three-dimensional Euclidean space. We start with the consideration of the way the sets representing various entities are transformed when we pass from one system of rectangular co-ordinates to another. A Tensor may be a physical entity that can be described as a Tensor only with respect to the manner of its representation by means of multi-sux sets associated with different system of axes such that the sets associated with different system of co-ordinate obey the transformation law for Tensor. We have employed sux notation for tensors of any order, we could also employ single letter such A,B to denote Tensors.