Vector Analysis and Cartesian Tensors PDF Download

Author: D. E. Bourne
Publisher: Academic Press
ISBN: 1483260704
Category : Mathematics
Languages : en
Pages : 271

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Book Description
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.

Author: George Frederick James Temple
Publisher: Courier Corporation
ISBN: 9780486439082
Category : Mathematics
Languages : en
Pages : 114

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Book Description
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.

Author: Harold Jeffreys
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 0

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Book Description

Author: G. Temple
Publisher: Courier Corporation
ISBN: 0486154548
Category : Mathematics
Languages : en
Pages : 108

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Book Description
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.

Author: James Kenyon Knowles
Publisher: Oxford University Press on Demand
ISBN: 9780195112542
Category : Mathematics
Languages : en
Pages : 120

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Book Description
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.

Author: Donald Edward Bourne
Publisher: CRC Press
ISBN: 1351085972
Category : Mathematics
Languages : en
Pages : 314

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Book Description
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.

Author: Robert F. Snider
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110564866
Category : Science
Languages : en
Pages : 266

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Book Description
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.

Author: Rutherford Aris
Publisher: Courier Corporation
ISBN: 048613489X
Category : Mathematics
Languages : en
Pages : 320

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Book Description
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.

Author: L. G. Jaeger
Publisher: Elsevier
ISBN: 1483138720
Category : Technology & Engineering
Languages : en
Pages : 124

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Book Description
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.

Author: P C Kendall
Publisher: Routledge
ISBN: 1351405616
Category : Mathematics
Languages : en
Pages : 391

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Book Description
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.