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 : Mathematics
Languages : en
Pages : 114

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Book Description

Author: Robert F. Snider
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110564866
Category : Science
Languages : en
Pages : 268

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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: Donald Edward Bourne
Publisher: CRC Press
ISBN: 1351094424
Category : Mathematics
Languages : en
Pages : 274

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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: 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: Rutherford Aris
Publisher: Courier Corporation
ISBN: 048613489X
Category : Mathematics
Languages : en
Pages : 322

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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: William Smyth
Publisher:
ISBN: 9781794807525
Category :
Languages : en
Pages : 186

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Book Description
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.

Author: David Melvin Henderson
Publisher: AIAA (American Institute of Aeronautics & Astronautics)
ISBN:
Category : Mathematics
Languages : en
Pages : 234

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Book Description
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.

Author: Siegfried Hess
Publisher: Springer
ISBN: 331912787X
Category : Science
Languages : en
Pages : 449

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Book Description
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.