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.
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 314 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.
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.
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 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Vector and Tensor Analysis Second Edition written by Eutiquio C. Young and published by CRC Press. This book was released on 1992-12-22 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised and updated throughout, this book presents the fundamental concepts of vector and tensor analysis with their corresponding physical and geometric applications - emphasizing the development of computational skills and basic procedures, and exploring highly complex and technical topics in simplified settings.;This text: incorporates transformation of rectangular cartesian coordinate systems and the invariance of the gradient, divergence and the curl into the discussion of tensors; combines the test for independence of path and the path independence sections; offers new examples and figures that demonstrate computational methods, as well as carify concepts; introduces subtitles in each section to highlight the appearance of new topics; provides definitions and theorems in boldface type for easy identification. It also contains numerical exercises of varying levels of difficulty and many problems solved.
Download or read book Vector and Tensor Analysis written by Eutiquio C. Young and published by . This book was released on 1978 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A History of Vector Analysis written by Michael J. Crowe and published by Courier Corporation. This book was released on 1994-01-01 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.
Download or read book A Brief on Tensor Analysis written by James G. Simmonds and published by Springer Science & Business Media. This book was released on 2012-10-31 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.
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.
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.
Download or read book Applications of Vector Analysis and Complex Variables in Engineering written by Otto D. L. Strack and published by Springer Nature. This book was released on 2020-04-18 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the application of mathematical methods and theorems tosolve engineering problems, rather than focusing on mathematical proofs. Applications of Vector Analysis and Complex Variables in Engineering explains the mathematical principles in a manner suitable for engineering students, who generally think quite differently than students of mathematics. The objective is to emphasize mathematical methods and applications, rather than emphasizing general theorems and principles, for which the reader is referred to the literature. Vector analysis plays an important role in engineering, and is presented in terms of indicial notation, making use of the Einstein summation convention. This text differs from most texts in that symbolic vector notation is completely avoided, as suggested in the textbooks on tensor algebra and analysis written in German by Duschek and Hochreiner, in the 1960s. The defining properties of vector fields, the divergence and curl, are introduced in terms of fluid mechanics. The integral theorems of Gauss (the divergence theorem), Stokes, and Green are introduced also in the context of fluid mechanics. The final application of vector analysis consists of the introduction of non-Cartesian coordinate systems with straight axes, the formal definition of vectors and tensors. The stress and strain tensors are defined as an application. Partial differential equations of the first and second order are discussed. Two-dimensional linear partial differential equations of the second order are covered, emphasizing the three types of equation: hyperbolic, parabolic, and elliptic. The hyperbolic partial differential equations have two real characteristic directions, and writing the equations along these directions simplifies the solution process. The parabolic partial differential equations have two coinciding characteristics; this gives useful information regarding the character of the equation, but does not help in solving problems. The elliptic partial differential equations do not have real characteristics. In contrast to most texts, rather than abandoning the idea of using characteristics, here the complex characteristics are determined, and the differential equations are written along these characteristics. This leads to a generalized complex variable system, introduced by Wirtinger. The vector field is written in terms of a complex velocity, and the divergence and the curl of the vector field is written in complex form, reducing both equations to a single one. Complex variable methods are applied to elliptical problems in fluid mechanics, and linear elasticity. The techniques presented for solving parabolic problems are the Laplace transform and separation of variables, illustrated for problems of heat flow and soil mechanics. Hyperbolic problems of vibrating strings and bars, governed by the wave equation are solved by the method of characteristics as well as by Laplace transform. The method of characteristics for quasi-linear hyperbolic partial differential equations is illustrated for the case of a failing granular material, such as sand, underneath a strip footing. The Navier Stokes equations are derived and discussed in the final chapter as an illustration of a highly non-linear set of partial differential equations and the solutions are interpreted by illustrating the role of rotation (curl) in energy transfer of a fluid.
Download or read book Vector and Tensor Analysis written by George E. Hay and published by Courier Corporation. This book was released on 1953-01-01 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Remarkably comprehensive, concise and clear." — Industrial Laboratories "Considered as a condensed text in the classical manner, the book can well be recommended." — Nature Here is a clear introduction to classic vector and tensor analysis for students of engineering and mathematical physics. Chapters range from elementary operations and applications of geometry, to application of vectors to mechanics, partial differentiation, integration, and tensor analysis. More than 200 problems are included throughout the book.
Download or read book A Student s Guide to Vectors and Tensors written by Daniel A. Fleisch and published by Cambridge University Press. This book was released on 2011-09-22 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author.
Download or read book Tensors Differential Forms and Variational Principles written by David Lovelock and published by Courier Corporation. This book was released on 2012-04-20 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
Download or read book Mathematical Methods for Engineers and Scientists 2 written by Kwong-Tin Tang and published by Springer Science & Business Media. This book was released on 2006-11-30 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to help students feel comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.
Download or read book Vectors and Tensors by Example written by Richard E. Haskell and published by CreateSpace. This book was released on 2015-09-25 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: If you have been confused by vectors, vector calculus, tensor analysis, or quaternions, this book is for you. Packed with examples, including Matlab examples, this book will show you: How to use Matlab to calculate dot and cross products, and solve linear equations; How to prove any vector identity using Cartesian tensors; How to derive the expressions for gradient, divergence, Laplacian, and curl in any curvilinear coordinate system; How to understand covariant and contravariant components of a vector; The meaning of Christoffel symbols in covariant differentiation; How to derive the curvature tensor; How quaternions can be used to describe vector rotations in 3-D space.
