[PDF] Introduction To Vectors And Tensors eBook

Author : Ray M. Bowen
Publisher : Springer
Page : 224 pages
File Size : 44,38 MB
Release : 1976-05-31
Category : Mathematics
ISBN :

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To Volume 1 This work represents our effort to present the basic concepts of vector and tensor analysis. Volume 1 begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume 2 begins with a discussion of Euclidean manifolds, which leads to a development of the analytical and geometrical aspects of vector and tensor fields. We have not included a discussion of general differentiable manifolds. However, we have included a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold. In preparing this two-volume work, our intention was to present to engineering and science students a modern introduction to vectors and tensors. Traditional courses on applied mathematics have emphasized problem-solving techniques rather than the systematic development of concepts. As a result, it is possible for such courses to become terminal mathematics courses rather than courses which equip the student to develop his or her understanding further.

Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 23,40 MB
Release : 2015
Category : Mathematics
ISBN : 142141564X

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It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.--Gary White, editor of The Physics Teacher "American Journal of Physics"

Author : A. I. Borisenko
Publisher : Courier Corporation
Page : 292 pages
File Size : 20,58 MB
Release : 2012-08-28
Category : Mathematics
ISBN : 0486131904

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Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.

Author : Daniel A. Fleisch
Publisher : Cambridge University Press
Page : 206 pages
File Size : 39,10 MB
Release : 2011-09-22
Category : Science
ISBN : 9780521171908

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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.

Author : C. E. Springer
Publisher : Courier Corporation
Page : 258 pages
File Size : 34,43 MB
Release : 2013-09-26
Category : Mathematics
ISBN : 048632091X

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Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.

Author : Robert C. Wrede
Publisher : Courier Corporation
Page : 436 pages
File Size : 25,30 MB
Release : 2013-01-30
Category : Mathematics
ISBN : 0486137112

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Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.

Author : Rutherford Aris
Publisher : Courier Corporation
Page : 322 pages
File Size : 26,90 MB
Release : 2012-08-28
Category : Mathematics
ISBN : 048613489X

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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 : Juan R. Ruiz-Tolosa
Publisher : Springer Science & Business Media
Page : 675 pages
File Size : 46,88 MB
Release : 2005-12-08
Category : Computers
ISBN : 3540270663

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This textbook deals with tensors that are treated as vectors. Coverage details such new tensor concepts as the rotation of tensors, the transposer tensor, the eigentensors, and the permutation tensor structure. The book covers an existing gap between the classic theory of tensors and the possibility of solving tensor problems with a computer. A complementary computer package, written in Mathematica, is available through the Internet.

Author : George E. Hay
Publisher : Courier Corporation
Page : 210 pages
File Size : 23,62 MB
Release : 1953-01-01
Category : Mathematics
ISBN : 0486601099

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"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.

Author : D. E. Bourne
Publisher : Academic Press
Page : 271 pages
File Size : 26,69 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483260704

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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.