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eBook Vector and Tensor Analysis with Applications (Dover Books on Mathematics) ePub

eBook Vector and Tensor Analysis with Applications (Dover Books on Mathematics) ePub

by A. I. Borisenko,I. E. Tarapov,Richard A. Silverman

  • ISBN: 0486638332
  • Category: Mathematics
  • Subcategory: Math Science
  • Author: A. I. Borisenko,I. E. Tarapov,Richard A. Silverman
  • Language: English
  • Publisher: Dover Publications; New edition edition (October 1, 1979)
  • Pages: 288
  • ePub book: 1669 kb
  • Fb2 book: 1498 kb
  • Other: doc mobi lit lrf
  • Rating: 4.8
  • Votes: 246

Description

Series: Dover Books on Mathematics. Paperback: 288 pages.

Series: Dover Books on Mathematics.

Brought to you by the number 7. VECTOR AND TENSOR ANALYSIS WITH APPLICATIONS by A. I. BORISENKO and .

Also, systematic study of the differential and integral calculus of vector and tensor functions of space and time, more.

Definition of vectors and discussion of algebraic operations on vectors leads to concept of tensor and algebraic operations on tensors. Also, systematic study of the differential and integral calculus of vector and tensor functions of space and time, more. Concise, eminently readable text. Worked out problems, solutions.

Finally, vector and tensor analysis is considered from both a rudimentary . Dover books on mathematics.

Finally, vector and tensor analysis is considered from both a rudimentary standpoint, and in its fuller ramifications, concluding the volume. The strength of the book lies in the completely worked out problems and solutions at the end of each chapter. In addition, each chapter incorporates abundant exercise material. concise, clear and comprehensive treatmen. Prof. Henry G. Booker, University of California, San Diego.

Tarapov To read this book, upload an EPUB or FB2 file to Bookmate.

Vector and Tensor Analysis with Applications. Concise and readable, this text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. It also includes a systematic study of the differential and integral calculus of vector and tensor functions of space and time. Worked-out problems and solutions. To read this book, upload an EPUB or FB2 file to Bookmate.

A very important book in the area of Vector and Tensor Analysis. 12 November 2018 (14:50). Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.

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Электронная книга "Vector and Tensor Analysis with Applications", A. Tarapov. Эту книгу можно прочитать в Google Play Книгах на компьютере, а также на устройствах Android и iOS. Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "Vector and Tensor Analysis with Applications" для чтения в офлайн-режиме.

Поиск книг BookFi BookSee - Download books for free. Vector and Tensor Analysis with Applications (Dover)(266s). Vektornyj analiz i nachala tenzornogo ischislenija (3e iz. 1966)(ru)(L)(T)(127s). Vector and Tensor Analysis with Applications (Dover)(300dpi)(T)(266s). 9 Mb. Vector and Tensor Analysis with Applications. A. Tarapov, Richard A. Silverman. Категория: Mathematics, Algebra, Linear algebra.

Finally, vector and tensor analysis is considered from both a rudimentary standpoint . Publisher: Dover : Aug 28, 2012ISBN: 9780486131900Format: book.

" … the exposition is clear and the choice of topics is excellent …" Prof. R. E. Williamson, Univ. of Sussex, Brighton, EnglandThis concise introduction to a basic branch of applied mathematics is indispensable to mathematicians, physicists and engineers. Eminently readable, it covers the elements of vector and tensor analysis, with applications of the theory to specific physics and engineering problems. It lays particular stress on the applications of the theory to fluid dynamics.The authors begin with a definition of vectors and a discussion of algebraic operations on vectors.The vector concept is then generalized in a natural way, leading to the concept of a tensor. Chapter Three considers algebraic operations on tensors. Next,the authorsturn to a systematic study of the differential and integral calculus of vector and tensor functions of spaceand time. Finally, vector and tensor analysis is considered from both a rudimentary standpoint, and in its fuller ramifications, concluding thevolume.The strength of the booklies in the completely worked out problems and solutions at the end of each chapter. In addition, each chapter incorporates abundant exercise material. Intended primarily for advanced undergraduates and graduate students of math, physics and engineering, the work is self-contained and accessible to any student with a good background in calculus.Vector and Tensor Analysis With Applications is one of a series of SELECTED RUSSIAN PUBLICATIONS IN THE MATHEMATICAL SCIENCES,several of which have already been published by Dover. The authors are distinguished Russian mathematicians and specialists in gas dynamics and numerical analysis. Richard A. Silverman, editor of the series as well as editor and translator of thisvolume, has revised and improved the original edition and added a bibliography." … a concise, clear and comprehensive treatment …" Prof. Henry G. Booker, University of California, San Diego

Comments

Kizshura Kizshura
Finally a user-friendly book that explains from A to Z, clearly and cleanly, what tensors are. It also gives explanations and examples that use real-world physical applications that are both comprehensive and comprehensible.

To wit: Scalars and vectors are tensors of orders “zero” and “one” respectively. They are special cases of a larger class of objects called “a tensor of order n,” whose specification within any coordinate system requires three numbers called its components.

The key property of a tensor is the transformation law of its components, that is to say, how its components in one coordinate system are related to its components in another coordinate system. The precise form of this transformation law is a consequence of the physical or geometric meaning or properties of the tensor. Properly formulated, physical laws are “invariant under shifts and rotations from one coordinate system to another.

A second order tensor is a quantity uniquely defined by its nine components. Examples of second order tensors are the stress tensor, the moment of inertia tensor, and the deformation tensor.

Just as is the case with lower order tensors, higher order tensors may also be manipulated and operated on so that they then can be used to facilitate solving a wide variety of physical problems.

By manipulated and operated on, we mean that tensors can be contracted and multiplied; that there are symmetric and antisymmetric tensors.; that they can be reduced to their principle axes, converted to rectilinear coordinates, their eigenvalues and eigenvectors can be computed, etc.

And then we move on to tensor functions where we very quickly bump into the idea of a “tensor field.” By a tensor field, we mean a rule or a function that assigns a unique value of a tensor to each point of a certain vector space. All the algebraic operations considered on lower order tensors, may apply equally to functions operating on tensor fields.

For instance, if we consider functions on a curve in space, we can define its tensor fields with respect to line integration between points on the curve or within the field itself, similarly for surfaces in three-space. The Theorems of Gauss, Green and Stokes are special cases of tensor fields, defined with respect to curves and surfaces in space.

Surely by now, everyone gets the idea: All these things can be generalized across physical entities and across operations. Having concrete examples just puts meat on the bones, solidifying the ideas. Five stars
Macage Macage
It is a good book I like the first two chapters, its is very useful two understand the basics idea if tensors.Also applications help a lot to complement the reading.
X-MEN X-MEN
I was first exposed to tensors in college, and the experience was so unpleasant and bewildering that I switched to quantum mechanics. QM made sense to me; tensors did not.

Decades later, I had a real need for tensors in my job, so I had to learn them. I bought and read a half-dozen well-rated books from Amazon, but only this book worked. The exposition is mathematically rigorous, but the content is also well-motivated. Their explanation of "The Tensor Concept" is the subject of a dedicated chapter; it alone is worth the price of the book. Its presentation encapsulates the book's style, so I'll preview it here.

A standard, one-dimensional vector is a ray in space, with direction and length independent of the coordinate system. As the coordinate system changes (e.g. rotate and/or stretch the axes), the coordinate values change, but the vector is the same. (Indeed, that's how you figure out the new coordinate values!)

The most simple example of mapping one vector into another is multiplication by a two dimensional matrix. Here is the golden insight: if the input and output vectors are coordinate independent, then there must be some kind of coordinate-independent function that defines the mapping, and it is called a tensor. In short, a mixed rank-2 tensor is the coordinate independent version of a matrix.

They work through the transformation rules of a standard vector to establish notation, then work through the exact corresponding process to get the transformation rules for the matrix. Instead of just asserting that "A Tensor is something which transforms the following way", they start with the intuitive notion and present a simple derivation of the transformation rule. For example, they state up front that the reason why the tensor transforms is that there is a change in basis vectors. Some descriptions never mention what is causing the tensor to 'transform' -- they just assume you already know. An excellent precept of math education is "Never memorize, always re-derive" (because memorizing what you don't understand may get you through the next test, but it deprives one of the foundation necessary to get through the test after next). The presentation in this book follows that precept beautifully (e.g. starting at transformation of bases and deriving the transformation laws). The Soviets were famous for their mathematical education, and this book reflects the excellence of that educational approach.

Similarly, the dot product of two vectors defines a scalar. If the scalar is coordinate independent, then there must be a coordinate independent function from vectors to numbers. It is a different kind of rank-1 tensor. When they do the same basic derivation, the distinction between covariant and contravariant indicies becomes crystal clear. If the components of the vector are a "contravariant" tensor, then this "different kind" is a "covariant" tensor. They also explain the relationship between reciprocal basis systems, and illustrate in clear pictures why whatever is "covariant" in one system is "contravariant" in the other, and vice versa. So they finally made clear what was so confusing about "covariant" and "contravariant": there is no fundamental distinction, and it just depends on which arbitrary choice of coordinate system one makes.

That's the first 100 pages. The next 150 present the "applications" portion. Once the basic concept is clear, the rest is fairly straightforward algebra. Again, it is quite well presented, but the main value to me was the conceptual foundation.
Zamo Zamo
This book is a translation from the Russian of a regarded text written in the 1960's. Taking this into account you cannot expect to find a state-of-the-art exposition of the subject. However, the book is written in a very concise and focused style, making it endurable. Its clear introduction to many delicate topics (covariant derivatives, metric tensors, geodesics, etc.) is still valuable even now when the differential form approach seems to have won the battle. Also, the sections it devotes to integral theorems look more in touch with current trends in mathematics than most of the classical texts at this level.
Nuadabandis Nuadabandis
It clearly introduce covariant , contravariant component of tensor and metric tensor ,covariant derivative and Christoffel symbols.Many solved problems at the end of each Chapter make the text easy to understanding.
Shakagul Shakagul
All of the basic concepts of introductory Tensor Analysis were adequately dealt with in a relatively clear and concise way; however, the numerous errors, oversimplifications, and oversights was a constant source of annoyance and doubt.