Ebook Free Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov
Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov. Provide us 5 mins and we will certainly show you the most effective book to review today. This is it, the Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov that will certainly be your best selection for much better reading book. Your 5 times will certainly not spend lost by reading this internet site. You could take the book as a resource to make far better principle. Referring guides Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov that can be positioned with your needs is at some point tough. Yet right here, this is so very easy. You can find the very best thing of book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov that you can check out.
Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov
Ebook Free Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov
Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov. The industrialized modern technology, nowadays assist every little thing the human requirements. It includes the daily tasks, jobs, workplace, home entertainment, and also more. Among them is the excellent net connection and computer system. This problem will alleviate you to assist among your pastimes, reading routine. So, do you have ready to read this book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov now?
To get rid of the issue, we now provide you the technology to obtain the book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov not in a thick published documents. Yeah, reading Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov by on the internet or getting the soft-file just to review could be among the methods to do. You may not feel that reading an e-book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov will serve for you. But, in some terms, May people effective are those that have reading habit, included this kind of this Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov
By soft data of the publication Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov to review, you could not require to bring the thick prints all over you go. At any time you have willing to check out Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov, you could open your gadget to review this publication Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov in soft file system. So very easy and also quick! Reviewing the soft documents book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov will provide you very easy way to check out. It could likewise be faster due to the fact that you can read your publication Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov anywhere you desire. This on the internet Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov can be a referred book that you can delight in the remedy of life.
Due to the fact that book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov has terrific benefits to review, many people now increase to have reading routine. Sustained by the established innovation, nowadays, it is simple to download the e-book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov Even guide is not alreadied existing yet in the marketplace, you to hunt for in this site. As just what you could find of this Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov It will really alleviate you to be the first one reading this book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov as well as obtain the perks.
Selected Russian Publications in the Mathematical Science
- Sales Rank: #4420324 in Books
- Published on: 1968
- Original language: English
- Number of items: 1
- Binding: Hardcover
- 257 pages
Most helpful customer reviews
54 of 56 people found the following review helpful.
Finally -- a clear explanation of tensors
By Kindle Customer
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.
29 of 31 people found the following review helpful.
A clear development of vector and tensor concepts.
By A Customer
I have a solid foundation in vector analysis, but never felt comfortable with tensors and generalized coordinates, yet these are necessary for much of modern physics. This book was an ideal fit for my background. It presented a clear and steady development of both tensor and vector concepts with illustrations and examples. Covariant and contravariant components, metrics, and generalized coordinates were developed alongside of orthogonal basis concepts. Then, after the first half of the book developed the tools, the second half of the book presented analysis covering such topics as Stokes and Gauss' theorem, finishing with the fundamental theorem of vector analysis. My only complaint is that the book ended where it did. A section on more advanced tensor concepts would have fit in nicely.
23 of 24 people found the following review helpful.
Dated, but well-written and complete
By Bernardo Vargas
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.
Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov PDF
Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov EPub
Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov Doc
Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov iBooks
Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov rtf
Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov Mobipocket
Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov Kindle
