Download PDF Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov
Nonetheless, reading guide Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov in this website will lead you not to bring the printed book almost everywhere you go. Simply store the book in MMC or computer system disk as well as they are offered to read at any time. The flourishing system by reading this soft documents of the Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov can be introduced something brand-new practice. So now, this is time to prove if reading could boost your life or not. Make Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov it undoubtedly work and get all advantages.
Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov
Download PDF Vector & Tensor Analysis With Applications, by A I Borisenko, I.E. Tarapov
Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov. Eventually, you will uncover a brand-new adventure and also knowledge by spending more money. However when? Do you believe that you need to acquire those all needs when having much money? Why don't you attempt to get something straightforward at initial? That's something that will lead you to know more concerning the globe, adventure, some locations, past history, amusement, as well as much more? It is your personal time to continue reviewing routine. Among the books you could enjoy now is Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov here.
Right here, we have countless e-book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov and also collections to review. We likewise offer alternative types and type of the publications to look. The enjoyable e-book, fiction, history, unique, science, and various other sorts of books are offered below. As this Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov, it becomes one of the preferred publication Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov collections that we have. This is why you remain in the right site to view the outstanding publications to possess.
It won't take even more time to download this Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov It won't take even more money to publish this publication Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov Nowadays, people have actually been so clever to utilize the technology. Why don't you use your gizmo or various other device to conserve this downloaded soft documents e-book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov This method will certainly let you to consistently be gone along with by this book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov Naturally, it will be the most effective pal if you review this publication Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov until completed.
Be the first to obtain this book now and obtain all reasons you require to read this Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov The e-book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov is not simply for your duties or requirement in your life. Books will always be a good close friend in each time you review. Now, allow the others recognize for this page. You could take the benefits and discuss it likewise for your good friends and individuals around you. By by doing this, you can truly obtain the definition of this book Vector & Tensor Analysis With Applications, By A I Borisenko, I.E. Tarapov profitably. Just what do you consider our concept right here?
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
