Vector and Tensor Analysis with Applications

I must agree with the other reviewer, this is a excellent book if you want to have clear ideas about the most basic tensor concepts. In other books of tensors, you start to see transformations of coordinates with any sense, you can't understand anything and after closing the book you forget everything, that kind of books treat tensor analysis like if it would be an alphabet soup . This is not the case, if goes slowly and explaining not only the how (that is in all the books) but the WHY. I love this book, finally it helped me a lot to undertand so many things. Five stars.

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.

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.

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.