Vector and Tensor Analysis With Applications

Rating:
Summary: Good coverage of concepts, but full of errors.
Review: 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.

Rating:
Summary: Dated, but well-written and complete
Review: 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.

Rating:
Summary: Must Dig to Find Errors
Review: While using this to study vector and tensor calculus, I worked through the concepts being presented and also found a number of errors. Wasn't sure if that was a good thing (that I was understanding the material and was able, therefore, to find the errors) or a bad thing (that they were there in the first place). I give it a ranking of 3 because it presents the concepts well (well enough for the student to find the mistakes). But, it should not be the only text a student uses.