What textbook would you suggest for undergraduates to learn about tensors? I am looking for an introductory book about tensors and tensor calculus.
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A lot depends on whether you're looking for a treatment for mathematics students or for engineering/physics students, and thus it would help if you said more about your background and about your reasons for learning the material. If you're looking for something relevant to engineering/physics, then one or more of the books briefly discussed in this answer might be useful to you. – Dave L. Renfro May 14 '21 at 13:25
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My question refers more for mathematics student as me. – 領域展開 May 14 '21 at 13:30
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2For a mathematics, then maybe A Brief on Tensor Analysis by Simmonds or Tensor Geometry by Dodson/Poston. Both are supposedly directed toward engineering/physics students, but both are also written from a fairly mathematical viewpoint. At a more advanced level, there's a lot about tensors (and explaining the difference between math and physics notations for them) in A Comprehensive Introduction to Differential Geometry by Spivak. – Dave L. Renfro May 14 '21 at 13:38
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dig into the ad hoc tags here in MSE, there are a lot of them related to – janmarqz May 14 '21 at 15:26
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1Tensor analysis on manifolds by Bishop and Goldberg is inexpensive (Dover) and quite modern despite the publication date and modest prerequisites. – Andrew D. Hwang May 14 '21 at 17:12
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I've always liked The Geometry of Physics by Frankel. – vb628 May 15 '21 at 07:34
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I think it's worth looking at A Student's Guide to Vectors and Tensors. – littleO May 24 '21 at 13:44
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Thanks everyone for answering and recommending me those books, much appreciated. – 領域展開 May 24 '21 at 20:08
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There are a lot of good references discussing the topic in different ways. Let me list some of my favourites:
- The Geometry of Physics - T. Frankel
- Geometry, Topology and Physics - M. Nakahara
- Analysis on Manifolds - J. Munkres
- Multilinear Algebra - W. Greub
- Linear Algebra via Exterior Products - S. Winitzki
- Advanced Linear Algebra - S. Roman
The first two books treat a large amount of subjects in mathematics, including tensor calculus, geometry etc. The aim is to provide a bridge between mathematics and physics. In Munkres's book, you will find a nice exposition about tensor products of vector spaces, which is used in the study of multivariate integrals. Greub's book is a more abstract account on the subject (and, in my opinion, more advanced), but a very nice reference too. Maybe Winitzki's book is more appropriate for you, since the book is a linear algebra-type of book, so it has proofs for theorems and some nice tools for direct applications too. Roman's book also treats the case of tensor products of vector spaces.
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