What is a good textbook to start learning tensors?

  • Context: Linear Algebra 
  • Thread starter Thread starter Feynman.12
  • Start date Start date
  • Tags Tags
    Tensors Textbook
Click For Summary

Discussion Overview

The discussion revolves around recommendations for textbooks to learn about tensors, particularly in the context of preparing for studies in particle physics, general relativity, and quantum field theory. Participants share various resources and express their preferences regarding the suitability of different texts for introducing tensor notation and related concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses a desire to learn tensors as a prerequisite for studying particle physics and general relativity.
  • Another participant recommends several Schaum's series books, including "Schaum Tensor Calculus," "Schaum Vector Analysis," and "Schaum Differential Geometry," as good options for learning tensors.
  • A participant suggests that the Wikipedia page on tensors provides a good overview, noting that many textbooks may overlook broader concepts in favor of detailed technicalities.
  • Chapter 3 of "A First Course in General Relativity" by Bernard Schutz is recommended as an accessible introduction to tensors, though the same participant expresses reservations about the book's treatment of general relativity.
  • Another suggestion includes Chapter 8 of "Linear Algebra Done Wrong" by Sergei Treil, which is noted for its overall quality in linear algebra and availability for free download.
  • One participant mentions the challenge of finding a satisfactory book that covers classical vector analysis in a way that is relevant for early physics students, indicating a preference for more practical applications over abstract treatments.
  • H. Stephan's "Relativity - An Introduction to Special and General Relativity" is highlighted as a good resource for understanding the Ricci calculus in holonomic coordinates.

Areas of Agreement / Disagreement

Participants present multiple competing views on the best resources for learning tensors, with no consensus on a single recommended textbook. Different preferences for the level of mathematical rigor and practical applicability are evident.

Contextual Notes

Some participants note the limitations of existing texts in addressing the needs of physics students, particularly regarding the treatment of vector analysis and the balance between abstract and practical approaches.

Feynman.12
Messages
14
Reaction score
0
I am currently an undergraduate physics and applied mathematics student, and have wanted to go ahead in my course to learn about particle physics and general relativity. However, these topics, along with Quantum field theory which I want to learn about later, are taught in tensor notation. So Firstly, before i start studying these subjects, I will start tensors!
 
Physics news on Phys.org
Schaum Tensor Calculus.
Schaum Vector Analysis
Schaum Differential Geometry
Here is the best options which I can recommend you
 
Chapter 3 of "A first course in general relativity" by Bernard Schutz. I doubt that there's an easier introduction to the essential stuff about tensors. If you also read chapters 1-2, you will get the best intro to SR there is. I'm less enthusiastic about this book's treatment of GR. It's not mathematical enough for me.

Chapter 8 of "Linear algebra done wrong" by Sergei Treil. This is also the best book on linear algebra, so you will undoubtedly find the rest of the book very useful as well. It can be legally downloaded for free.
 
I was also inclined to suggest a GR book for intro to tensor analysis/differential geometry. However, there usually you find the treatment in terms of holonomic coordinates or the abstract coordinate free treatment, but usually only a minority of physics students need these ever in their lives and for sure not in the first semesters. There you usually need the classical vector analysis of 3D Euclidean space in Cartesian and orthonormal curvilinear coordinates. I've not found a book, where this is done in a way which completely satifies me, I must admit. A very good review is found in my favorite classical-physics books: A. Sommerfeld, Lectures on Theoretical Physics, vol. II (Fluid Dynamics).

Of the many books on GR, for my taste the best intro to this topic (in terms of the Ricci calculus in holonomic coordinates) is found in

H. Stephan, Relativity - An introduction to special and general relativity, 3rd edition, CUP 2004
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
12
Views
11K
Replies
6
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 11 ·
Replies
11
Views
5K
  • · Replies 17 ·
Replies
17
Views
9K