What is the Best Tensor Analysis Text for Engineering Applications?

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SUMMARY

The discussion centers on finding an effective tensor analysis textbook suitable for engineering applications, particularly for a chemical engineer pursuing a master's in electrical engineering. "Applications of Tensor Analysis" by A.J. McConnell is highly recommended for its comprehensive coverage of rank 3 tensors, fluid applications, and its affordability as a Dover publication. The user expresses a desire for a text that introduces rank 3 tensors in a 3D matrix format before transitioning to index notation, which can be complex for beginners.

PREREQUISITES
  • Understanding of advanced engineering mathematics
  • Familiarity with fluid mechanics concepts
  • Basic knowledge of tensor notation and operations
  • Interest in applications of rank 3 and rank 4 tensors
NEXT STEPS
  • Research "Applications of Tensor Analysis" by A.J. McConnell for comprehensive coverage
  • Explore resources on rank 3 tensors in 3D matrices
  • Study index notation and its applications in tensor analysis
  • Investigate the relationship between tensor analysis and Riemannian geometry
USEFUL FOR

This discussion is beneficial for chemical engineers, electrical engineering students, and anyone interested in applying tensor analysis to fluid dynamics and advanced mathematical concepts in engineering.

rppearso
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Hello,

Does anyone know of a REALLY good tensor analysis text. I am a chemical engineer who is working on a masters in EE and would like a text that covers fluids applications as well as rank 3 EE applications and even some rank 4 general relativity would be nice to see.

It would also be nice to see some rank 3 tensors in a 3D matrix to start with before jumping into indexes which can have confusing notation.

Hopefully someone can let me know of some really good texts that can take me from advanced engineering math (the highest math I have completed) and take me into tensors.

I have looked on amazon as well but am still unsure.
 
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I think "Applications of Tensor Analysis" by A.J. McConnell is hard to top, and it seems to cover all the topics you mention. (Although matrix notation is abandoned early on. You'll probably warm up to index notation once you get used to it.)

The book is an old classic that Dover picked up, so it's cheap, too! :o)

https://www.amazon.com/dp/0486603733/?tag=pfamazon01-20
 
Thank you, that is perfect. I figure I will get the index method down but it would be nice to see the full blown rank 3 matrix at least on the front end so I can reference it if I get confused later on. For that price I may also get the fluids specific paper back text as well.

I love these little books, hopefully this is on par with grad div curl which saved my behind in the 2 semester series of 300 level E&M.

Would this also help me understand ramian geometry and manifold theory?
 

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