Master Tensor Calculus with Our Introductory Tensors Book

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The discussion centers on the challenges faced in understanding tensor calculus within an introductory general relativity (GR) course, particularly when using D'Inverno's textbook, which is perceived as moving too quickly. Participants suggest alternative resources for learning tensors, highlighting Sean Carroll's book as a helpful option. Recommendations also include differential geometry texts by Seth Warner and Noel J. Hicks, which introduce concepts early, and Spivak's Volume 2, noted for its detailed explanation of the transition from classical to modern tensor notation. Additionally, Simmonds' book on tensors is praised for its clarity and effectiveness, especially after completing a first semester of graduate studies.
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So the tensor calculus part of my into to GR class is kicking my butt. I'm using the book by D'Inverno, but I feel like he's going too quickly over tensor calculus. Is there a more introductory text on tensors that I missed out on?

I've taken courses on linear algebra before, but not differential geometry. I feel like there's a huge gap between the two and was looking for something to bridge it.
 
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Sean Carroll's book is pretty good for this.
 
some differential geometry books treat this early, like the books by seth warner and noel j hicks. but the treatment by spivak in vol 2 os his big set is more detailed and explains the translation from classical (upper and lower indices) to modern (conceptual, multilinear) notation.
 
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i am self learning physics. have you ever worked your way backwards again after finishing most undergrad courses? i have textbooks for junior/senior physics courses in classical mechanics, electrodynamics, thermal physics, quantum mechanics, and mathematical methods for self learning. i have the Halliday Resnick sophomore book. working backwards, i checked out Conceptual Physics 11th edition by Hewitt and found this book very helpful. What i liked most was how stimulating the pictures...

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