An Introduction to Tensor Calculus(grinfeld.org)
grinfeld.org
An Introduction to Tensor Calculus
https://grinfeld.org/books/An-Introduction-To-Tensor-Calculus/
7 comments
I have his book and others relating to tensor analysis and its good as is his YouTube channel, if anyone is after a gentler introduction to differential geometry I've recently discovered this book "Curvature of Space and Time, with an Introduction to Geometric Analysis" by Iva Stavrov. It glosses over and leaves out a lot of the proofs and topology discussions etc and gives a good overview to get started.
Edit: a link https://smile.amazon.com/Curvature-Introduction-Geometric-An...
Edit: a link https://smile.amazon.com/Curvature-Introduction-Geometric-An...
Pretty nice overview, I'd highly recommend Hartl's gravity for a physics focused introduction to tensor calculus along with an actual application centric usage of the same: https://www.amazon.com/Gravity-Introduction-Einsteins-Genera...
I dunno why there is so much interest in this subject. Just knowing basic calculus and linear algebra will cover the majority of applications. Why does the chapter on matrix multiplication come 7 chapters after "The Christoffel Symbol". I think there are better guides than this, shorter and more to the point and better organized. Start with Cartesian tensors and polar coordinate transforms.
> Just knowing basic calculus and linear algebra will cover the majority of applications.
I'm confused by your comment. It's a book on tensor calculus, not a book on linear algebra or calculus (or a book on machine learning), right? It's like seeing a book on calculus and complaining linear algebra is sufficient. Or seeing a book on linear algebra and complaining matrix multiplication is sufficient. The text isn't teaching how to massage N-dimensional NumPy arrays, it's teaching the algebra surrounding an object.
I'm confused by your comment. It's a book on tensor calculus, not a book on linear algebra or calculus (or a book on machine learning), right? It's like seeing a book on calculus and complaining linear algebra is sufficient. Or seeing a book on linear algebra and complaining matrix multiplication is sufficient. The text isn't teaching how to massage N-dimensional NumPy arrays, it's teaching the algebra surrounding an object.
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It always used to be the case that the main reason people learned tensor calculus was General Relativity (as well as some other bits of theoretical physics). I know machine learning is a popular and growing field, but I suspect theoretical physics remains the main reason people learn it.
because machine learning is finding and descending the steepest gradient in lots of dimensions.
you don't need curved cordinates or covariant derivatives for that
> I think there are better guides than this
Care to share?
Care to share?
It would be cool to have some kind of PDF export! Definitely seems very educational nevertheless.
Supporters do get access to PDFs of his draft books. These are rewrites of his original book on tensor calculus [1]. I worked through most of the original and I thought it was quite good.
[1] https://www.amazon.com.au/Introduction-Tensor-Analysis-Calcu...
[1] https://www.amazon.com.au/Introduction-Tensor-Analysis-Calcu...
Need more examples in the beginning of why tensors. The Euler example is good but not clear. But overall at least the introduction is good.
I have no relationship to Pavel and just want to support his efforts.
[1] https://grinfeld.org/