Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: dwightf on 03/01/2016 17:16:07
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Have this book and looking to work up to it. I have some others, too (Christmas presents, all). Have Calculus III (multivariable, covers 3 space) under my belt, currently working through the book Sheldon Axler's "Linear Algebra Done Right".
Current library of books:
"Linear Algebra Done Right"
"Calculus of Variations"
"Tensor Analysis on Manifolds"
"Tensors, Differential Forms, and Variational Principles"
"Differential Geometry"
"Curvature in Mathematics and Physics"
I would like suggestions on most natural order to work through these. Which of this are must haves to properly tackle Noether, if even parts of these books? Or maybe references to go to when hitting a tough patch with Neuenschwander's coverage of Noether? Is there something important that is missing? Thank you in advance for your help.
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https://gravityandlevity.wordpress.com/2011/01/20/problems-you-can-solve-just-by-looking-at-them-the-meaning-of-noethers-theorem/ (https://gravityandlevity.wordpress.com/2011/01/20/problems-you-can-solve-just-by-looking-at-them-the-meaning-of-noethers-theorem/)
http://math.ucr.edu/home/baez/noether.html (http://math.ucr.edu/home/baez/noether.html)
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Thank you for the links.
However....
...problems-you-can-solve-just-by-looking-at-them-the-meaning-of-noethers-theorem...
"In the end, I really haven’t done justice to Noether’s Theorem, which has tremendous consequences in field theory and pure mathematics as well in as the normal mechanics of particles."
Addressing that acknowledged shortcoming is the point of going further to Neuenschwander's fuller treatment. I was just looking for someone with experience with the book itself and hopefully at least some of the other ones listed. Barring that, it'll be Plan B; Just try and see if it works.
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I have a copy of Emmy Noether's Wonderful Theorem. I don't think there is an easy way round picking up the concepts.
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Not looking for or expecting an "easy way". [8D] Just looking to make sure the order was logical. If a Calculus III (multivariable**) plus "Linear Algebra Done Right" and first year college Calculus based physics (heat, mech, light, & electromagnetic) and passing knowledge of what QM and GR are about would be enough appropriate background. Or if I should go to one of those other books (or something not listed) first.
** New account here so I can't link to syllabus but he's overview of material covered
- calculus operations on vector-valued functions, including derivatives, integrals, curvature, displacement, velocity, acceleration, and torsion.
- calculus operations on functions of several variables, including partial derivatives, directional derivatives, and multiple integrals.
- extrema and tangent planes
- Fundamental Theorem of Line Integrals, Green's Theorem, the Divergence Theorem, and Stokes' Theorem.
- cylindrical and spherical coordinate systems, three space vector operations.
- graphic and algebraic understanding of quadratic surfaces.
- concepts of limits and continuity to multivariable functions.
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If you can pick up linear algebra and advanced calculus that should be enough. As for QM and GR I doubt if you need go that far. For a very quick run through the basics Linear Algebra for Dummies can get you there fast although the ordering of the topics is a bit of a mix up and reviewing previous material has to be done a lot if you are new to the subject. You could try an undergraduate text but that might slow you down. As far as advanced calculus goes I would try Advanced Calculus (Dover Books on Mathematics) by David V. Widder. It is an older text but has very good reviews and is inexpensive.
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Those are the goods I was looking for, questions answered! Thank you for the tip on that extra book, too, I'll look into that.
[:I]
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One last point. Where you have Linear Algebra Done Right, I have Applied Linear Algebra (Noble and Daniel). This shows the applications of the methods as the book progresses. I would be interested to see how you get on with your text.
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I will try to remember to report back. It could be a little bit. About to start the second pass on Linear Algebra Done Right, working out the problems it provides. Also have a competition, exams, and an admissions interview coming up so might be March before done the first pass of the book.