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I just enrolled for my PhD and after a few weeks I find that I am not very comfortable with n dimensional calculus and the related geometry behind it. Since its never late to learn anything in mathematics, I want to quickly revise the basics and the fundamental concepts so that I get a solid grasp of the subject. Can anyone suggest a way of achieving this ? Thanks.

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  • $\begingroup$ If you really want to be thorough (this depends on your field of study) you could study abstract manifold calculus. I think both A Comprehensive Introduction to Differential Geometry (volume 1) by Spivak or Introduction to Smooth Manifolds by John M Lee are good books on this $\endgroup$ – user160738 Jul 21 '17 at 16:31
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I would suggest using the material here https://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/index.htm

In addition I would buy a schaum's outline on multivariable calculus and work through as many problems as you can. I don't think there is a quick way to do this. I found a solid grasp of these ideas ideas essential for most of my PhD course work.

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