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I am in a particular situation that I am doing Master's in a Computer Science related degree, and I would like to take the course on Convex Optimisation which is taught by the Machine Learning department of our University. I did my undegrad almost 10 years ago and my memories of maths courses are quite sparse. The pre-requirements for this course are Linear Algebra and Multivariable Calculus. As for the former, I have already been going through Gilbert Strang's OCW lectures and working the problems from his book. The latter is what my question is about - I've got some disjoint knowledge of Calculus already, and also I have been going through the Spivak's Calculus book. I have considered 2 options so far:

My question is what would be the most optimal way to get up to speed with Multivariable Calculus. In particular professor mentioned things we need to understand such as Vector spaces, Taylor theorem for multivariable case, level sets. I already have a fairly good understanding of Taylor expansion in single variable case, and I can imagine how it could be generalised to many variables, but I still need to do my homework. I am not necesserily looking to cherry pick certain topics and be done with it, I would like to learn everything properly, but maybe you can advice me something considering the time constraints that I have. Thank you.

Update: Subsequently I found Massively Multivariable Open Online Calculus Course by Ohio State University at Coursera and I am really liking it. It is reach in examples, builds up intuition, but also provides formal proofs where necessary. It is largely a text based course, without any video lectures, but it does not bother me, as long as it guides me through. As suggested by others I will also go through the lectures at OCW.

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  • $\begingroup$ mathoverflow.net/questions/54430/… maybe related. $\endgroup$ – user35603 Apr 19 '14 at 9:49
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    $\begingroup$ Thanks, this is quite a comprehensive list. $\endgroup$ – SimpleMan Apr 19 '14 at 15:16
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    $\begingroup$ :O Stewart is awesome! That guy has lots of examples from finance, economics, physics, chemistry, etc! $\endgroup$ – BCLC Dec 12 '14 at 10:11
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I would suggest Prof Adrian Banner from Princeton University. His lectures on multivariable calc are awesome.

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I would honestly take the classes again if possible. If not possible, then I would definitely study the OCW from Denis Auroux because I think it's the best. Find out what concepts are most widely used and then concentrate your studying on those things as well.

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I think MITOCW would be best recommended. Also, edx.org and coursera.org are a good recommendation. I say this due to the fact that the websites provide one-on-one assistance and lots of other information to you would find intrest in looking into. This should give you a general idea of what to expect. However looking at the websites yourself is the true test to you potential needs.

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For me a great playlist of lectures in multivariable calculus is if you want to speed up is:

https://www.youtube.com/watch?v=GnQY0CjgCZg&list=PL576C313B98C1419E

by Evans Lawrence.

The only thing missing here is Taylor Theorem.

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