Equation 3 belongs to Augustin-Louis Cauchy NOT Newton! Also the fundamental theorem of calculus should be on the list too.
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It's always Euler
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damn freak didn't leave any maths left for the rest of us
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Euler [E44] is the first who gave a 'proof' but his proof is not satisfactory http://eulerarchive.maa.org/pages/E044.html The first proof in modern math is given by Schwarz https://archive.org/details/gesammeltemathem02schwuoft/page/274 …
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そしてその証明は、最近では教科書にすら書いてない。
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If f is second order differentiable and these partial derivatives are continuous!
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1/2 You would not believe the grief I received when grading two hundred homework papers in vector calculus I deducted a point if students didn’t mention the C^2 necessity for the swap. The professor sided with the students. Lesson learned.
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Only true if f is C2 though, Schwarz theorem
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what is c2?
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