Youtor
Clever Clairaut Proof
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=wLkXUmVKyi4
In this video, I give a very clever proof of Clairaut's theorem, which says that if the partial derivatives f_xy and f_yx are continuous at a point, then must be equal. Usually this is proved using difference quotients, but here I give a proof using double integrals. I also give a nice proof using Green's theorem. This is a must-see video for multivariable calculus lovers! • Clairaut Counterexample: • Clairaut Counterexample • Fubini Counterexample: • Fubini Counterexample • Green's Theorem: • Green's Theorem • Multivariable Calculus Playlist: • Multivariable Calculus • Partial Derivatives Playlist: • Partial Derivatives • Subscribe to my channel: / drpeyam • Check out my TikTok channel: / drpeyam • Follow me on Instagram: / peyamstagram • Follow me on Twitter: / drpeyam • Teespring merch: https://teespring.com/stores/dr-peyam
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