Uploaded February 2020 | Updated September 2026, 2 weeks ago
Clairaut's theorem, also known as Schwarz's theorem or Young's theorem, says that mixed partial derivatives are equal regardless of order: fₓᵧ = fᵧₓ. In this video, we go through an intuitive explanation based on visual geometry, then some algebra!
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Clairaut's theorem, also known as Schwarz's theorem or Young's theorem, says that mixed partial derivatives are equal regardless of order: fₓᵧ = fᵧₓ. In this video, we go through an intuitive explanation based on visual geometry, then some algebra!
Full Valuable Vector Calculus playlist: youtube.com/playlist?list=PLug5ZIRrShJHgsWPng59fFFoqn183aO-1
New math videos every Monday and Friday. Subscribe to make sure you see them!
![Introduction and Derivation of F[x]-Modules](https://i.ytimg.com/vi/H44q_Urmts0/mqdefault.jpg "Introduction and Derivation of F[x]-Modules
Modules over a polynomial ring have very important applications to linear algebra. Here we prove some basic properties of F[x]-modules and show how they are related to vector spaces over a field.
Ring & Module Theory playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJExMapwnaKTFXDYbKeWDXq7
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Music: C418 - Pr Department")
