Multivariable Calculus 13 | Schwarz's Theorem

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This video is about the symmetry of the second-order partial derivatives.

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(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

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Nice video ! We used this theorem a lot back when I was taking physics lessons, but we never proved it although the proof is so straightforward ! I see that it can easily be extended for higher derivatives too with the exact same argument

StratosFair

ooh Schwartz's theorem! also I hope you talk about the total derivative and nth order total derivatives

mastershooter

As usual, great content.
Do you intend to cover line / surface integrals / Stokes and Divergence theorems / implicit function theorem?

eitancohen

The eta that you get for v(h1, h2) and v(h1, 0) could be different. So, IMO the proof is not correct. Please correct me if I'm wrong!

mayankjangid

Does it mean that solving a partial equation:
Uxx + Uyx = 0
Is the same as solving
Uxx + Uxy = 0 ??
d/dx(Ux+Uy)=0
Ux+Uy-c=0

whatitmeans

It is also known as "clairaut's theorem."

sayanjitb

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