Another Proof of Clairaut's Theorem

@article{McGrath2014AnotherPO,
  title={Another Proof of Clairaut's Theorem},
  author={Peter J. McGrath},
  journal={The American Mathematical Monthly},
  year={2014},
  volume={121},
  pages={165 - 166}
}
  • Peter J. McGrath
  • Published 2014
  • Mathematics, Computer Science
  • The American Mathematical Monthly
Abstract This note gives an alternate proof of Clairaut's theorem—that the partial derivatives of a smooth function commute—using the Stone–Weierstrass theorem. 

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SHOWING 1-4 OF 4 REFERENCES
Functions of a Complex Variable
In earlier chapters, complex-valued functions appeared in connection with Fourier series expansions. In this context, while the function assumes complex values, the argument of the function isExpand
Calculus on Manifolds
The equations of mathematical physics are typically ordinary or partial differential equations for vector or tensor fields over Riemannian manifolds whose group of isometries is a Lie group. It isExpand
Calculus (Fifth Edition)
Calculus on Manifolds