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58 votes
22 answers
12k views

Which high-degree derivatives play an essential role?

Q. Which high-degree derivatives play an essential role in applications, or in theorems? Of course the 1st derivative of distance w.r.t. time (velocity), the 2nd derivative (acceleration), and the ...
2 votes
2 answers
2k views

Commuting of exterior derivative and contraction (vector-valued forms)

$\newcommand{\sig}{\sigma}$ $\newcommand{\tr}{\operatorname{tr}_{\eta}}$ $\newcommand{\al}{\alpha}$ $\newcommand{\be}{\beta}$ $\newcommand{\til}{\tilde}$ Let $E$ be a smooth vector bundle over a ...