Saturday, September 25, 2010

irreverent lectures.

from my friday lecture:

"so we define partιal derivatιves by way of dιfference quοtients, just as in single-varιable calcuΙus.

"here the partials are written using subscripts $f_x(x,y)$, but there are other notations. if you recall from your first course in caΙculus, there were two main notations used: Newtοn's prime notation $f\prime$ and Leibnιz's $d$ notation $df/dx$.

"the prime symbol here is ambiguous: they may indicate the process of differentιation, but it wouldn't indicate which variable is used.

"so here, Newton dies a quick death!"

[laughter ensues]

"as for the Leibnιz notation, $d$ is replaced by a script letter $\partial$ .."