In beginning calculus, the first derivative takes center stage, the second derivative more of an afterthought for determining max or min. In PDE the second derivative has equal (if not more) importance; i.e. Laplace's equation, wave eq, heat eq, etc.
Replying to @mathematicsprof
Second derivatives are more symmetrical than first derivatives, in the same way that x^2 is more symmetrical than x. The former admits a reflection symmetry, x --> -x. The latter does not. This simple remark is actually very close to the heart of the matter.
12:34 PM - 22 Jan 2019
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