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Pointwise vs. Uniform Convergence

Comparison Pointwise convergence means at every point the sequence of functions has its own speed of convergence (that can be very fast at some points and very very very very slow at others). ...
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Addition is to Integration as Multiplication is to ______

If $f\colon [a,b] \to (0,\infty)$, then the closest analogue to a multiplicative integral of $f$ is $${\prod}_a^b \,f(x)^{dx} \;\underset{\mathrm{def}}{=}\; \exp\left(\int_a^b \ln f(x)\,dx\right).$$ ...
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What is integration by parts, really?

Integration by parts is a corollary of the product rule: $(uv)' = uv' + u'v$ Take the integral of both sides to get $uv = \int u \ dv + \int v \ du$. If you were supposed to remember it separately ...