Maths Blog: TracingCurves

Special integrals: M-dimensional Gaussian

Regular readers of this blog will know that I love my integrals. For those that share the same enjoyment, I recommend this channel that often covers integrals from the MIT integration bee. For example, see...

Simply beautiful: Finding the covariant basis from seemingly nothing

Seeing how I wrote a new post yesterday in the area of tensor analysis, I was reminded of the beautiful result below. It likely would have made it onto this blog at some point, so I thought I would quickly ...

Understanding metric elements for cylindrical coordinates

The metric tensor is ubiquitous when arriving at a certain level in one's physics career. When it comes to cyndrilical coordinates, there is a useful way to remember its deeper meaning through a rather simp...

Differentiate sin(sin(sinx))

In passing I came across this expression the other day, \ To put it in words, we have a composite function: the sin of the sin of the sin(x). I like this expression quite a lot and for a few reason...

Leibniz Rule: Differentiating under the integral sign (special case)

I recently wrote a short piece on the general case of the Leibniz Rule. In that article I alluded to how there is also a special case of the rule, in which the limits of integration are constants as opposed t...