For increments in calculus which notation is prefered, lower or uppercase delta? Where does the different notations come from?

Question

anonymous · Answer

i.e $$\delta x$$ or $$\Delta x$$

sparrow2 · Answer

as i remember they come from leibniz and newton, i think the first one was used by newton and they are the same(do not have any value which you use)

anonymous · Answer

The first one looks cooler though I might be biased, I guess the second one is easier to draw? XD

zzr0ck3r · Answer

The second one is the standard. I have never seen the first one. 

$\delta$ is used in advanced calculus to mean a very small distance. There is a small difference here (no pun intended).

anonymous · Answer

It might just be my teacher's choice :D

anonymous · Answer

I personally prefer the first one in expressing perturbations