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I'm just saying "D" because I can't immediately type the symbol here and it was easier just to use that. Not least, I didn't know if that was the formula you meant.

But as I say, immediately above the formula it says:

"For a pulse of width ∆t, the critical time ..."

So that really is saying exactly what that cluster of symbols means. There will be things like this everywhere as you read stuff. Things are rarely completely undefined, but you are expected to be reading along.

And you need to work. I just typed this into DDG:

"What does ∆t mean?"

The very first hit is this:

https://en.wikipedia.org/wiki/Delta_%28letter%29

That gives you a lot of context for what the symbol means, and this is the sort of thing you'll need to do. You need to stop, look at the thing you don't understand, read around in the nearby text, then type a question (or two, or three) into a search engine.

I'll use this as an example for the point I'm trying to make in my comment https://news.ycombinator.com/item?id=29341727

Please don't take this the wrong way. It is not meant to be demeaning, and it is not meant to be gatekeeping (quite the contrary!). But: If you do not know what a derivative is, then learning that that symbol means derivative (assuming that it does, I have not actually looked at what you link to) will help you next to nothing. OK, you'll have something to google, but if you don't already have some idea what that is, there is no way you will get through the paper that way.

I hope you take this as motivation to take the time to properly learn the fundamentals of mathematics (such as for example calculus for the topic of derivatives).

The triangle, or “delta”, is used to indicate a tiny change in the following variable.

Let’s say you go on a journey, and the distance you’ve travelled so far is “x” and the time so far is “t”.

Then your average velocity since the beginning is x / t .

But, if you want to know your current velocity, that would be delta x divided by delta t .

The delta is usually used in a “limiting” sense - you can get a more accurate measurement of your velocity by measuring the change in x during a tiny time interval. The tinier the interval, the more accurate the estimate of current velocity.

What I’m talking about here is the first steps in learning differential calculus. You could look for that at kahnacademy.com. You might also benefit by looking at their “precalculus” courses.

Just keep plugging away at it, the concepts take awhile to seep in. Attaining mathematical maturity takes years.

I would say that delta is typically used to mean difference of any magnitude (i.e. Δt could mean 2 hours).

Yes, small changes usually use lowercase delta, e.g. δt. Not to be confused with the derivative symbol dt, nor with the partial derivative symbol ∂t !

Before I continued my maths learning after highschool (ie before UK A-levels) I learnt the Greek alphabet to make it easier to understand maths notations as I could 'voice' (internally) all the funny glyphs adopted from Greek.

At uni I learnt how to properly write an ampersand (for logic classes) and how to write Aleph and Beth (for pure maths, particularly transcendental numbers).

Some professors have a fondness for the more confusing Greek letters (lowercase xi, lowercase eta) ... is it n or eta, epsilon or xi, ...

https://en.wikipedia.org/wiki/Riemann_sum usually uses ∆. See also the explanation of ∆ at https://en.wikipedia.org/wiki/Derivative#Explanations .

That's the sense in which I'm using ∆, which is common, at least in the US.

But this is a physics paper, that isn't how you use uppercase delta in physics. It is just a range. In physics however you do a ton of approximations all the time in ways mathematicians hate (you don't care about errors smaller than you can measure), so uppercase delta is often approximated with derivatives etc, but it isn't a derivative. Math in physics is way more practical and uses very different techniques than math in math, often because physicists invented the math first and mathematicians later went and formalized it.

True. To continue my example, the average velocity in the last hour would be taken with a ∆t of 60 minutes.

BTW ... you say:

> Maybe it's just a too advanced paper for my knowledge.

Maybe it is for now ... the point being that if you start at the beginning, chip away at it, search for terms on the 'net, read multiple times, try to work through it, and then ask people when you're really stuck, that's one way of making progress.

You can, instead, enroll in an on-line course, or night-school, and learn all this stuff from the ground up, but it will almost certainly take longer. Your knowledge would be better grounded and more secure, but learning how to read, investigate, search, work, then ask, is a far greater skill that "taking a course".

Others have answered your specific question about the delta symbol, but there are deeper processes/problems/questions here:

* Not all concepts or values or represented by a single glyph, sometimes there are multi-glyph "symbols", such as "Δt" in your example.

* When you see a symbol you don't recognise, read the surrounding text. The symbol will almost always be referenced or described.

* The notation isn't universal. Often it's an aid to your memory, to write in a succinct form the thing that has been described elsewhere.

* In these senses, it's very much a language more akin to natural languages than computer languages. The formulas are things used to express a meaning, not things to be executed.

* Specific questions about specific notation can be answered more directly, but to really get along with mathematical notation you need to "read like math" and not "read like a novel".

* None of this is correct, all of it is intended to give you a sense of how to make progress.