Room for Peter and J. M.

Peter

02:56

Hello J.M.

J. M.

Hello. How may I be of service?

Peter

I would like to know if you can help me out with something. What is you math "level"?

J. M.

@Peter Why not just ask the question you need to ask, and I'll be the judge of whether I can be useful? ;)

Peter

Well, you helped me in some questions, and I'm out of sinc with this page's UTN

So answerers are scarce now

J. M.

@Peter UTN? Sorry, I am already juggling too many initialisms... :)

Peter

03:00

the international time

J. M.

Ah, UTC.

Peter

aaaaaa right

J. M.

Anyway... you were about to ask something?

Peter

So this is what I'm, asking for some days now

And I haven't received an answer, although I guess it isn't too hard.

My main concern is $ t_i - t_{i-1} = \Delta{x_i}$ versus $\displaystyle \frac{t_i}{t_{i-1}}= \Delta{x_i}$

J. M.

There's a $t$ in one side, and an $x$ in the other... what gives?

Peter

03:07

sorry i mean t on both

I corrected that on the question too

J. M.

...and the convention I'm accustomed to for forward differences is that $\Delta t_i=t_{i+1}-t_i$.

Peter

Ok. You can put it that way.

J. M.

Backward differences usually use something like $\nabla t_i=t_i-t_{i-1}$.

In any event: so this is a difference calculus query?

Peter

Right. My question is if I can interpret the change in the "difference function" as a change in the integral's integrator.

i.e. R.Stietljes $\alpha{t_{i+1}}- \alpha{t_{i}}= \alpha\Delta t_i$

J. M.

Wait, wait, now you're starting to use terms not in the way I am used to...

What is $\alpha$ supposed to be here?

Peter

03:12

The integrator. I should have put $\alpha(t_{i+1})-\alpha(t_{i})$

J. M.

I presume you're going from Riemann sums to the integral itself in the limit of infinitely many strips?

Peter

right

did you see the question?

J. M.

This is the first time I've seen this use of "integrator". What are you trying to tell me here?

Maybe things become clearer if you point me to the question to begin with...

Were you talking about this?

Peter

Yes!

I thought you had read it.

J. M.

@Peter No I have not; I have been occupied with a myriad other things.

Peter

03:16

Sorry then.

J. M.

But getting back to the matter at hand: for starters, what you keep calling an "integrator" is in fact a "differential".

Peter

In a Riemann Stieltjes integral $\int f d\alpha$, dont you call $\alpha$ the integrator?

J. M.

Now, these quotients you are looking at, they are indeed a different way to partition your area. Unfortunately, one can no longer interpret these as differences, because they aren't differences.

@Peter The term I'm accustomed to is "differential". In more advanced contexts, "measure".

For $\int f(x)\mathrm dx$, $\mathrm dx$ is the differential; $x$ is the dummy variable.

Peter

Ok. I'm not that advanced.

Yes I know.

J. M.

Again, these are quotients, so their limit as you increase the number of partitions cannot be thought of as a differential. Only differences can be "turned" to differentials.

As you can see, it's a slightly more difficult way to proceed for evaluating the integral, and that should convince you why the approach is not too popular.

Peter

03:21

In my opinion it is easier, since it avoids Bernoulli's Polynomials.

J. M.

@Peter Ah, then we have a difference of opinion. I happen to consider Bernoulli quite useful. :)

Peter

I know. Usefull for those who know the closed form. But I think finding the close form of a geomtric series is easier.

Do you agree with that¿

J. M.

Just about the same for me, actually. On the other hand, I'm not somebody you should be considering "orthodox".

Peter

Why do you say so?

J. M.

Let's just say most of the math I have had to use for answering questions here were not learned in the classroom...

Peter

03:26

I do not know how this will affect my rep, but I'm a self taught math "student",

J. M.

@Peter Then we are more or less alike. :)

Peter

Have you started or will you start college studies?

J. M.

I have been done with the university many years ago.

Peter

Then you have some "formal" studies. (I'm starting this year.)

J. M.

Not really, the mathematics I had was exceedingly minimal. I'm not a mathematician.

Peter

03:30

Oh I see. Well. What do you think about this? Finding a function such that $$\alpha \left( {{t_{i + 1}}} \right) - \alpha \left( {{t_i}} \right) = \frac{{{t_{i + 1}}}}{{{t_i}}}$$

I'm thinking about the logarithm right now. Or something similar

Is latex even rendered here?

J. M.

One needs a certain bookmarklet for the purpose. Have you checked meta?

@Peter I still don't see why the need for $\alpha$...

Peter

nay. what do I need¿

@JM weel I want a function that satisfies that equality.

J. M.

@Peter See here.

@Peter $\alpha(x)$ is your unknown function?

Peter

right

I found the bookmark! nice!

J. M.

This does not look to be one of those easy functional equations, at least since $t_i$ is completely unspecified.

Peter

03:36

Ok. I'll make a new question to see what i get.

Thanks, then. By the way, which country are you from?

J. M.

@Peter I am in the Philippines. I see you are Argentine?

Peter

Yes.

J. M.

I need to be off for the time being. I am sorry I cannot be more helpful.

See you at another time.

Peter

See you

Transcript for

$Mathematics$ Room for Peter and J. M.