Dave

...and now it's down again! Hurrah! (There's a rather nasty bug in the code that needs fixing, I'll get onto it tomorrow).

Muahahaha. And whatnot. Yes, evolution is great fun. Especially Evolutionary Game Theory, that's a right laugh.

Turn it off. Digital's definately the way to go.

I've never heard to the infinitessimal difference operator myself, but sure. No, I objected to the fact that you wanted to set [math]dt = t_2 - t_1[/math]. dt is supposed to be infinitessimal and as such it can't be defined like this. [math]Plus you are ignoring whether you take the limit from the left, or the right.[/math] No, I'm not. If you want to take a limit from the right or left, then the notation used is commonly [math]\lim_{h\to 0^{+}}[/math] and [math]\lim_{h\to 0^{-}[/math]. This is the "proper" definition of the limit: [math]\lim_{x\to c} f(x) = l \Leftrightarrow \forall \epsilon > 0 \exists \delta > 0 \text{ such that } |x-c| < \delta \Rightarrow | f(x) - l | < \epsilon[/math]. As you can see, we're taking values of x around a neighbourhood of c, not just to the left or right. I've given you my reasoning

Let's go through this. You've stated already that you'd like to declare: [math]\Delta f(x) = f(x+h) - f(x)[/math]. Okay. I can deal with that. Now, the idea is that, yes, you have some small change [math]h = \Delta t[/math]. So, we divide through by this: [math]\frac{\Delta f(x)}{\Delta t} = \frac{f(x+h) - f(x)}{h}[/math]. Now, taking [math]\Delta t \to 0[/math], [math]\lim_{\Delta t \to 0} \frac{\Delta f(x)}{\Delta t} = \frac{df}{dt}[/math]. The idea being that you divide through by some finite amount to start off with, and as you let that finite amount get arbitrarily small, we obtain the derivative. Setting dt = 1 just doesn't make sense.

My point was that it's not supposed to be a number. (i'm splitting this thread off btw, it's got far too off-topic now).

How can dt be a number if it's supposed to be an infinitessimal quantity?

My thoughts exactly. We can continue this elsewhere, Johnny5

Sure, you could: but what is dt? It's meaningless by itself.

You need to use \lim instead of just lim

I don't really get where you're coming from to be honest. I've said it twice now: d/dt is an operator. It's not a fraction. You can't divide everything by dt. It's a nice, shorthand way of writing things down, and it's the right kind of idea, but it doesn't detract from the fact that it doesn't actually sense from a strictly mathematical point of view.

I'm certainly not missing the limit concept. Yes, the idea is to divide by some infinitessimaly small quantity, but I'm trying to teach/give examples of using proper mathematical notation.

Ah yes, so I did. No matter, it's there now

My qualm with it is that you can't just "divide" by dt. I know that we all do, but it's not proper - d/dt is an operator, and as such you can't really mess around with it that much. A much nicer (and quicker) way of doing it is just to use the definition of the derivative, which I haven't really put down. [math]\frac{d}{dx} f(x) = \frac{f(x+h) - f(x)}{h}[/math] A simple re-arrangement can give you the answer.

Moving this to the Chemistry forum, don't think it belongs here

Indeed. We can't really check otherwise

That's not particularly easy due to the nature of the problem (elliptic orbits are a bit nasty to deal with). You might want to take a look at Orbiter, which is a space simulator (free). It's rather good - perhaps qiute a way off what you were thinking - but it gives you an idea about how complex these things can become.

Indeed. The ability to veto is far too high when it comes to the security council.

What do you mean?

y = 673x2 + 2348x - 28734.

Plugging it into mathematica would suggest that elliptic integrals are indeed needed. However, I don't really have any experience at all in this field. If anyone else cares to step in...?

Unfortunately, I changed my essay title after doing a bit of research. The new title is "Chaotic Systems and Strange Attractors" - only about 4,000 words, but it's enough I found the Gamma function to be very interesting, but it was very much labour intensive trying to find enough material that was "different" and easy enough that I could quickly digest it and get it into the essay. I did have quite a lot of fun scouring the journals though.

I believe it measures the amount of solar radiation that is reflected away from the planet.

Salinaty measures the concentration of salt that you find in the water. The salinaty of the water affects the density, and due to the fluid dynamics you get faster moving streams of water.

Quite. I doubt I'll watch any kind of documentary on the Iraq situation. I don't want to know. I've always been opposed to it, and to see it on the news every day is quite enough (to be brutally honest).