Main Question or Discussion Point
Hey Mathwonk, just a quickie. When I think of a differential, it is written as y=y(t), and dy= dy/dt * dt. When I see this, I think of it as we want to deal with only the variable y. But y(t) is a function of t. So we set y=y(t), so that y is a variable by itself. As a consequence, we usually want to integrate with resepct to y. But if we take the derivative of y(t), we get dy/dt. But we want the change in y, not y(t) with respect to t, which is why we multiply by an increment of dt. This leaves a change in dy only. I know dy/dt is not a fraction, but In a sense, this is what is happening. Is this interpretation wrong? I also know that dy/dt is the slope, and multiplying it by dt, gives you the value dt away, but it seems like they are two ways of looking at the same thing.