The output of lower device is the Antiderivative/indefinite integral of its input and the upper is the derivative of its input with respect to time. My first version put out functions that were proportional to the functions in question, but now they are exact.
The tank was the only way I could get a sinusoid at 1 rad/s. You know the drill -- charge the cap then switch it over to the inductor.
For those of you who have not studied calculus at all, a derivative is the rate at which a function is changing at any point. If you think of the distance you have traveled from some staring point while in motion, your speed at any time will be the derivative of distance. Its the rate at which your distance is changing.
An antiderivative is the sum of all the time a function has spent above or below zero. So if you now look at your speed as a function of time, your acceleration will be the derivative and the total distance traveled is now the Antiderivative.
I hope that clears things up a little. Electronic differentiators and integrators when viewed in the frequency domain act as high or low pass filters, respectively. They also find many other uses. I hope this has cleared things up a little.
-J
