What do the derivative or the integral of amplitude of a seismogram mean? I'm doing a project in which I'm analyzing earthquake seismogram waves. I used a program to graph the exact amplitudes and how they changed over the course of a single earthquake. For the project I need to incorporate calculus, so I was wondering, what does finding the derivative of amplitude do? And what does finding the integral get you? 

The integral is the area under the entire wavelength, but I was wondering if it was equivalent to energy released, or some sort of geology/physics thing I didn't understand. Thank you.
This is a very simple answer, and it depends on the what the seismometer is measuring. I'm assuming you mean the time derviative/intdegral  $\frac\partial{\partial{}t}$ or  $\int{dt}$

Most seismometers measure displacement over time or velocity over time (series). So taking the time derivative will give you the spectral velocity or the spectral acceleration respectively when you take their derivatives.

When you take the integral of displacement, you calculate the total area displaced over time, and when you take the integral of velocity, you calculated the displacement. 

It's all physics 101 really!