Just started learning about double integrals literally $10$ minutes ago. I have a fairly good grip on the Riemann integral and so far it seems very similar, but we are just working with volumes instead of areas.
My question is this: we approximate the volume under the surface of a function by subdividing the total volume into little blocks with volume themselves. To do this we use the notation,
$$V \approx \sum_{i=1}^{n} \sum_{j=1}^{m}f(x_i,y_j)\Delta A.$$ I know this is essentially adding up all the smaller volumes of the rectangular prisms, but I'm not quite sure I get exactly what the double summation means. Does it mean we sum up all the possible combinations of $i's$ and $j's$ from $1$ to $n$ and $m$?
I'm guessing this is a little trivial but I've never actually used this double sum before so I just want to make sure exactly what it means and how I would calculate it. Thanks.
