As a first exercise working with Jordan content, let’s consider how it behaves at the boundary of a region. I’ve used this term a few times when it’s been pretty clear from context, but let me be clear. We know about the interior and closure of a...

We’ve got Riemann’s condition, which is necessary and sufficient to say that a given function is integrable on a given interval. In one dimension, this really served us well, because it let us say that continuous functions were integrable. We could...

Yesterday we defined the Riemann integral of a multivariable function defined on an interval . We want to move towards some understanding of when a given function is integrable on a given interval . First off, we remember how we set up Darboux sums....

Our coverage of multiple integrals will actually parallel our earlier coverage of Riemann integrals pretty closely. Only now we have to change our notion of “interval” to a higher-dimensional version. For the moment, the only shapes we’ll integrate...

Sorry I’ve been a little busy this weekend and the Sunday post slipped my mind. I’m actually sort of glad it did, because last night I went to see Precious, and was surprised to see Lenny Kravitz in his first acting role. Evidently he’ll be the lead...