# Vector Calculus Problem

1. Jan 22, 2015

### Nicolaus

Hi, I need help getting a start on this exercise.

Let R be the unit square.
Find sequence of partitions such that the mesh size goes to zero as sequence goes to infinity -> for this, is this just a series of sub rectangles whose respective areas shrink at the same rate with respect to one another?

Find a sequence of partitions such that the max area of a sub rectangle tends to 0 while the mesh size of partition does not tend to zero as the limit approaches infinity of sequence of partitions.

2. Jan 22, 2015

### jbunniii

How are you defining "mesh size"? I'm guessing it is the maximum side length of any of the rectangles in the partition? If so, consider dividing the unit square into $N$ rectangles of equal size, with length $1$ and width $1/N$. Then the mesh size is $1$ regardless of how many rectangles you use.

3. Jan 24, 2015

### Nicolaus

The mesh size is defined as the Euclidean normal of the sub rectangle