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Vector Calculus Problem

  1. Jan 22, 2015 #1
    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. jcsd
  3. Jan 22, 2015 #2


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    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.
  4. Jan 24, 2015 #3
    The mesh size is defined as the Euclidean normal of the sub rectangle
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