Vector Calculus Problem

  • Thread starter Nicolaus
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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.
 

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

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