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Math 2210 Problem Set 6:Key Due Thursday March 11th
 

Summary: Math 2210 Problem Set 6:Key
Due Thursday March 11th
Problem 1 For quadrilaterals with corners given below, fins transforms T that map
the unit square in the u - v plane into the given quadrilateral in the x - y plane.
(i) (0,0), (1,2), (4,1), (3,-1),
(ii) (1,2), (3,3), (4,2), (2,1), and
(iii) (0,0), (1/2,3/2), (1,-1), (1/2, -5/2).
Solution 1(i)
T =
x = u + 3v
y = 2u - v
Solution 1(ii)
T =
x = 2u + v + 1
y = u - v + 2
Solution 1(iii)
T =
x = u/2 + v/2
y = 3u/2 - 5v/2
Problem 2 Compute the Jacobian of each of the transforms in Problem 2 and find

  

Source: Ashlock, Dan - Department of Mathematics and Statistics, University of Guelph

 

Collections: Mathematics