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Jacobian transformation, find new limits

  • #1
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Homework Statement


jacobian.png



Homework Equations





The Attempt at a Solution


What I don't understand is how I'm supposed to find those limits for U and V. That's not at all what I'm getting. I've tried solving for the max and min x,y coordinates from the given graphs but that doesn't yield the correct answer.
 

Answers and Replies

  • #2
STEMucator
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Look at the original equations you are given:

##x - 2y = 0##
##x - 2y = 4##
##3x - y = 1##
##3x - y = 8##

Applying your transformation yields:

##u = 0##
##u = 4##
##v = 1##
##v = 8##

These yield your limits.
 
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  • #3
vela
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It quite often helps to make a sketch of the region. What do the u=constant and v=constant lines look like in the xy-plane?
 
  • #4
HallsofIvy
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What I don't understand is how I'm supposed to find those limits for U and V. That's not at all what I'm getting. I've tried solving for the max and min x,y coordinates from the given graphs but that doesn't yield the correct answer.
It unfortunate that you did not tell us how you tried "solving for the max and min x, y coordinates" since if you had we might be able to point out your mistake. All I can say is that if you have "u= x- 2y", one of the boundaries is x- 2y= 0 and the other is x- 2y= 4, u= 0 and 4 pretty much leaps out at you- u= x- 2y= 0 and u= x- 2y= 4!
 

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