Jacobian transformation, find new limits

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Homework Help Overview

The discussion revolves around finding new limits for variables U and V in the context of a Jacobian transformation related to a set of linear equations. Participants are exploring how to determine these limits based on given graphs and equations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Some participants express confusion about how to derive the limits for U and V, indicating difficulties in interpreting the graphs and equations provided. Others suggest that sketching the region may aid in understanding the relationships between the variables.

Discussion Status

The conversation includes attempts to clarify the transformation process and the boundaries involved. While some guidance has been offered regarding the limits derived from the equations, there remains a lack of consensus on the correct approach to finding these limits, with participants exploring different interpretations.

Contextual Notes

Participants note the absence of specific details regarding the methods used to find the maximum and minimum coordinates, which may be contributing to the confusion. The original equations and their transformations are central to the discussion, but the exact nature of the graphs is not fully detailed.

Feodalherren
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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.
 
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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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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?
 
Feodalherren said:
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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