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Math Help - Image after Transformation

  1. #1
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    Image after Transformation

    Alright, so I've got to "Find the image of the set S after the given transformation."

    S is the square bounded by the lines u=0, u=1, v=0, v=1; x=v, y=u(1+v^2)

    How do I do this? I've found the Jacobian to be -u but I don't even know how to use that for this problem. Can someone please start me in the correct direction.
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  2. #2
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    I think I've figured it out. Basically I took all the existing boundry curves/lines, and converted them. The Jacobian wasn't used. But I ended up getting a figure that looks like the area underneath y=x^2+1 from 0 to 1. Does that sound correct?
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  3. #3
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    Quote Originally Posted by Rhode963 View Post
    Alright, so I've got to "Find the image of the set S after the given transformation."

    S is the square bounded by the lines u=0, u=1, v=0, v=1; x=v, y=u(1+v^2)

    How do I do this? I've found the Jacobian to be -u but I don't even know how to use that for this problem. Can someone please start me in the correct direction.
    Since x= v, v= 0 and v= 1 become x= 0 and x= 1. The other sides are harder. Since y= u(1+ v^2) and x= v, we can rewrite that as y= u(1+ x^2) so that u= \frac{y}{1+ x^2}. Now u= 0 becomes \frac{y}{1+ x^2}= 0 or y= 0. Finally, u= 1 becomes \frac{y}{1+ x^2}= 1 or y= 1+ x^2, a parabola. That's exactly what you have!
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