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Frostbite

  • 2 years ago

Any good techniques to plot a function of two variables by hand - or how do we do it anyway?

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  1. klimenkov
    • 2 years ago
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    The general way is to plot many different points that satisfy your equation and then to draw a curve through them.

  2. Frostbite
    • 2 years ago
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    Well i am reading in my math book "Functions of Several Variables" trying to figure out what they mean, but find it quite hard. They constantly refure to something called outlines and contours (don't know if it is called outlines but best translation i can do so far)

  3. klimenkov
    • 2 years ago
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    Oh, may be you are asking about surfaces.. I thought about equation \(F(x,y)=0\).

  4. Frostbite
    • 2 years ago
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    surfaces yea

  5. JakeV8
    • 2 years ago
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    you can hold one of the 3 variables constant and plot the remaining 2-variable equation... such as a y = mx + b line, with z or f(x,y) held constant is like looking at the edge of the plane that would occur if you extended that line into the 3rd dimension

  6. JakeV8
    • 2 years ago
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    or a parabola on an x-y plane would extend into a "trough" shape when you extend it. More complicated functions in 2 variables are not simple 2 dimensional curves extended into 3 dimensional space, though.

  7. Frostbite
    • 2 years ago
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    Still i find it quite hard to see how they come up with this (see attachment)

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  8. Frostbite
    • 2 years ago
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    that is the function f(x,y)=x^2-xy+y by the way

  9. JakeV8
    • 2 years ago
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    ouch... hurts my brain!

  10. JakeV8
    • 2 years ago
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    I am not sure how to generate those graphs easily by hand... sorry!

  11. klimenkov
    • 2 years ago
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    |dw:1349108764775:dw|

  12. Frostbite
    • 2 years ago
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    Well thanks for trying. might just be a nutt to crack and then you can do it everytime.

  13. klimenkov
    • 2 years ago
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    Try to write it like this \(f(x,y)=x^2+y(1-x)\). Let x be a constant and draw a line in a plane x=const. Do this several times. Next let y=const and then try to find out what you've got.

  14. Frostbite
    • 2 years ago
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    Yea okay i have it on a sketch infront of me - i think.

  15. klimenkov
    • 2 years ago
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    Why do you need to draw it?

  16. klimenkov
    • 2 years ago
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    Can you send a photo of what you've got?

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