Expression 12: "x" squared plus StartFraction, "y" squared Over 4 , EndFraction less than 1 left brace, "z" equals 0 , right bracex2+y24<1z=0
12
"lift" the domain onto the surface z=f(x,y)
13
the blue boundary part
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Expression 15: "f" left parenthesis, "x" , "y" , right parenthesis left brace, "x" squared plus StartFraction, "y" squared Over 4 , EndFraction equals 1 , right bracefx,yx2+y24=1
15
and the pink interior part
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Expression 17: "f" left parenthesis, "x" , "y" , right parenthesis left brace, "x" squared plus StartFraction, "y" squared Over 4 , EndFraction less than 1 , right bracefx,yx2+y24<1
17
Let's parameterize the boundary path on the surface.
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Expression 19: "C" equals left parenthesis, cos "t" , 2 sin "t" , "f" left parenthesis, cos "t" , 2sin "t" , right parenthesis , right parenthesisC=cost,2sint,fcost,2sint
19
hit the below "play icon" to see the parameterization in action:
