When we have a simple one variable function $y = f(x)$, $f(x)$ gives the height of function/curve at an arbitrary point $x$, but if we have a multivariate function $u = f(x,y)$, what does it give us?
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It's simply still the height… – Ѕᴀᴀᴅ Mar 14 '18 at 10:52
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In the case of multivariate functions, you can think of the domain of the function ($(x,y)$ in this case) as a two-dimensional plane. Then the $u$-coordinate can be a height, sort of like a mountain or similar. – Matti P. Mar 14 '18 at 10:54
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Similar to cross product between 2 vectors? – MR. Raindrop Mar 14 '18 at 10:55
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Why not visiting Wolfram Alpha and playing around with different functions $u(x,y)$?
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