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What is a parametrized surface? How does one describe a surface
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What is a parametrized surface? How does one describe a surfacethis way, and why is it useful? What are the trade-offs? That is,how does studying parametrized surfaces simplify things, and whatcomplications do we have to deal with? What is regularity in thiscontext, and why is it important?
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ANSWERparametrizedsurfaceA parametric surface is a surface in the Euclideanspacewhichis defined by a parametric equation with two parameters Parametric representation is a very general way to specify asurface as well as implicit representation Surfaces that occur intwo of the main theorems of vector calculus Stokes theorem andthe divergence theorem are frequently given in a parametric formThe curvature and arc length of curves on the
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