Parametric Representation of Surfaces
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Standard parametric surfaces
Equations are omitted for technical reasons - download the original pdf
Parametric representation of the cylinder: In Cartesian coordinates the cylinder is [Equation goes here - download the original pdf to see it.] Let R be the region of the uv-plane given by [Equation goes here - download the original pdf to see it.] Then a parametric representation of the cylinder with radius a and height 2 where the axis of symmetry is the z -axis is given by [Equation goes here - download the original pdf to see it.] The curves give parallel circles on the cylinder; the curves [Equation goes here - download the original pdf to see it.] give vertical straight lines.
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Contents of
Parametric Representation of Surfaces
1 Surfaces in xyz-space
2 The need for a parametric representation
3 Standard parametric surfaces
4 Parametric representation of the sphere
5 Parametric representation of the cone
6 Tangent plane
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