Parametric Representation of Surfaces
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The need for a parametric representation
Line integrals [Equation goes here - download the original pdf to see it.] are written in terms of the parametric representation [Equation goes here - download the original pdf to see it.] In order to generalise results about line integrals to surfaces we require a parametric representation of a surface. Since surfaces are two dimensional, they require two parameters, u and v. The parametric representation of a surface is a vector function of the form [Equation goes here - download the original pdf to see it.] This parametric representation maps the two-dimensional region R in the uv-plane to a surface, S, embedded in Euclidean three-dimensional space, The need for a parametric representation. Every point, The need for a parametric representation is mapped to a point [Equation goes here - download the original pdf to see it.]. [Diagram goes here - download the original pdf to see it.]
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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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