In Sections 19.1 and 19.2 we consider some basic notions of a parametrized surface and a regular surface (analogous definitions for curves were studied in Section 5.1). In Section 19.3 we use a number of MAPLE commands to produce surfaces by various methods. In Section 19.4 we calculate and plot tangent planes and normal vectors of a surface. As an application we solve the conditional extremum problems in space (see the two-dimensional case in Section 5.6). In Section 19.5 we use changes in coordinates and linear transformations in space to calculate and plot an osculating paraboloid at the point of a surface. This elementary approach is given only for methodical reasons. In Section 19.6 we consider parametrized and implicitly defined surfaces with singularities.
KeywordsSingular Point Tangent Plane Smooth Point Klein Bottle Level Curf
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