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Section 1 Goals

After completing your work on this section, you should be able to:

  • Recognize a surface from a given parameterization.

  • Find a parameterization for surfaces that fall into the following families including any necessary bounds on the parameters:

    • Planes
    • Graphs of functions of two variables
    • Cylindrical-type surfaces (surfaces whose cross-sections are concentric circles)
  • Use a parameterization of a surface to find tangent vectors to a surface at a point.
  • Use a parameterization of a surface to find a normal vectors to a surface at a point.
  • Define a smooth surface.
  • Define and specify an orientation on a surface.
  • Recognize whether a given parameterization for an oriented surface is orientation-preserving or orientation-reversing.
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