Surfaces

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Surfaces
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Constructing Functions of Several Variables

• The temperature at points in the xy-plane is
  proportional to the square of the distance of the
  point to the origin. Write the temperature as a
  function of x and y.

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Constructing Functions of Several Variables

• The ideal gas law states that the pressure of a
  gas is proportional to its temperature and
  inversely proportional to its volume. Write a
  function that represents the pressure of a gas in
  terms of its temperature and volume.

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Graphs of Functions of Several Variables
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Examples
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Quadratic Surfaces
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Ellipsoid
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Sketching Surfaces
A trace of a surface is the intersections of a
surface with a plane. A sequence of traces for a
surface form a wire mesh that represents the
surface.
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Ellipsoid
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Elliptic Cone
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Hyperboloid of Two Sheets
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Hyperboloid of One Sheet
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Elliptic Cylinder
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Hyperbolic Cylinder
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Parabolic Cylinder
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Hyperbolic Paraboloid
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Elliptic Paraboloid
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Identify and Sketch the Surfaces