Math Insight

Pages similar to: Surfaces as graphs of functions

• Surfaces defined implicitly
  Graphing surfaces defined implicitly through an equation.
• The elliptic paraboloid
  Description of the elliptic paraboloid with interactive graphics that illustrate cross sections and the effect of changing parameters.
• The hyperbolic paraboloid
  Description of the hyperbolic paraboloid with interactive graphics that illustrate cross sections and the effect of changing parameters.
• Surfaces of revolution
  A description of how surfaces of revolutions are graphs of functions of two variables that depend only on the radius.
• Quadric surfaces
  Surfaces that are the graphs of quadratic equations.
• Cross sections of a surface
  A sketch of how to determine the cross sections of surfaces and use them to understand the shape of a surface.
• The ellipsoid
  Description of the ellipsoid with interactive graphics that illustrate cross sections and the effect of changing parameters.
• The double cone
  Description of the double cone with interactive graphics that illustrate cross sections and the effect of changing parameters.
• The hyperboloid of one sheet
  Description of the hyperboloid of one sheet with interactive graphics that illustrate cross sections and the effect of changing parameters.
• The hyperboloid of two sheets
  Description of the hyperboloid of two sheets with interactive graphics that illustrate cross sections and the effect of changing parameters.
• A line or a plane or a point?
  Examples showing how the graph of an equation depends on the underlying dimension, becoming a line or a point or a plane.
• Level sets
  A introduction to level sets. Illustrates level curves and level surfaces with interactive graphics.
• Level set examples
  Examples demonstrating how to calculate level curves and level surfaces.
• Function notation
  A description of how we denote functions.
• Translation, rescaling, and reflection
  An illustration using interactive graphics how to translate, rescale, and reflect graphs of functions of two variables.
• An introduction to parametrized curves
  An introduction to how a vector-valued function of a single variable can be viewed as parametrizing a curve. Interactive graphics illustrate the way in which the function maps an interval onto a curve.
• An introduction to parametrized surfaces
  An introduction to how a vector-valued function of two variables can be viewed as parametrizing a surface. Interactive graphics illustrate the way in which the function maps a planar region onto a surface.
• Surface area of parametrized surfaces
  An introduction to surface area of parametrized surfaces, illustrated by interactive graphics.
• Orienting surfaces
  How to orient a surface by choosing a normal vector.
• Domain of functions
  How to determine the domain of a function.

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