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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