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Section 13.6
Equations of Cylinders and Quadric Surfaces
“Other Graphs in 3space”
In this section we shall consider other types of surfaces. In order to
sketch such curves, we consider
crosssections
with planes (also called
traces
).
1.
Cylinders
Though we have previously considered cylinders as a surface shaped
like a pipe, in multivariable calculus, there is a more general deFnition
of a cylinder, and there are many other graphs which are considered
“cylinders” according to the formula deFnition which do not look like
pipes. The formal deFnition of a cylindrical surface is the following:
DeFnition 1.1.
A cylinder is a surface that consists of all lines (called
rulings) that are parallel to a given line and pass through a given curve
in some plane.
To avoid confusion, we shall usually refer to the cylinders which are
shaped like a pipe as
pipe cylinders
, and general cylinders satisfying
this deFnition a cylindrical surface (or cylinder for short). Of course,
a pipe cylinder is a cylindrical surface i.e. it consists of parallel lines,
all of which all pass through a circle (see illustration below).
2
1
0
1
2
2
1
0
1
2
1.0
0.5
0.0
0.5
1.0
There are many other examples of cylindrical surfaces.
Example 1.2.
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 Fall '08
 Stefanov
 Calculus, Equations

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