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4.1. LINEAR MAPPINGS
415
θ
r
P
y
x
Figure 4.1: Polar Coordinates as a mapping
It is also possible (and, as we shall see, useful) to think of a system of one
or more equations in several variables as a single equation involving a
mapping: for example, the system of two equations in three unknowns
b
x
2
+
y
2
+
z
2
= 1
x
+
y
−
z
= 0
which geometrically represents the intersection of the unit sphere with the
plane
x
+
y
=
z
can also be thought of as ±nding a “level set” for the
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 Spring '08
 ALL
 Calculus, Equations, Polar Coordinates

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