University
Maths Notes: Calculus – Level Curves
We need a method of visualising a function of two variables,
We
can find the value of
for
any
by
substitution, but cannot plot
in
two dimensions. We can however equate
withand
construct a plot in three dimensions, or we can put
where
is
a constant and plot the set of points
satisfyingfor
various values of
The
set of points satisfyingis
called a level curve of
The
relationship between a 3D sketch of
and
the level curves ofis
shown below.
Each value ofdefines
a level curve of
shown
by the black contour lines above. We may reduce the sketch to two
dimensions by labelling each contour with the associated(or
constant).
