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).
