Our book does not define a monotonically increasing and decreasing
function very well (see page 4).

A function f is increasing if the values of f(x)
increase as x increases.

A function f is decreasing if the values of f(x)
decrease as x increases.

It is not clear, for instance,
whether a constant function is increasing.

The Wikipedia entry for
increasing
function is a conventional way to resolve any ambiguity.

For instance, according to the Wikipedia definition, a constant
function is both monotonically increasing and monotonically decreasing,
but not strictly monotonically increasing or
strictly monotonically decreasing.

The definition of monotonicity in our book appears to be
equivalent (given the interpretation above!) to the definition
of strict monotonicity

Lecture of November 3

The details of the two examples done in class are here

What if a quantity is proportional to two other quantities?

This is a comment in regard to one homework problem about
illumination. The statement "Illumination is proportional to
the cosine of an angle and inversely proportional to the square
of the distance from the light source" results in the formula