Every
student entering UCLA's Masters in Applied
Economics has studied calculus at some stage.
However, a typical university level course
offered by a mathematics department focuses
almost exclusively on the relationship between
two variables, x and y. If, for each x there is
a unique y, then the relationship is called a
function and we write y = f(x).
However in economics it is very often the case that
x is not a number but an array of numbers (or
'vector') . For example this array might be a list
of the quantities of different inputs used by a firm
in the production of a commodity. Then y = f(x) maps
each array of inputs into the output that the firm
can produce. (This is called a production function.)
Understanding the
calculus of functions of this type is critical to
economic modelling.