|UBC Calculus Online Course Notes|
Functions: Stars of the Show
The starring roles of this course are played by functions. Functions are pretty simple things---they just express a relationship between two different quantities. Perhaps you have thought, "the faster I drive, the quicker I'll arrive at UBC." If so, then you understand the idea of a function. You are stating that there is a relationship between the speed at which you drive and the time it takes before you arrive at your destination.
It's difficult to overstate the importance of functions in science
since science aims to understand the relationship between different
quantities and to make predictions based on this understanding. For
instance, if we have a polluted river and take some steps to clean it
up, we will need to judge how effective our methods are. To do this,
we might like to know how polluted the river is so many days after we
take action. In this situation, there is a function which relates
time to the amount of pollution in the river. We might like to
understand this relationship so that we could predict when the river
will no longer be dangerous for the fish in it.
For your consideration: