Primer on calculus
Calculus is the study of functions and the way that they change. There are two major processes in calculus: differentiation and integration. Differentiation takes a function and produces a new function—called the derivative—that is the best linear approximation at each point. (You may see this described as the gradient of the function. Integration is often described as anti-differentiation—indeed, differentiating the integral of a function does give back the original function—but is also an abstract description of the area between the graph of the function and the 
axis, taking into account where the curve is above or below the axis.
Abstractly, the derivative of a function 
at a point 
is defined as a limit (which we won’t describe here) of the quantity:
This is because this small number 
becomes smaller and smaller. This is the difference in 
divided by the difference in 
, which is why the derivative...