**Calculus** is the mathematical study of change. Central to Calculus is the Limit, which, very loosely speaking, is the value a function gets closer and closer to, as its independent variable gets closer and closer to something else. For example, 1/n gets closer and closer to zero when n gets closer and closer to infinity.

With the concept of the **limit** in mind, then the Derivative is the instantaneous rate in change of something — that is, the **limit** of the average rate of change of that thing over h units (think: seconds) as h approaches zero. You can think of the **derivative** as the instananeous slope (or the slope of the tangent line) of the graph of a function.

Once you understand the derivative, then think about what is in many ways the inverse operation: the Integral is the limit of the sum of a whole bunch of little rates of change in value to get the total value of something. You can think of the **integral**, or, more properly, the Definite integral as the signed area above the x axis and under the graph of a function between two specific values of x. The Indefinite integral is simply the **Anti-derivative**. That is, if you find the indefinite integral of a function, and then differentiate it (by the same variable), you get back the original function.

A differential equation is an equation that relates a function to its derivatives. Example: *f'*(*x*) = *f*(*x*). (This equation is more often denoted $ \frac{\mathrm{d}y}{\mathrm{d}x}=y $, or *y' * = *y*, where *y* is assumed to be a function of some independent variable, typically *x*.)