© 2015 Shmoop University, Inc. All rights reserved.

Basic Elements

What are the nuts and bolts of calculus? What makes it tick? You’ve come to the right place. Most of the basic elements are probably new concepts, and some seem complicated at first glance.

The first basic element is the function. We saw functions back in algebra. They usually look something like this: f(x) = x. A function is a rule, when we plug a value into the function, we’ll get another (or the same) value out. In each function, there is also an independent variable and a dependent variable .

Another major concept is the limit. A limit is a value that the dependent variable is approaching as the independent variable approaches a value. As boats approach their docks, functions approach values. One way to find a limit of a function is to plug in values close to the desired value into the independent variable and see what the dependent variable is approaching.

The concept of a slope is an idea from algebra. It’s the (change in y) divided by the (change in x). A derivative is essentially a slope. Instead of finding the slope of a straight line, though, we can find the slope at any point on a curvy line.

An integral is a way to find an area. Integrals can be used to find the area of a circle, a square, or an irregular wavy enclosed region (think of a fancy pool). It’s essentially the opposite operation of a derivative, and it’s another way to pull more data from a graph.

People who Shmooped this also Shmooped...