Calculus is sometimes defined as ‘the mathematics of change’. The whole point of calculus is to take the conventional rules and principles of mathematics and apply them to dynamic situations where one or more variable is changing. In particular, calculus provides you with the tools to deal with rates of change.
There are actually two ‘big ideas’ in calculus, called differentiation and integration. These are both techniques that can be applied to algebraic expressions. As you will discover, one is the converse of the other. Algebraically, what this means is that, if you start with some function f(x) and differentiate it, then integrating the result will get you back, roughly speaking, to your original function f(x). And the same idea is true in reverse – if you first choose to integrate f(x), then differentiating the result will get you back to your original function f(x). The notation used for integration is the sign ∫, which is the oldfashioned, elongated letter ‘S’.