Calculus/Introduction

Calculus is the math pertaining to slopes (or 'steepness') and areas under curves. I will define that a slope of, say 2 means that if you move 1 unit forwards, you move 2 units up, and that the same applies for any other number

Prerequisites

 * The four basic operations (+,-,*,/)
 * Maybe algebra (subtle introduction in Section 2)

The Derivative
The derivative is the math name for the math of slopes. To give an example, the word 'parabola' means that, for example, if you walk 4 meters away from it, the parabola is 4*4=16 meters above your head, and this holds true if you walked any other distance from it (and replaced the 4 with the actual distance!). Now, if you got a friend to walk up the parabola directly overhead, they would feel a slope of 2*4=8, and the same would be true if you replace 4 with anything else, and you kept the 2 because you think that 2 matters more than 8 to you...

To write this down, we say: $${dy \over dx}=2x$$, and in this case, $${dy \over dx}$$ means 'slope' and x means how far you walked away from the center of the parabola.

The integral
The integral is the math name for the math of areas under curves. To give an example, if you gave me a number, which I'll call x, I can give you the integral of y=x (the height, y is the same as the horizontal distance, x), which is the area of the blue triangle. Notice that the blue triangle is half of a square with side length x. This implies that the blue triangle's area is x*x/2, and thus, the integral of x is x*x/2.

To write this down, we say: $$\frac{x*x}{2}=\int x dx$$. $$\int dx$$ means that you're taking the area under a curve and the x between the sign and the dx represents the y value. Had y=x*x, it would have looked like this: $$\int x*x dx$$, with x*x representing the y value.