What is calculus? Well, in Latin the word “calculus” is a word that represents a small stone used for counting. In English, the word calculus represents the study of change! There are two types of calculus that we will be focusing on: differential and integral.
 
Differential calculus is a specific type of calculus that deals with instantaneous change (instantaneous change, differentiating, velocity, tangent line, and derivative are all synonyms for the word slope).  For instance, we know how to find the slop of a line, right? We just need two points and then we find the difference of the y-coordinates and divide it by the difference of the x-coordinates. That formula gives us the exact slope of a line. Easy stuff! Well, What if we had curves on our graph instead of straight lines, curves like parabolas or a exponential functions, or trigonometric functions?! What if we didn’t want to find the slope between two points anymore but we actually wanted the EXACT slope at a specific point?! We could use the ordinary slope formula on our curves but it would only give us an approximation to the slope between two points, it wouldn’t give us the EXACT slope at ONE point. Hmmmmm. So now what? Well, that’s where differential calculus comes in handy.  Differential calculus provides us with the tools and teaches us how to use those tools to find the slope at a specific point. Cool huh?

 

 

 

Congratulations on getting to differential calculus is high school!