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1: INTRODUCTION TO DIFFERENTIATION
Calculus: the branch of mathematics that deals with how things change. It's split into two main areas—differentiation and integration. In this introduction, I'll be focusing specifically on differentiation, which is all about understanding rates of change and the slope of curves.
Unlike a normal rectangle (attached below), whose area can be quantified by the product of the length and width, real-world shapes are more complex. They aren't always so straightforward.
Think of the arc of a thrown basketball: it most certainly will not have a constant slope by virtue of projectile motion. This is where differentiation comes in, making it easier to calculate the instantaneous rate of change.
At its core, differentiation is the process of finding the derivative of a function. The derivative tells us how a function is changing at any given point. In more visual terms, it's the slope of the tangent line to a curve at a particular point. Let's see this manifest a solved problem:
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