Why Calculus Is Necessary
Understanding the "why" behind the methods.
Differentiation
The art of measuring instantaneous change.
Differentiation is about finding the slope (or gradient) at any single point on a curved line. This slope tells us the instantaneous rate of change.
Key Application:
A primary use of differentiation is to find the maximum or minimum value of a function. This is crucial in many fields, like finding the launch angle for maximum projectile range, or minimizing material usage in manufacturing.
Integration
The art of summing up infinite slices.
Integration is fundamentally about finding the area under a curve. It's like adding up an infinite number of infinitesimally thin rectangles to get a precise total.
The Big Picture:
Integration is the inverse of differentiation. They are two sides of the same coin, a relationship known as the Fundamental Theorem of Calculus.