2024/09/17　微分・積分

Differentiation is drawing a tangent line at the most protruding point of a curve, while  

Integration is considering the curve as a collection of infinitely thin rectangles.

In other words, both differentiation and integration are attempts to somehow relate the troublesome concept of curves to straight lines.

In this world, there are more curves than straight lines. However, curves and curved surfaces are very troublesome to calculate. The essence of differentiation and integration lies in the attempt to relate these troublesome things to straight lines.

This captures the core idea behind calculus—simplifying complex, naturally occurring curves by associating them with straight lines for easier analysis and computation.