Introducing calculus

Calculus is a branch of mathematics that studies the rate of change, such as the slope of a curve at any point. It is a fundamental subject widely used in many areas, including physics, economics, finance, optimization, artificial intelligence (AI), and more. Calculus was first developed by two gentlemen in the late 17th century: Gottfried Leibniz and Isaac Newton. Newton first developed calculus to analyze physical systems, while Leibniz independently developed the resulting notations we use today. Compared with basic math, which uses operations such as addition or subtraction, calculus applies functions and integrals to study the rate of change. Here, the rate of change can be regarded as the velocity, measuring how fast f(x) changes as x changes. Such changes also have a direction, meaning whether f(x) increases or decreases as x increases.

Similarly, we can measure how fast the rate of change of f(x) changes as x changes. Such a measure is called acceleration...