Differential equations are mathematical equations that relate some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.
They are fundamental to many fields of science and engineering, allowing us to describe phenomena such as the motion of waves, the flow of heat, and the behavior of circuits. 🌊🔥⚡
Differential equations can be categorized by order, linearity, and whether they are ordinary or partial:
The study of differential equations began with Isaac Newton and Gottfried Wilhelm Leibniz, who independently developed calculus in the late 17th century. Their work laid the groundwork for modern physics and engineering.