The Heat Equation

The heat equation is a mathematical model that describes how heat spreads through a material over time. Think of a room where a heater warms the air; the heat moves from the hot spots to cooler areas, eventually balancing out. The equation captures this process, showing how temperature changes at each point depend on the temperatures of neighboring points. It applies to many contexts, like how a metal rod heats up or cools down, helping us predict temperature distribution over time in various systems.