Mathematics - Differential Equations - Partial differential equations introduction - The Big Three PDEs

10 steps: (1) PDEs involve partial derivatives of a function of multiple variables. (2) HEAT EQUATION: ∂u/∂t = k·∂²u/∂x². Temperature u(x,t) evolves over time. (3) Physical meaning: heat flows from hot to cold; rate depends on curvature of temperature profile. (4) WAVE EQUATION: ∂²u/∂t² = c²·∂²u/∂x²