Partial Differential Equations
Differential equations containing unknown multivariable functions and their partial derivatives with respect to multiple independent variables.
Governing formula
Elliptic (Laplace), Parabolic (Heat), Hyperbolic (Wave)
SI unit
Multivariable Differential Equations
In depth
Classified into Elliptic (∇²u = 0, steady state), Parabolic (∂u/∂t = α ∇²u, diffusion), and Hyperbolic (∂²u/∂t² = c² ∇²u, wave propagation) PDEs. Solved analytically via separation of variables or numerically via finite elements.
Examples in the real world
Solving the 3D wave equation for acoustic sound propagation and the heat equation for thermal conduction.