Equations · equation
Gradient
Calculus · 1853
- Equation
- ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)
- Field
- Calculus
- Year
- 1853
Symbols
f a scalar field — a number at every point, like temperature or pressure · ∇f a vector at every point, pointing uphill, with the slope as its length
Significance
Where a field rises fastest, and how fast. Heat flows down the temperature gradient (Fourier's law), water down the pressure gradient, and a conservative force is minus the gradient of its potential energy — F = −∇U — which is what makes a ball roll downhill. Hamilton introduced the ∇ symbol in 1837; the vector reading of it is Gibbs's.
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.