bigtriangledown
Represents a large downward-pointing triangle operator commonly used in mathematical notation for gradient, divergence, or similar operations.
Overview
Serves as a prominent mathematical operator in advanced calculus, vector analysis, and differential geometry, particularly when working with vector fields and multivariable functions.
- Often employed to denote the gradient operator in its downward form
- Appears in physics equations related to potential fields and fluid dynamics
- Frequently used in tensor calculus and differential operators
- Can represent a backward difference operator in numerical analysis
- Sometimes used in theoretical physics to denote certain quantum operators
Examples
Expressing the gradient operator in vector calculus.
\bigtriangledown f(x,y,z) = \frac{\partial f}{\partial x}\mathbf{i} + \frac{\partial f}{\partial y}\mathbf{j} + \frac{\partial f}{\partial z}\mathbf{k}
Showing the Laplacian operator in mathematical physics.
\bigtriangledown^2 \phi = \frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} + \frac{\partial^2 \phi}{\partial z^2}
Representing the divergence of a vector field.
\bigtriangledown \cdot \mathbf{F} = \frac{\partial F_x}{\partial x} + \frac{\partial F_y}{\partial y} + \frac{\partial F_z}{\partial z}