Laplace equation: What is the difference between divergence operator and gradient operator both represented by $\nabla$? (in wikipedia article) Here is the beginning of the article of Laplace equation of wikipedia **Laplace's equation** is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties. This is often written as $$ \nabla^2f = 0\quad\text{or}\quad\Delta f = 0 $$ where $\Delta= \nabla \cdot \nabla = \nabla^2$ is the **Laplace operator** and $\nabla$ is divergence operator (also symbolized "div"), $\nabla$ is the gradient operator (also symbolized "grad"), and $f(x,y,z)$ is a twice-differentiable real-valued function. The Laplace operator therefore maps a scalar function to another scalar function My question: In this definition, what is the difference between divergence operator and gradient operator both represented by $\nabla$?

You left out a tiny detail. The wikipedia article states $\
abla\cdot$ is the divergence operator. Along with the dot product applied to a vector yields the divergence. $\
abla$ itself applied to some function is the classical gradient vector.