1. The symbol \nabla (called "nabla" or "del") is a vector differential operator used in vector calculus. 2. It is defined as \nabla = \left(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z}\right) in three-dimensional Cartesian coordinates. 3. \nabla is used to compute gradient, divergence, and curl of scalar and vector fields. 4. For a scalar function $f(x,y,z)$, the gradient is given by $$\nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right).$$ 5. For a vector field $\mathbf{F} = (F_x, F_y, F_z)$, the divergence is $$\nabla \cdot \mathbf{F} = \frac{\partial F_x}{\partial x} + \frac{\partial F_y}{\partial y} + \frac{\partial F_z}{\partial z}$$ and the curl is $$\nabla \times \mathbf{F} = \left(\frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z}, \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x}, \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y}\right).$$ 6. These operations are fundamental in physics and engineering, especially in electromagnetism and fluid dynamics.