Double Integrals in Polar Coordinates

Double Integrals in Polar Coordinates

Fubini’s Theorem in Polar Coordinates The polar conversion formulas are used to convert from rectangular to polar coordinates: \begin{equation} x=r \cos \theta, \quad y=r \sin \theta, \quad r=\sqrt{x^2+y^2}, \quad \tan \theta =\frac{y}{x}. \end{equation} Theorem. (Fubini’s Theorem in Polar Coordinates) If

Divergence and Curl of a Vector Field Young woman, physics teacher draws a diagram of the electric field

Divergence and Curl of a Vector Field

The Divergence and Curl Definition. Let $\mathbf{V}$ be a given vector field. The divergence of $\mathbf{V}$ is defined by div $\mathbf{V}=\nabla \cdot \mathbf{V}$ and the curl of $\mathbf{V}$ is defined by curl $\mathbf{V}=\nabla \times \mathbf{V}$ where \begin{equation} \nabla =\frac{\partial }{\partial