me22b135.tex

\section{ME22B135}

     \item Name: Jadhav Bhargavi Sandip
     \item Github User id: 
Bhargavi-JAdhav 
     \item Divergence Theorem

$$\int_V (\nabla\cdot \vec{A}) \cdot dV = \oint\vec{A} \cdot\vec{ds} $$
 Divergence theorem in vector calculus relates the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.\footnote{Reference: \href{https://en.wikipedia.org/wiki/Divergence\_theorem}}
 The divergence of a vector field $\vec{A}(= A_x i + A_y j + A_z k )$ is defined as a dot product of the $\nabla$ operator with $\vec{A}$
 that is :
 $$\nabla\cdot \vec{A} = \frac{\partial A_x}{\partial x} i + \frac{\partial A_y}{\partial y} j + \frac{\partial A_z}{\partial z} k $$
  Divergence can also be defined as flux per unit volume.\footnote{Reference: Introduction to classical mechanics by David Morin, Appendix B}