
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 20th, 2016, 05:19 AM  #1 
Newbie Joined: Feb 2016 From: UK Posts: 2 Thanks: 0  Divergence of a vector
Hi, I was wondering if you could help me. I'm trying to get the divergence of my vector: [cos(x)sin(y) + picos(y)sin(x), picos(x)sin(y) + (picos(y)(sin(x)), picos(y)sin(x) + cos(x)sin(y)] however, to take the divergence of something, it is usually (dP/dx, dM/dy, dN/dz) but since there is no z component in the bottom of the vector, does that mean that it goes to 0? if so, can I cancel the vector down to a 1x2 instead of a 1x3 if needs be? Thank you! 
March 1st, 2016, 03:18 PM  #2 
Senior Member Joined: Dec 2015 From: somewhere Posts: 647 Thanks: 94 
$\displaystyle divf=\nabla \cdot f$ or $\displaystyle \nabla_{x,y} \cdot \left( \begin{array}{c} P \\ Q \\R\end{array} \right)=\nabla_{x,y,z} \cdot \left( \begin{array}{c} P \\ Q \\emptyor0\end{array} \right) $ Since $\displaystyle R\vec{k}\cdot 0 = 0 \cdot A\vec{k}$ it shows that your way is correct Last edited by idontknow; March 1st, 2016 at 03:20 PM. 
March 18th, 2016, 09:08 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
The "divergence" of a vector valued function is NOT a vector as you show. $\displaystyle \nabla \cdot \left< P, Q, R\right>=\frac{\partial P}{\partial x}+ \frac{\partial Q}{\partial y}+ \frac{\partial R}{\partial z}$. Here, since R does not depend on z, that last derivative will be 0. Last edited by greg1313; April 29th, 2016 at 04:13 AM. 

Tags 
divergence, vector 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
vector field, divergence, curl  harley05  Calculus  3  June 10th, 2014 10:16 AM 
Vector field, curl and divergence question  solrob  Applied Math  2  November 10th, 2013 09:06 AM 
Convergence and divergence  razzatazz  Real Analysis  8  May 10th, 2013 11:30 PM 
Vector Calculus Divergence of a Vector Field  MasterOfDisaster  Calculus  2  September 26th, 2011 09:17 AM 
Divergence of a series  patient0  Real Analysis  5  December 11th, 2010 06:17 AM 