My Math Forum  

Go Back   My Math Forum > College Math Forum > Differential Equations

Differential Equations Ordinary and Partial Differential Equations Math Forum


Reply
 
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!
mojojojo17 is offline  
 
March 1st, 2016, 03:18 PM   #2
Senior Member
 
Joined: Dec 2015
From: somewhere

Posts: 512
Thanks: 79

$\displaystyle divf=\nabla \cdot f$ 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
\\empty-or-0\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.
idontknow is offline  
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.
Country Boy is offline  
Reply

  My Math Forum > College Math Forum > Differential Equations

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





Copyright © 2019 My Math Forum. All rights reserved.