# Vector analysis math **URL:** \ **Category:** Factual Questions\ **Created:** [October 9, 2001, 12:01am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211 "2001-10-09T00:01:27Z")\ **Posts on this page:** 13\ **Page:** 1
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [October 9, 2001, 12:01am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/1 "2001-10-09T00:01:27Z")
I was paging through my old electrodynamics text and stumbled on the following in a chapter on potentials and fields. Rho is a function of **r** and t, or rho( **r** , t) **Del** rho = [d( **rho** )/dt] ( **del** t) I am sadly at a loss to understand where this last equation came from, and help would be appreciated. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [October 9, 2001, 12:18am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/2 "2001-10-09T00:18:57Z")
When using Del, you’re talking about a 3-D surface. The purpose of Del, as I recall, is to find the gradient - or, the extrema of the surface…to the best of my knowledge. You’ll recall Del is a calculus function involving partial derivatives. As I recall, the Del finds what is called the gradient. If you’d like more info, I’ll crack open my Calculus book, and see if I can help you. However, this part of Calc I just accepted without trying to understand. While you are using it to define an electromagnetic field, I know it is used in topography and weather maps, for example. I was a ME (mechanical engineer), and this has little application for my purposes - so I’m a bit rutsy here. - Jinx ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 9, 2001, 12:22am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/3 "2001-10-09T00:22:25Z")
It looks like a vector version of the chain rule. My vector analysis background is slightly non-existent, so consider this an educated guess. On preview, I see what **Jinx** said, and I think (s)he’s right on, although I don’t have my calc book. Try looking up the definition of del; if it is the gradient, then I’m pretty sure the original equation follows from the chain rule. ---
**Author:** ![Strainger](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/strainger/32/244_2.png) [@Strainger](https://boards.straightdope.com/u/Strainger)\ **Post date:** [October 9, 2001, 12:40am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/4 "2001-10-09T00:40:16Z")
Like **Jinx** said, Del doesn’t have much use for a mechanical engineer (not the mechanical engineer making this post, anyway. I’ve long forgotten this since my emag class). I just want to step in and restate the OP’s formula taking advantage of the new Symbol font capability. [sym] **Ñ** r[/sym]=(d[sym] **r** [/sym]/dt)[sym] **Ñ** [/sym]t Is that pretty much how it looked? Or should it be a partial derivative, i.e. [sym] **Ñ** r[/sym]=([sym]¶ **r** [/sym]/[sym]¶[/sym]t)[sym] **Ñ** [/sym]t ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 9, 2001, 12:49am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/5 "2001-10-09T00:49:59Z")
> [@](#): > > \*Originally posted by Strainger \* > \*\*Is that pretty much how it looked? Or should it be a partial derivative, i.e. > > [sym] **Ñ** r[/sym]=([sym]¶ **r** [/sym]/[sym]¶[/sym]t)[sym] **Ñ** [/sym]t \*\* It should definitely be a partial derivative, as [sym] **r** [/sym] is a function of two variables. ---
**Author:** ![Strainger](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/strainger/32/244_2.png) [@Strainger](https://boards.straightdope.com/u/Strainger)\ **Post date:** [October 9, 2001, 12:55am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/6 "2001-10-09T00:55:36Z")
That’s what I figgered. Also, I missed bolding the first [sym]r[/sym], which indicates that I’m also missing a dot or cross. I found [this link](http://web.mit.edu/wwmath/vectorc/summary.html) while doing a search on vectors and gradients. Does it help? On a related note, I can’t _believe_ how much of this stuff I’ve forgotten. ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [October 9, 2001, 1:23am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/7 "2001-10-09T01:23:00Z")
> [@](#): > > Strainger wrote: > > Is that pretty much how it looked? Or should it be a partial derivative, i.e. Yep, that’s how it should look… how did you do that? What I can’t figure out is where the d(rho)/dt came from. The Del operator that I’m familiar with is strictly spatial. [d/dx **x** + d/dy **y** + d/dz **z**] d should be the symbol for a partial Derivative, but I don’t know how to do that. ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [October 9, 2001, 1:28am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/8 "2001-10-09T01:28:07Z")
Actually since I don’t know how to do the hat symbol for a unit vector I should have used **i** , **j** , **k** ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [October 9, 2001, 1:36am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/9 "2001-10-09T01:36:18Z")
It’s me again. > [@](#): > > Strainger wrote: > > That’s what I figgered. Also, I missed bolding the first r, which indicates that I’m also missing a dot or cross. There’s no dot or cross involved del(scaler) is the gradient and it’s a vector. Thanks so far, and keep trying guys this is driving me crazy. ---
**Author:** ![Manlob](https://avatars.discourse-cdn.com/v4/letter/m/96bed5/32.png) [@Manlob](https://boards.straightdope.com/u/Manlob)\ **Post date:** [October 9, 2001, 2:36am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/10 "2001-10-09T02:36:47Z")
There may be a couple of typos. If t is time, **del** (t) would normally be zero unless time is a function of position. Also, the scalar function, rho, is more likely to be a function of the scalar, r, instead of a vector, **r**. If you meant rho(r,t), then it is true that: **del** (rho)= d(rho)/dr **del** ® Which is similar to what your book says with r instead of t. ---
**Author:** ![g8rguy](https://avatars.discourse-cdn.com/v4/letter/g/7cd45c/32.png) [@g8rguy](https://boards.straightdope.com/u/g8rguy)\ **Post date:** [October 9, 2001, 2:42am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/11 "2001-10-09T02:42:59Z")
Well, it looks to me like you’ve just got d[sub]i[/sub][sym]r[/sym] = d/dt [sym]r[/sym] \* d[sub]i[/sub]t. Isn’t that just the chain rule, with [sym]r/sym = [sym]r[/sym][t( **r** )]? ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [October 9, 2001, 4:05am UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/12 "2001-10-09T04:05:45Z")
> [@](#): > > \*Originally posted by Ring \* > Yep, that’s how it should look… how did you do that? \*\* The symbol font is now available. See the ATMB thread [http://boards.straightdope.com/sdmb/showthread.php?threadid=90639](http://boards.straightdope.com/sdmb/showthread.php?threadid=90639) ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [October 9, 2001, 2:33pm UTC](https://boards.straightdope.com/t/vector-analysis-math/86211/13 "2001-10-09T14:33:01Z")
Thanks **g8rguy** it _was_ a composite function, and Thanks to bibliophage, I’ll see if I can figure out how to use that stuff.