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-   -   Vector calculus gradients (http://www.physicsforums.com/showthread.php?t=593298)

calculusisrad Apr4-12 02:30 AM

Vector calculus gradients
 
1. The problem statement, all variables and given/known data
Find a function f(x,y,z) such that F = (gradient of F).


3. The attempt at a solution
I don't know :(
I'm so confused
Please help me!!

tiny-tim Apr4-12 04:46 AM

hi calculusisrad! :smile:
Quote:

Quote by calculusisrad (Post 3849202)
Find a function f(x,y,z) such that F = (gradient of F).

do you mean "Find a function f(x,y,z) such that F = (gradient of f)" ?

(only scalars have gradients, there's no gradient of a vector)
i don't understand either :confused:

is either f or F given in the question?

calculusisrad Apr4-12 11:54 AM

Re: Vector calculus gradients
 
Sorry, yes you're right. The gradient of f should not be bolded.

1MileCrash Apr4-12 01:15 PM

Re: Vector calculus gradients
 
Think about what a gradient is. If I told you to find the gradient of a function, what would you do?

You would differentiate the function wrt x, and that is the i component of the gradient, you would differentiate the function wrt y, and that is the j component, and then you would differentiate the function wrt z, and that is the k component.

Now, we are going in reverse. What is the reverse of differentiation?

calculusisrad Apr4-12 09:48 PM

Re: Vector calculus gradients
 
I completely forgot the biggest part of the problem. WOW. Sorry about that!!!

Let F = (2xye^z)i + ((e^z)(x^2))j + ((x^2)y(e^z)+(z^2))k

NOW find a function f(x,y,z) such that F = Gradient of f.

Sorry about that. Please answer :)

DivisionByZro Apr4-12 09:53 PM

Re: Vector calculus gradients
 
"Please answer"? How about you show some effort first? You should have read the forums rules by now.

calculusisrad Apr4-12 10:06 PM

Re: Vector calculus gradients
 
This was due last Thursday, I'm horribly behind on homework, I'm desperate here.

Dick Apr4-12 10:16 PM

Re: Vector calculus gradients
 
Quote:

Quote by calculusisrad (Post 3850566)
This was due last Thursday, I'm horribly behind on homework, I'm desperate here.

It's pretty easy to guess a form for f that works. Start guessing. That's often the easiest way to solve problems like this. What's a likely form for f given the first component of F?

HallsofIvy Apr5-12 07:09 AM

Re: Vector calculus gradients
 
You know what the definition of "gradient" is, so use that.
[itex]\frac{\partial f}{\partial x}=[/itex] what?
[itex]\frac{\partial f}{\partial y}=[/itex] what?
[itex]\frac{\partial f}{\partial z}=[/itex] what?


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