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Vector calculus gradients

  1. Apr 4, 2012 #1
    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!!
     
  2. jcsd
  3. Apr 4, 2012 #2

    tiny-tim

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    hi calculusisrad! :smile:
    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?​
     
  4. Apr 4, 2012 #3
    Sorry, yes you're right. The gradient of f should not be bolded.
     
  5. Apr 4, 2012 #4
    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?
     
  6. Apr 4, 2012 #5
    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 :)
     
  7. Apr 4, 2012 #6
    "Please answer"? How about you show some effort first? You should have read the forums rules by now.
     
  8. Apr 4, 2012 #7
    This was due last Thursday, I'm horribly behind on homework, I'm desperate here.
     
  9. Apr 4, 2012 #8

    Dick

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    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?
     
    Last edited: Apr 4, 2012
  10. Apr 5, 2012 #9

    HallsofIvy

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    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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