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Doubts regarding gradient operator

  1. Jul 26, 2014 #1

    utkarshakash

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    Gold Member

    1. The problem statement, all variables and given/known data
    I need some help regarding the gradient operator. I recently came across this statement while reading Griffith's Electrodynamics
    "The gradient ∇T points in the direction of maximum increase of the function
    T."


    Wolfram Alpha also states that "The direction of ∇f is the orientation in which the directional derivative has the largest value and |∇f| is the value of that directional derivative. "

    I'm finding it difficult to absorb this thing without any reasonable explanation. Can someone help?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 26, 2014 #2

    vanhees71

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    2016 Award

    Take a scalar field, [itex]T(\vec{x})[/itex] and calculate the directional derivative in direction of the unit vector [itex]\vec{n}[/itex] at a fixed point [itex]\vec{x}=\vec{x}_0[/itex]. How is it related to the gradient? In which direction do have to choose [itex]\vec{n}[/itex] such that (modulus of) the directional derivative becomes maximal?
     
  4. Jul 26, 2014 #3
  5. Jul 27, 2014 #4

    utkarshakash

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    Gold Member

    Thank you very much! This article explains it very nicely.
     
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