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Directional derivative question

  1. Jan 11, 2014 #1
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    I've done the first part, but I'm stuck on the second paragraph of the question. Maybe I'm being stupid, I don't even understand exactly what is meant by, 'the level curve'.

    I also don't quite understand the whole concept of directional derivative. When it says, 'the gradient in the direction making an angle A with the x-axis, how should I think of this? what does the gradient mean in this context?

    because when its just a simple curve/line on an xy axis, I know what the 'gradient' means, it is literally how much 'y' changes per unit x along that curve/line. But when I'm told about a 'gradient in a direction', I'm confused.
     
  2. jcsd
  3. Jan 11, 2014 #2

    tiny-tim

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    hey, question dude! :smile:
    think of the 3D graph, z = f(x,y)

    you can make a 2D contour map showing the lines of equal height

    those contours are the level curves :wink:
    the directional derivative in the direction (cosθ,sinθ) is df(kcosθ,ksinθ)/dk

    it's the rate at which f increases if you go along the line y/x = tanθ :smile:
     
  4. Jan 11, 2014 #3

    Ray Vickson

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    You are supposed to show your work, confused or not (those are PF rules). I don't see how you can have done the first part (which involves directional derivatives) but then claim you do not understand directional derivatives. I would need to see your work in order to grasp what is going on.
     
  5. Jan 11, 2014 #4
    Thanks a lot!!! I understand whats going on now. Before I was just plugging in the numbers without knowing the concepts properly.
     
  6. Jan 11, 2014 #5
    Sorry about that, what I meant to get across, was that I understood the method in a sort of algorithmic way, but didn't understood the reason behind steps due to not understanding some basic stuff like 'level curve'. Anyway its sorted now.
     
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