1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Directional derivative question

  1. Jan 11, 2014 #1

    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


    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted