Notices
Results 1 to 7 of 7

Thread: directional derivative ...

  1. #1 directional derivative ... 
    Forum Freshman
    Join Date
    Jun 2007
    Posts
    60
    ok..I have been learning for quite a bit but am having hard time visualizing how it works.
    Can anyone explain me the derivation of the directional derivative ( the logic behind it ).

    Thx,


    www.physics-gallo.blogspot.com
    " If you give up i'm sure it'll give quite relief. No one will bother you or even pay attention to you. It feels alright but is still very painful."
    Reply With Quote  
     

  2.  
     

  3. #2 Re: directional derivative ... 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by newspaper
    ok..I have been learning for quite a bit but am having hard time visualizing how it works.
    Can anyone explain me the derivation of the directional derivative ( the logic behind it ).

    Thx,
    Let f be a function defined on n-space and let x be a point in n-space and let v be an n-vector. Now consider the function g of the real variable t defined by g(t)=f(x+tv). Then g'(0) is the directional derivative of f at x in the direction of v. You get it by looking at the function f restricted to a line through x in the direction of v. The set of points x+tv for fixed x and v as t varies is just that line.


    Reply With Quote  
     

  4. #3 Re: directional derivative ... 
    Forum Freshman
    Join Date
    Jun 2007
    Posts
    60
    Quote Originally Posted by DrRocket
    Quote Originally Posted by newspaper
    ok..I have been learning for quite a bit but am having hard time visualizing how it works.
    Can anyone explain me the derivation of the directional derivative ( the logic behind it ).

    Thx,
    The real variable t defined by g(t)=f(x+tv). Then g'(0) is the directional derivative of f at x in the direction of v. You get it by looking at the function f restricted to a line through x in the direction of v. The set of points x+tv for fixed x and v as t varies is just that line.
    Could you explain a little more about it, if you don't mind.
    I appreciate your help. :wink:
    www.physics-gallo.blogspot.com
    " If you give up i'm sure it'll give quite relief. No one will bother you or even pay attention to you. It feels alright but is still very painful."
    Reply With Quote  
     

  5. #4 Re: directional derivative ... 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by newspaper
    Quote Originally Posted by DrRocket
    Quote Originally Posted by newspaper
    ok..I have been learning for quite a bit but am having hard time visualizing how it works.
    Can anyone explain me the derivation of the directional derivative ( the logic behind it ).

    Thx,
    The real variable t defined by g(t)=f(x+tv). Then g'(0) is the directional derivative of f at x in the direction of v. You get it by looking at the function f restricted to a line through x in the direction of v. The set of points x+tv for fixed x and v as t varies is just that line.
    Could you explain a little more about it, if you don't mind.
    I appreciate your help. :wink:
    Why don't you try to explain how you look at it. I have given you one way that I look at it. If I could see your ideas, correct or otherwise, then I could perhaps understand what is confusing you on what is basically a simple geometric idea.
    Reply With Quote  
     

  6. #5  
    Forum Freshman
    Join Date
    Jun 2007
    Posts
    60
    Hi dr. rocket

    The derivative of 'f' in the direction u at point p is :



    This is the definition i have learnt. Its just that i am failing to visualize it. I have a very bad habit of not going forward until i can visualize it.

    Thx,
    www.physics-gallo.blogspot.com
    " If you give up i'm sure it'll give quite relief. No one will bother you or even pay attention to you. It feels alright but is still very painful."
    Reply With Quote  
     

  7. #6  
    Forum Freshman
    Join Date
    Oct 2008
    Posts
    19
    Im not quite sure what you are asking to hear but what helped me understand the concept of directional derivatives was that they are the rate of change of the function f(x,y,z) in the direction of the unit vector u=<a,b,c>. So to find the rate of change of the function you would then need to take the partial derivatives of each variable and multiply it by its corresponding direction in the unit vector to find the rate of change in a certain direction.

    Hope that helps!
    Reply With Quote  
     

  8. #7  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by newspaper
    Hi dr. rocket

    The derivative of 'f' in the direction u at point p is :



    This is the definition i have learnt. Its just that i am failing to visualize it. I have a very bad habit of not going forward until i can visualize it.

    Thx,
    Look at what you wrote and think of it geometrically. You fixed a point P and a direction u. Then you have a new function of and you took the derivative of that new function a the point That new function was precisely the function f restricted to a line passing through P in the direction u.
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •