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Math Help - Help with the gradient operator

  1. #1
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    Help with the gradient operator

    If i need to describe how the direction of grad(f) (for a specific f) varies in space by considering grad(f) on surfaces given by f(x,y,z)=constant, how do I do this? What is the question asking? What relevence does grad(f) on a surface f(x,y,z)=constant have?

    Any hints or tips appreciated

    Thanks
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  2. #2
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    Re: Help with the gradient operator

    Quote Originally Posted by darren86 View Post
    If i need to describe how the direction of grad(f) (for a specific f) varies in space by considering grad(f) on surfaces given by f(x,y,z)=constant, how do I do this? What is the question asking? What relevence does grad(f) on a surface f(x,y,z)=constant have?

    \nabla f\left( {x_0 ,y_0 ,z_0 } \right) is the normal of the tangent plane to the surface f(x,y,z)=C at the point (x_0 ,y_0 ,z_0).
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  3. #3
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    Re: Help with the gradient operator

    Quote Originally Posted by Plato View Post
    \nabla f\left( {x_0 ,y_0 ,z_0 } \right) is the normal of the tangent plane to the surface f(x,y,z)=C at the point (x_0 ,y_0 ,z_0).

    Thanks for your reply. If f(x,y,z) = x^2+y^2 for instance what can be said about how the direction of grad(f) varies in space (by considering surfaces where f=constant)?

    I don't think it is sufficient to just say that for points on any surface f=constant, gradf will be normal to the surface. What else can be said?
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  4. #4
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    Re: Help with the gradient operator

    Quote Originally Posted by darren86 View Post
    I don't think it is sufficient to just say that for points on any surface f=constant, gradf will be normal to the surface. What else can be said?
    I don't really understand what you are attempting to do.

    We can also say that \nabla f points in the direction of maximum increase in the field and \|\nabla f\| is the rate of maximum increase.
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