Surfaces and Gradients

Visualize how gradients relate to surfaces.

The points (x,y,z) satisfying w=f(x,y,z)=u (x^2)+ v (y^2) + (z^2) for a particular value of w form the surface shown. As w varies, the surface deforms along the normals defined by the vector field ∇f=((∂f)/(∂x))(Overscript[i, ->])+((∂f)/(∂y)) (Overscript[j, ->])+((∂f)/(∂z))(Overscript[k, ->]), the gradient of f, represented by the arrows.

Due to the complex nature of this Demonstration, there may be a delay between changing the variables and updating the graph.

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Contributed by: Nevin Raj

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