directional derivative उदाहरण वाक्य

Here one considers a modification of the directional derivative by a certain linear operator, whose components are called the Christoffel symbols, which involves no derivatives on the vector field itself.
More precisely, when is differentiable, the dot product of the gradient of with a given unit vector is equal to the directional derivative of in the direction of that unit vector.
The covariant formulation of the directional derivative of any tensor field along a vector v ^ \ gamma may be expressed as its contraction with the covariant derivative, e . g .:
where \ partial _ X and \ partial _ Y denote the operations of taking the directional derivatives with respect to " X " and " Y ", respectively.
This form has 64 coefficients a _ { ijk }; requiring the function to have a given value or given directional derivative at a point places one linear constraint on the 64 coefficients.

Both a directional derivative and a functional derivative are expressed as real numbers, the first in case of a finite number of variables and the second for an infinite number so to say.
The primary difference from the usual directional derivative is that the covariant derivative must, in a certain precise sense, be independent of the manner in which it is expressed in a coordinate system.
That means if you take a directional derivative in any direction, it will agree with what you'd get for the tangent space . talk ) 05 : 15, 17 December 2009 ( UTC)
This above definition can be generalized to real-valued functions " f " defined on subsets of "'R " "'n " using a weaker version of the directional derivative.
The constant C is easy to determine in the important special case described in terms of the directional derivative of X at a given point ( of the sphere ) in a given direction ( tangential to the sphere ).