| 11. | This extends the directional derivative of scalar functions to sections of vector bundles or principal bundles.
|
| 12. | The precise definition of the directional derivative depends on what formalization one is using for vector fields.
|
| 13. | This allows the abstraction of the notion of a directional derivative of a scalar function to general manifolds.
|
| 14. | This operator applied to a function gives the directional derivative of at in the direction of increasing with fixed.
|
| 15. | In differential geometry, the covariant derivative makes a choice for taking directional derivatives of vector fields along curves.
|
| 16. | The Hopf lemma implies that the directional derivative of in the direction of the outward normal is strictly positive.
|
| 17. | "' Hadamard derivative "'is a concept of directional derivative for maps between Banach spaces.
|
| 18. | Multivariate functions can be handled with the same efficiency and mechanisms as univariate functions by adopting a directional derivative operator.
|
| 19. | This means that the directional derivative depends only on the tangent vector of the curve at " p ".
|
| 20. | The Fr�chet derivative should be contrasted to the more general G�teaux derivative which is a generalization of the classical directional derivative.
|
