gradient theorem造句
例句與造句
- In the language of differential forms and exterior derivatives, the gradient theorem states that
- This case is called the gradient theorem, and generalizes the fundamental theorem of calculus ).
- The gradient theorem can then be applied to the optical path length ( as given above ) resulting in
- The converse statement of the gradient theorem also has a powerful generalization in terms of differential forms on manifolds.
- Just like the gradient theorem itself, this converse has many striking consequences and applications in both pure and applied mathematics.
- It's difficult to find gradient theorem in a sentence. 用gradient theorem造句挺難的
- The most familiar extensions of the fundamental theorem of calculus in higher dimensions are the divergence theorem and the gradient theorem.
- Thus, we have solved this problem using only Coulomb's Law, the definition of work, and the gradient theorem.
- The gradient theorem also has an interesting converse : any path-independent vector field can be expressed as the gradient of a scalar field.
- This powerful statement is a generalization of the gradient theorem from 1-forms defined on one-dimensional manifolds to differential forms defined on manifolds of arbitrary dimension.
- If \ mathbf { v } = \ nabla \ varphi for some C ^ 1 scalar field \ varphi so that \ mathbf { v } is a conservative vector field, then the Gradient Theorem states that
- The gradient theorem implies that line integrals through gradient fields are Work done by conservative forces does not depend on the path followed by the object, but only the end points, as the above equation shows.
- If the force "'F "'is derivable from a potential ( conservative ), then applying the gradient theorem ( and remembering that force is the negative of the gradient of the potential energy ) yields:
- A ( continuous ) gradient field is always a conservative vector field : its line integral along any path depends only on the endpoints of the path, and can be evaluated by the gradient theorem ( the fundamental theorem of calculus for line integrals ).
- The "'gradient theorem "', also known as the "'fundamental theorem of calculus for line integrals "', says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve.