Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Gradient_theorem> ?p ?o. }
Showing items 1 to 25 of
25
with 100 items per page.
- Gradient_theorem abstract "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.Let . ThenIt is a generalization of the fundamental theorem of calculus to any curve in a plane or space (generally n-dimensional) rather than just the real line.The gradient theorem implies that line integrals through gradient fields are path independent. In physics this theorem is one of the ways of defining a "conservative" force. By placing φ as potential, ∇φ is a conservative field. 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.The gradient theorem also has an interesting converse: any path-independent vector field can be expressed as the gradient of a scalar field. Just like the gradient theorem itself, this converse has many striking consequences and applications in both pure and applied mathematics.".
- Gradient_theorem wikiPageID "5337437".
- Gradient_theorem wikiPageRevisionID "594619469".
- Gradient_theorem hasPhotoCollection Gradient_theorem.
- Gradient_theorem subject Category:Articles_containing_proofs.
- Gradient_theorem subject Category:Theorems_in_calculus.
- Gradient_theorem type Abstraction100002137.
- Gradient_theorem type Communication100033020.
- Gradient_theorem type Message106598915.
- Gradient_theorem type Proposition106750804.
- Gradient_theorem type Statement106722453.
- Gradient_theorem type Theorem106752293.
- Gradient_theorem type TheoremsInCalculus.
- Gradient_theorem comment "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.Let . ThenIt is a generalization of the fundamental theorem of calculus to any curve in a plane or space (generally n-dimensional) rather than just the real line.The gradient theorem implies that line integrals through gradient fields are path independent.".
- Gradient_theorem label "Gradient theorem".
- Gradient_theorem label "Teorema del gradiente".
- Gradient_theorem label "Théorème du gradient".
- Gradient_theorem sameAs Théorème_du_gradient.
- Gradient_theorem sameAs Teorema_del_gradiente.
- Gradient_theorem sameAs m.0dg84k.
- Gradient_theorem sameAs Q287347.
- Gradient_theorem sameAs Q287347.
- Gradient_theorem sameAs Gradient_theorem.
- Gradient_theorem wasDerivedFrom Gradient_theorem?oldid=594619469.
- Gradient_theorem isPrimaryTopicOf Gradient_theorem.