Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
Differentiable functions
|
| gptkbp:describes |
Conditions under which a relation defines a function implicitly
|
| gptkbp:field |
gptkb:Mathematics
gptkb:Calculus Analysis |
| gptkbp:firstPublished |
19th century
|
| gptkbp:generalizes |
Inverse function theorem
|
| gptkbp:hasApplication |
gptkb:Physics
Economics Engineering Optimization |
| https://www.w3.org/2000/01/rdf-schema#label |
Implicit function theorem
|
| gptkbp:relatedTo |
Inverse function theorem
|
| gptkbp:requires |
Continuously differentiable functions
Non-vanishing partial derivative with respect to dependent variable |
| gptkbp:state |
If F(x, y) = 0 and certain conditions hold, y can be solved as a function of x near a point
|
| gptkbp:usedIn |
gptkb:Differential_geometry
Multivariable calculus Nonlinear analysis Solving equations involving several variables |
| gptkbp:bfsParent |
gptkb:Lagrange_inversion_theorem
|
| gptkbp:bfsLayer |
6
|