Euler's homogeneous function theorem
GPTKB entity
Statements (15)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
homogeneous functions
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| gptkbp:field |
gptkb:mathematics
calculus multivariable calculus |
| gptkbp:form |
x₁(∂f/∂x₁) + x₂(∂f/∂x₂) + ... + xₙ(∂f/∂xₙ) = kf(x₁, ..., xₙ)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Euler's homogeneous function theorem
|
| gptkbp:namedAfter |
gptkb:Leonhard_Euler
|
| gptkbp:publicationYear |
1760s
|
| gptkbp:state |
If f is a differentiable homogeneous function of degree k, then the sum over all variables of the variable times the partial derivative of f with respect to that variable equals k times f.
|
| gptkbp:usedIn |
economics
partial differential equations thermodynamics |
| gptkbp:bfsParent |
gptkb:Euler's_theorem_in_calculus
|
| gptkbp:bfsLayer |
8
|