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  2. Implicit function theorem - Wikipedia

    en.wikipedia.org/wiki/Implicit_function_theorem

    Thus, here, the Y in the statement of the theorem is just the number 2b; the linear map defined by it is invertible if and only if b ≠ 0. By the implicit function theorem we see that we can locally write the circle in the form y = g(x) for all points where y ≠ 0. For (±1, 0) we run into trouble, as noted before.

  3. Implicit function - Wikipedia

    en.wikipedia.org/wiki/Implicit_function

    An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the value of the function, with the others considered as the arguments. [ 1 ] : 204–206 For example, the equation x 2 + y 2 − 1 = 0 {\displaystyle x^{2}+y^{2}-1=0} of the unit circle defines y as an implicit function ...

  4. Implicit curve - Wikipedia

    en.wikipedia.org/wiki/Implicit_curve

    The implicit function theorem describes conditions under which an equation (,) = can be solved implicitly for x and/or y – that is, under which one can validly write = or = (). This theorem is the key for the computation of essential geometric features of the curve: tangents , normals , and curvature .

  5. Lyapunov–Schmidt reduction - Wikipedia

    en.wikipedia.org/wiki/Lyapunov–Schmidt_reduction

    For the case when the linear operator (,) is invertible, the implicit function theorem assures that there exists a solution () satisfying the equation ((),) = at least locally close to . In the opposite case, when the linear operator f x ( x , λ ) {\displaystyle f_{x}(x,\lambda )} is non-invertible, the Lyapunov–Schmidt reduction can be ...

  6. Category:Theorems in calculus - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_in_calculus

    Implicit function theorem; Increment theorem; Integral of inverse functions; Integration by parts; Integration using Euler's formula; Intermediate value theorem; Inverse function rule; Inverse function theorem

  7. Eigenvalue perturbation - Wikipedia

    en.wikipedia.org/wiki/Eigenvalue_perturbation

    In the next paragraph, we shall use the Implicit function theorem (Statement of the theorem ); we notice that for a continuously differentiable function : +,: (,) (,), with an invertible Jacobian matrix , (,), from a point (,) solution of (,) =, we get solutions of (,) = with close to in the form = where is a continuously differentiable ...

  8. Congo says mysterious disease killing dozens of kids finally ...

    www.aol.com/news/congo-says-mysterious-disease...

    "The mystery has finally been solved," Congo's health ministry says, after an unidentified disease outbreak started killing mainly women and children in a remote region.

  9. Steven G. Krantz - Wikipedia

    en.wikipedia.org/wiki/Steven_G._Krantz

    Krantz's monographs include Function Theory of Several Complex Variables, Complex Analysis: The Geometric Viewpoint, A Primer of Real Analytic Functions (joint with Harold R. Parks), The Implicit Function Theorem (joint with Harold Parks), Geometric Integration Theory (joint with Harold Parks), and The Geometry of Complex Domains (joint with ...