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  2. 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 ...

  3. Implicit function theorem - Wikipedia

    en.wikipedia.org/wiki/Implicit_function_theorem

    The unit circle can be specified as the level curve f(x, y) = 1 of the function f(x, y) = x 2 + y 2.Around point A, y can be expressed as a function y(x).In this example this function can be written explicitly as () =; in many cases no such explicit expression exists, but one can still refer to the implicit function y(x).

  4. Implicit and explicit functions - Wikipedia

    en.wikipedia.org/?title=Implicit_and_explicit...

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  5. Explicit and implicit methods - Wikipedia

    en.wikipedia.org/wiki/Explicit_and_implicit_methods

    For such problems, to achieve given accuracy, it takes much less computational time to use an implicit method with larger time steps, even taking into account that one needs to solve an equation of the form (1) at each time step. That said, whether one should use an explicit or implicit method depends upon the problem to be solved.

  6. Implicit curve - Wikipedia

    en.wikipedia.org/wiki/Implicit_curve

    However, the implicit function theorem gives conditions under which an implicit curve locally is given by the graph of a function (so in particular it has no self-intersections). If the defining relations are sufficiently smooth then, in such regions, implicit curves have well defined slopes, tangent lines, normal vectors, and curvature.

  7. Talk:Implicit function - Wikipedia

    en.wikipedia.org/wiki/Talk:Implicit_function

    Formally, a function f:X→Y is said to be an implicit function (defined by the equation R(x,y)=0) if it satisfies the equation R(x,f(x)) = 0 for all x∈X. That brings R into the definition. An analogy: it doesn't make much sense to say "p is a characteristic polynomial", but it does make sense to say "p is the characteristic polynomial of the ...

  8. Implicit surface - Wikipedia

    en.wikipedia.org/wiki/Implicit_surface

    Implicit surface of genus 2. Implicit non-algebraic surface (wineglass). In mathematics, an implicit surface is a surface in Euclidean space defined by an equation (,,) = An implicit surface is the set of zeros of a function of three variables. Implicit means that the equation is not solved for x or y or z.

  9. Function (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Function_(mathematics)

    Many other real functions are defined either by the implicit function theorem (the inverse function is a particular instance) or as solutions of differential equations. For example, the sine and the cosine functions are the solutions of the linear differential equation ″ + = such that