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  2. Oscillation (mathematics) - Wikipedia

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

    The oscillation of a function of a real variable at a point is defined as the limit as of the oscillation of on an -neighborhood of : = (, +).This is the same as the difference between the limit superior and limit inferior of the function at , provided the point is not excluded from the limits.

  3. Classification of discontinuities - Wikipedia

    en.wikipedia.org/wiki/Classification_of...

    The function in example 1, a removable discontinuity. Consider the piecewise function = {< = >. The point = is a removable discontinuity.For this kind of discontinuity: The one-sided limit from the negative direction: = and the one-sided limit from the positive direction: + = + at both exist, are finite, and are equal to = = +.

  4. List of limits - Wikipedia

    en.wikipedia.org/wiki/List_of_limits

    This is a list of limits for common functions such as elementary functions. In this article, the terms a, b and c are constants with respect to x.

  5. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input which may or may not be in the domain of the function. Formal definitions, first devised in the early 19th century, are given below. Informally, a function f assigns an output f(x) to every ...

  6. Oscillation - Wikipedia

    en.wikipedia.org/wiki/Oscillation

    Oscillation of a sequence (shown in blue) is the difference between the limit superior and limit inferior of the sequence. The mathematics of oscillation deals with the quantification of the amount that a sequence or function tends to move between extremes.

  7. Limit (mathematics) - Wikipedia

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

    Limit of a function. One-sided limit: either of the two limits of functions of a real variable x, as x approaches a point from above or below; List of limits: list of limits for common functions; Squeeze theorem: finds a limit of a function via comparison with two other functions; Limit superior and limit inferior; Modes of convergence. An ...

  8. Oscillation theory - Wikipedia

    en.wikipedia.org/wiki/Oscillation_theory

    The differential equation is called oscillating ... Teschl, G. (2009). "Relative oscillation theory, weighted zeros of the Wronskian, and the spectral shift function

  9. Oscillatory integral - Wikipedia

    en.wikipedia.org/wiki/Oscillatory_integral

    Many familiar distributions can be written as oscillatory integrals. The Fourier inversion theorem implies that the delta function, () is equal to ().If we apply the first method of defining this oscillatory integral from above, as well as the Fourier transform of the Gaussian, we obtain a well known sequence of functions which approximate the delta function: