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  2. Continuity equation - Wikipedia

    en.wikipedia.org/wiki/Continuity_equation

    A continuity equation is the mathematical way to express this kind of statement. For example, the continuity equation for electric charge states that the amount of electric charge in any volume of space can only change by the amount of electric current flowing into or out of that volume through its boundaries.

  3. Continuous function - Wikipedia

    en.wikipedia.org/wiki/Continuous_function

    Continuity of real functions is usually defined in terms of limits. A function f with variable x is continuous at the real number c, if the limit of (), as x tends to c, is equal to (). There are several different definitions of the (global) continuity of a function, which depend on the nature of its domain.

  4. Limit (mathematics) - Wikipedia

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

    An important class of functions when considering limits are continuous functions. These are precisely those functions which preserve limits , in the sense that if f {\displaystyle f} is a continuous function, then whenever a n → a {\displaystyle a_{n}\rightarrow a} in the domain of f {\displaystyle f} , then the limit f ( a n ) {\displaystyle ...

  5. Smoothness - Wikipedia

    en.wikipedia.org/wiki/Smoothness

    A function of class is a function of smoothness at least k; that is, a function of class is a ... The terms parametric continuity (C k) and geometric continuity ...

  6. Maxwell's equations - Wikipedia

    en.wikipedia.org/wiki/Maxwell's_equations

    Electric field from positive to negative charges. Gauss's law describes the relationship between an electric field and electric charges: an electric field points away from positive charges and towards negative charges, and the net outflow of the electric field through a closed surface is proportional to the enclosed charge, including bound charge due to polarization of material.

  7. Lipschitz continuity - Wikipedia

    en.wikipedia.org/wiki/Lipschitz_continuity

    In the theory of differential equations, Lipschitz continuity is the central condition of the Picard–Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial value problem. A special type of Lipschitz continuity, called contraction, is used in the Banach fixed-point theorem. [2]

  8. Modulus of continuity - Wikipedia

    en.wikipedia.org/wiki/Modulus_of_continuity

    A sublinear modulus of continuity can easily be found for any uniformly continuous function which is a bounded perturbation of a Lipschitz function: if f is a uniformly continuous function with modulus of continuity ω, and g is a k Lipschitz function with uniform distance r from f, then f admits the sublinear module of continuity min{ω(t), 2r ...

  9. List of mathematical abbreviations - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical...

    lsc – lower semi-continuity. lerp – linear interpolation. [5] lg – common logarithm (log 10) or binary logarithm (log 2). LHS – left-hand side of an equation. Li – offset logarithmic integral function. li – logarithmic integral function or linearly independent. lim – limit of a sequence, or of a function. lim inf – limit inferior.