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  2. Laplace transform applied to differential equations - Wikipedia

    en.wikipedia.org/wiki/Laplace_transform_applied...

    In mathematics, the Laplace transform is a powerful integral transform used to switch a function from the time domain to the s-domain. The Laplace transform can be used in some cases to solve linear differential equations with given initial conditions. First consider the following property of the Laplace transform:

  3. Laplace transform - Wikipedia

    en.wikipedia.org/wiki/Laplace_transform

    The Laplace transform can also be used to solve differential equations and is used extensively in mechanical engineering and electrical engineering. The Laplace transform reduces a linear differential equation to an algebraic equation, which can then be solved by the formal rules of algebra.

  4. List of Laplace transforms - Wikipedia

    en.wikipedia.org/wiki/List_of_Laplace_transforms

    The following is a list of Laplace transforms for many common functions of a single variable. [1] The Laplace transform is an integral transform that takes a function of a positive real variable t (often time) to a function of a complex variable s (complex angular frequency ).

  5. Integro-differential equation - Wikipedia

    en.wikipedia.org/wiki/Integro-differential_equation

    Consider the following second-order problem, ′ + + = () =, where = {,, <is the Heaviside step function.The Laplace transform is defined by, = {()} = ().Upon taking term-by-term Laplace transforms, and utilising the rules for derivatives and integrals, the integro-differential equation is converted into the following algebraic equation,

  6. Time-scale calculus - Wikipedia

    en.wikipedia.org/wiki/Time-scale_calculus

    A Laplace transform can be defined for functions on time scales, which uses the same table of transforms for any arbitrary time scale. This transform can be used to solve dynamic equations on time scales.

  7. Final value theorem - Wikipedia

    en.wikipedia.org/wiki/Final_value_theorem

    1.2.2 Final Value Theorem using Laplace transform of the derivative. ... Rule 1 was not satisfied in this example, in that the roots of the denominator are + ...

  8. Riemann–Lebesgue lemma - Wikipedia

    en.wikipedia.org/wiki/Riemann–Lebesgue_lemma

    In mathematics, the Riemann–Lebesgue lemma, named after Bernhard Riemann and Henri Lebesgue, states that the Fourier transform or Laplace transform of an L 1 function vanishes at infinity. It is of importance in harmonic analysis and asymptotic analysis .

  9. Inverse Laplace transform - Wikipedia

    en.wikipedia.org/wiki/Inverse_Laplace_transform

    Post's inversion formula for Laplace transforms, named after Emil Post, [3] is a simple-looking but usually impractical formula for evaluating an inverse Laplace transform. The statement of the formula is as follows: Let f ( t ) {\displaystyle f(t)} be a continuous function on the interval [ 0 , ∞ ) {\displaystyle [0,\infty )} of exponential ...