• some cases to solve linear differential equations with given initial conditions. First consider the following property of the Laplace transform: L { f ′...
    3 KB (657 words) - 16:23, 10 May 2025
  • operational calculus for the Laplace transform that could be used to study linear differential equations in much the same way the transform is now used in basic...
    75 KB (9,508 words) - 23:07, 6 July 2025
  • Thumbnail for Partial differential equation
    bundle Laplace transform applied to differential equations List of dynamical systems and differential equations topics Matrix differential equation Numerical...
    49 KB (6,800 words) - 08:09, 10 June 2025
  • (Vibration) Fundamental matrix (linear differential equation) Laplace transform applied to differential equations Sturm–Liouville theory Wronskian Loewy...
    5 KB (413 words) - 21:49, 5 November 2024
  • Thumbnail for Pierre-Simon Laplace
    probability was developed mainly by Laplace. Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of...
    107 KB (13,313 words) - 19:32, 7 June 2025
  • Thumbnail for Ordinary differential equation
    Examples of differential equations Laplace transform applied to differential equations List of dynamical systems and differential equations topics Matrix...
    44 KB (5,187 words) - 16:53, 2 June 2025
  • In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean...
    30 KB (4,682 words) - 23:08, 23 June 2025
  • application of integral transforms, consider the Laplace transform. This is a technique that maps differential or integro-differential equations in the "time" domain...
    13 KB (1,278 words) - 17:01, 18 November 2024
  • The telegrapher's equations (or telegraph equations) are a set of two coupled, linear partial differential equations that model voltage and current along...
    34 KB (4,745 words) - 20:26, 2 July 2025
  • Thumbnail for Laplace distribution
    theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called...
    22 KB (3,126 words) - 23:26, 19 June 2025
  • Thumbnail for Fourier transform
    Fourier transform and using these formulas, some ordinary differential equations can be transformed into algebraic equations, which are much easier to solve...
    177 KB (21,313 words) - 02:40, 6 July 2025
  • In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean...
    20 KB (3,344 words) - 15:39, 29 May 2025
  • they can be applied to other branches of mathematics. Fractional differential equations, also known as extraordinary differential equations, are a generalization...
    59 KB (7,991 words) - 06:52, 7 July 2025
  • the equation are partial derivatives. A linear differential equation or a system of linear equations such that the associated homogeneous equations have...
    30 KB (4,754 words) - 18:32, 3 July 2025
  • component. Applied to functions of continuous arguments, Fourier-related transforms include: Two-sided Laplace transform Mellin transform, another closely...
    7 KB (1,001 words) - 15:55, 27 May 2025
  • Thumbnail for Slope field
    Slope field (category Differential equations)
    Examples of differential equations Vector field Laplace transform applied to differential equations List of dynamical systems and differential equations topics...
    7 KB (986 words) - 04:14, 20 May 2025
  • Thumbnail for Heat equation
    specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier...
    58 KB (9,878 words) - 21:48, 4 June 2025
  • theorems on Laplace transform in n dimensions. The multidimensional Z transform can also be used to solve partial differential equations. One very important...
    24 KB (4,602 words) - 04:59, 25 March 2025
  • classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid...
    9 KB (1,476 words) - 23:52, 22 February 2025
  • Thumbnail for Euler equations (fluid dynamics)
    they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. The Euler equations can be applied to incompressible...
    79 KB (13,150 words) - 01:53, 26 May 2025
  • Thumbnail for Phasor
    the phasor transform can also be seen as a particular case of the Laplace transform (limited to a single frequency), which, in contrast to phasor representation...
    31 KB (4,997 words) - 10:09, 1 July 2025
  • Thumbnail for Bessel function
    appeared as solutions to definite integrals rather than solutions to differential equations. Because the differential equation is second-order, there...
    76 KB (12,308 words) - 06:31, 12 June 2025
  • the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation: ∇ 2 f = − k 2...
    20 KB (2,975 words) - 18:26, 19 May 2025
  • taking term-by-term Laplace transforms, and utilising the rules for derivatives and integrals, the integro-differential equation is converted into the...
    6 KB (828 words) - 23:38, 3 June 2025
  • Thumbnail for Green's function
    Green's function (category Differential equations)
    separation of variables, and Laplace transforms. Let L {\displaystyle L} be the general linear second-order differential operator defined on [ a , b ]...
    43 KB (5,810 words) - 23:26, 15 June 2025
  • dividing the Laplace transform of the output, Y ( s ) = L { y ( t ) } {\displaystyle Y(s)={\mathcal {L}}\left\{y(t)\right\}} , by the Laplace transform of the...
    15 KB (2,498 words) - 06:36, 5 May 2025
  • Thumbnail for Heaviside step function
    originally developed in operational calculus for the solution of differential equations, where it represents a signal that switches on at a specified time...
    14 KB (2,157 words) - 11:06, 13 June 2025
  • Thumbnail for List of topics named after Leonhard Euler
    of) differential equations (DEs). It is customary to classify them into ODEs and PDEs. Otherwise, Euler's equation may refer to a non-differential equation...
    15 KB (1,744 words) - 11:30, 13 June 2025
  • the Laplacian (or Laplace operator) in three variables is used to describe the response of a particular type of physical system to a point source. In...
    11 KB (1,910 words) - 01:17, 15 August 2024
  • time domain using differential equations, in the complex-s domain with the Laplace transform, or in the frequency domain by transforming from the complex-s...
    45 KB (6,774 words) - 01:00, 17 March 2025