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In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties.This is often written as = or =, where = = is the Laplace operator, [note 1] is the divergence operator (also symbolized "div"), is the gradient operator (also symbolized "grad"), and (,,) is a twice-differentiable real-valued function.
Three-body problem. Approximate trajectories of three identical bodies located at the vertices of a scalene triangle and having zero initial velocities. The center of mass, in accordance with the law of conservation of momentum, remains in place. In physics, specifically classical mechanics, the three-body problem is to take the initial ...
It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1770). [1]
t. e. In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. [1][2] A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. [3]
Symbolab. Symbolab is an answer engine [ 1 ] that provides step-by-step solutions to mathematical problems in a range of subjects. [ 2 ] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course ...
Initial value problem. In multivariable calculus, an initial value problem[a] (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to solving an initial value problem.
The notation convention chosen here (with W 0 and W −1) follows the canonical reference on the Lambert W function by Corless, Gonnet, Hare, Jeffrey and Knuth. [3]The name "product logarithm" can be understood as this: Since the inverse function of f(w) = e w is called the logarithm, it makes sense to call the inverse "function" of the product we w as "product logarithm".
Dirichlet problem. Problem of solving a partial differential equation subject to prescribed boundary values. In mathematics, a Dirichlet problem asks for a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region. [1]
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