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These include differential equations, manifolds, Lie groups, and ergodic theory. [4] This article gives a summary of the most important of these. This article lists equations from Newtonian mechanics, see analytical mechanics for the more general formulation of classical mechanics (which includes Lagrangian and Hamiltonian mechanics).
Examples of differential equations; Autonomous system (mathematics) Picard–Lindelöf theorem; Peano existence theorem; Carathéodory existence theorem; Numerical ordinary differential equations; Bendixson–Dulac theorem; Gradient conjecture; Recurrence plot; Limit cycle; Initial value problem; Clairaut's equation; Singular solution ...
Differential equations play a prominent role in many scientific areas: mathematics, physics, engineering, chemistry, biology, medicine, economics, etc. This list presents differential equations that have received specific names, area by area.
Binomial differential equation (′) = (,) Class of differential equation which may sometimes be solved exactly [3] Briot-Bouquet Equation: 1 ′ = (,) Class of differential equation which may sometimes be solved exactly [4]
In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as functions of time and space.
The order of the differential equation is the highest order of derivative of the unknown function that appears in the differential equation. For example, an equation containing only first-order derivatives is a first-order differential equation, an equation containing the second-order derivative is a second-order differential equation, and so on.
Euler equations; Fokker–Planck equation; Hamilton–Jacobi equation, Hamilton–Jacobi–Bellman equation; Heat equation; Laplace's equation. Laplace operator; Harmonic function; Spherical harmonic; Poisson integral formula; Klein–Gordon equation; Korteweg–de Vries equation. Modified KdV–Burgers equation; Maxwell's equations; Navier ...
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface. Right: The reduction in flux passing through a surface can be visualized by reduction in F or d S equivalently (resolved into components , θ is angle to ...