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This is a list of dynamical system and differential equation topics, ... Examples of differential equations; Autonomous system (mathematics) ... (physics) RLC circuit ...
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.
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.
An example of a nonlinear delay differential equation; applications in number theory, distribution of primes, and control theory [ 5 ] [ 6 ] [ 7 ] Chrystal's equation
A differential equation of motion, usually identified as some physical law (for example, F = ma), and applying definitions of physical quantities, is used to set up an equation to solve a kinematics problem. Solving the differential equation will lead to a general solution with arbitrary constants, the arbitrariness corresponding to a set of ...
Name Dim Equation Applications Landau–Lifshitz model: 1+n = + Magnetic field in solids Lin–Tsien equation: 1+2 + = Liouville equation: any + = Liouville–Bratu–Gelfand equation
Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are solutions of linear differential equations (see Holonomic function ).
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).
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