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Что (кто) такое ordinary differential equations - определение
MATHEMATICAL EQUATION INVOLVING DERIVATIVES OF AN UNKNOWN FUNCTION
Examples of differential equations; Differential equations/Examples; Differential equations of mathematical physics; Differential equations from Mathematical Physics; Differential equations from outside physics; Differental equations; Diff eq; Differential Equations; DiffyEq; Diffyeq; Separable ordinary differential equation; Exact first-order ordinary differential equation; Order (differential equation); Diff eq'n; Diffeq; Second order equation; Differential equations; Second-order differential equation; Higher order differential equation; Degree of a differential equation; Solutions of differential equations; Types of differential equations; Applications of differential equations; Differential Equation; History of differential equations; Differential equation solvers; Order of differential equation
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Ordinary differential equation
DIFFERENTIAL EQUATION CONTAINING ONE OR MORE FUNCTIONS OF ONE INDEPENDENT VARIABLE AND ITS DERIVATIVES
Ordinary differential equations; Ordinary Differential Equations; Inseparable differential equation; Ordinary Differential Equation; First-order ordinary differential equation; Variable coefficient; Inhomogeneous differential equation; Fundamental system; Ordinary Differential equation; Ordinary differential Equation; System of ordinary differential equations; Implicit differential equation; First order differential equation; Explicit ordinary differential equation; Inhomogeneous ordinary differential equation; First-order differential equation; Non-homogeneous differential equation; First order differential equations; Linear ordinary differential equations; System of ordinary differential equation; Particular integral; List of solvers for ordinary differential equations; List of solvers for ODEs; List of ODE solvers; Particular solution; Software for solving ordinary differential equations; Complementary function
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.
Inseparable differential equation
DIFFERENTIAL EQUATION CONTAINING ONE OR MORE FUNCTIONS OF ONE INDEPENDENT VARIABLE AND ITS DERIVATIVES
Ordinary differential equations; Ordinary Differential Equations; Inseparable differential equation; Ordinary Differential Equation; First-order ordinary differential equation; Variable coefficient; Inhomogeneous differential equation; Fundamental system; Ordinary Differential equation; Ordinary differential Equation; System of ordinary differential equations; Implicit differential equation; First order differential equation; Explicit ordinary differential equation; Inhomogeneous ordinary differential equation; First-order differential equation; Non-homogeneous differential equation; First order differential equations; Linear ordinary differential equations; System of ordinary differential equation; Particular integral; List of solvers for ordinary differential equations; List of solvers for ODEs; List of ODE solvers; Particular solution; Software for solving ordinary differential equations; Complementary function
In mathematics, an inseparable differential equation is an ordinary differential equation that cannot be solved by using separation of variables. To solve an inseparable differential equation one can employ a number of other methods, like the Laplace transform, substitution, etc.
System of differential equations
FINITE SET OF DIFFERENTIAL EQUATIONS TO BE SOLVED SIMULTANEOUSLY
Differential system; Draft:System of differential equations; System of partial differential equations
In mathematics, a system of differential equations is a finite set of differential equations. Such a system can be either linear or non-linear.
Differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.
Degree of a differential equation
In mathematics, the degree of a differential equation is the power of its highest derivative, after the equation has been made rational and integral in all of its derivatives.Order and Degree General Terms of Ordinary Differential Equations.
Examples of differential equations
Differential equations arise in many problems in physics, engineering, and other sciences. The following examples show how to solve differential equations in a few simple cases when an exact solution exists.
differential equation
¦ noun an equation involving derivatives of a function or functions.
Exact differential equation
TYPE OF DIFFERENTIAL EQUATION
Total differential equation; Solutions of exact differential equations
In mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in physics and engineering.
List of named differential equations
WIKIMEDIA LIST ARTICLE
List of differential equations
In mathematics, differential equation is a fundamental concept that is used in many scientific areas. Many of the differential equations that are used have received specific names, which are listed in this article.
Maxwell's equations
!['''n'''}} is the [[unit normal]]. (The curl of a vector field doesn't literally look like the "circulations", this is a heuristic depiction.)](https://commons.wikimedia.org/wiki/Special:FilePath/Curl theorem in EM.svg?width=200 "'''n'''}} is the [[unit normal]]. (The curl of a vector field doesn't literally look like the \"circulations\", this is a heuristic depiction.)")
!['''B'''}} field, which has no magnetic charges as shown. The outward [[unit normal]] is '''n'''.](https://commons.wikimedia.org/wiki/Special:FilePath/Divergence theorem in EM.svg?width=200 "'''B'''}} field, which has no magnetic charges as shown. The outward [[unit normal]] is '''n'''.")
![In a [[geomagnetic storm]], a surge in the flux of charged particles temporarily alters [[Earth's magnetic field]], which induces electric fields in Earth's atmosphere, thus causing surges in electrical [[power grid]]s. (Not to scale.)](https://commons.wikimedia.org/wiki/Special:FilePath/Magnetosphere rendition.jpg?width=200 "In a [[geomagnetic storm]], a surge in the flux of charged particles temporarily alters [[Earth's magnetic field]], which induces electric fields in Earth's atmosphere, thus causing surges in electrical [[power grid]]s. (Not to scale.)")
SET OF PARTIAL DIFFERENTIAL EQUATIONS THAT DESCRIBE HOW ELECTRIC AND MAGNETIC FIELDS ARE GENERATED AND ALTERED BY EACH OTHER AND BY CHARGES AND CURRENTS
Maxwell's Equations; Maxwells equations; Maxwell equations; Maxwell equation; Maxwell's equation; Maxwell's laws; Maxwell's theory; Maxwell Laws; Maxwell's field equations; Maxwell Equations; Laws of electromagnetism; Maxwell theory; Maxwell's Equation; Maxwell's Laws; Maxwell field equations; Maxwell electrodynamics; Maxwell’s equations; Maxwell Law; Great papers of James Clerk Maxwell; Great papers of james clerk maxwell; Maxwell's four equations; Maxwell's differential equations; Table of Maxwell equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
Википедия
Differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.
Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.
