linear differential equation
hamugeš-e degarsâne-yi-ye xatti
Fr.: équation différentielle linéaire
An equation in which the → dependent variable y
and all its differential coefficients occur only
in the first degree. A linear differential equation of → order
order n has the form:
Fr.: équation linéaire
An equation composed of first degree variables and representing a straight line.
linearized differential equation
hamugeš-e degarsâneyi-ye xatti
Fr.: équation différentielle linéarisée
A differential equation that has been derived from an original nonlinear equation.
Fr.: équations de Maxwell
A set of four fundamental equations that describe the electric and
magnetic fields arising from varying electric charges and magnetic fields,
electric currents, charge distributions,
and how those fields change in time. In their vector differential form,
these equations are:
→ maxwell. It should be emphasized that the equations originally published by James Clerk Maxwell in 1873 (in A Treatise on Electricity and Magnetism) were 20 in number, had 20 variables, and were in scalar form. The German physicist Heinrich Rudolf Hertz (1857-1894) reduced them to 12 scalar equations (1884). It was the English mathematician/physicist Oliver Heaviside (1850-1925) who expressed Maxwell's equations in vector form using the notations of → gradient, → divergence, and → curl of a vector, thus simplifying them to the present 4 equations (1886). Before Einstein these equations were known as Maxwell-Heaviside-Hertz equations, Einstein (1940) popularized the name "Maxwell's Equations;" → equation.
Fr.: équation de Navier-Stokes
Fr.: équation de Newton
In → geometric optics, an expression relating the → focal lengths of an → optical system (f and f') and the object x and image x' distances measured from the respective focal points. Thus, ff' = xx'. Same as Newton's formula.
Fr.: équation non-dimensionnelle
An equation that is independent of the units of measurement as it only involves nondimensional numbers, parameters, and variables.
nonhomogeneous linear differential equation
hamugeš-e degarsâne-yi-ye xatti nâhamgen
Fr.: équation différentielle linéaire non homogène
A → linear differential equation if Q(x)≠ 0 on interval I.
ordinary differential equation
hamugeš-e degarsâneyi-ye šunik
Fr.: équation différentielle ordinaire
Fr.: équation paramétrique
Any of a set of equations that defines the coordinates of the dependent variables of a curve or surface in terms of one or more independent variables or parameters.
partial differential equation
hamugeš-e degarsâne-yi bâ vâxane-ye pâri
Fr.: équation différentielle aux dérivées partielles
A type of differential equation involving an unknown function (or functions) of several independent variables and its (or their) partial derivatives with respect to those variables.
Fr.: équation personnelle
A systematic observational error due to the characteristics of the observer.
Fr.: équation de perturbation
Any equation governing the behavior of a → perturbation.
Fr.: équation de Poisson
An equation (∇2φ = 4πGρ) which relates the gravitational (or electromagnetic) potential to the mass density (or charge density).
Fr.: équation polaire
An equation for a curve written in terms of the → polar coordinates.
Fr.: équation polynomiale
Fr.: équation quadratique
An equation with the general form of ax2 + bx +c = 0, in which the highest power of the unknown is the second power (square).
Fr.: équation quartique
An equation containing unknowns of the fourth power; the general form: ax4 + bx3 + cx2 + dx + e = 0.
Fr.: équation quintique
An equation containing unknowns of the fifth power.
radiation transfer equation
hamugeš-e tarâvâž-e tâbeš
Fr.: équation de transfert radiatif, ~ de rayonnement