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: → linear; → differential; → equation. |
linear equation hamugeš-e xatti 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. Linearized, p.p. of → linearize; → differential; → equation. |
Maxwell's equations hamugešhâ-ye Maxwell 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. |
Navier-Stokes equation hamugeš-e Navier-Stokes Fr.: équation de Navier-Stokes One of a set of → differential equations that describes the motion of a → fluid as a function of → pressure, → density, total external force, and → viscosity. See also → Euler equation. Named after Claude-Louis Navier (1785-1836), a French engineer and physicist, and George Gabriel Stokes, → stokes; → equation. |
Newton's equation hamugeš-e Newton 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. |
nondimensional equation hamugeš-e nâvâmuni Fr.: équation non-dimensionnelle An equation that is independent of the units of measurement as it only involves nondimensional numbers, parameters, and variables. → non-; → dimensional; → equation. |
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. → nonhomogeneous; → linear; → differential; → equation. |
ordinary differential equation hamugeš-e degarsâneyi-ye šunik Fr.: équation différentielle ordinaire A → differential equation in which the unknown function depends on only one → independent variable, as contrasted with a → partial differential equation. → ordinary; → differential; → equation. |
parametric equation hamugeš-e pârâmuni 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. → parametric; → equation. |
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. → partial; → differential; → equation. |
personal equation hamugeš-e tanumi Fr.: équation personnelle A systematic observational error due to the characteristics of the observer. |
perturbation equation hamugeš-e partureš Fr.: équation de perturbation Any equation governing the behavior of a → perturbation. → perturbation; → equation. |
Poisson's equation hamugeš-e Poisson Fr.: équation de Poisson An equation (∇^{2}φ = 4πGρ) which relates the gravitational (or electromagnetic) potential to the mass density (or charge density). → Poisson distribution; → equation. |
polar equation hamugeš-e qotbi Fr.: équation polaire An equation for a curve written in terms of the → polar coordinates. |
polynomial equation hamugeš-e bolnâmin Fr.: équation polynomiale An equation of the form a_{0} + a_{1}x + a_{2}x^{2} + ... + a_{n}x^{n}, where a_{0} ... a_{n} are → real numbers and a_{n}≠ 0. Same as → algebraic equation. → polynomial; → equation. |
quadratic equation hamugeš-e câruši Fr.: équation quadratique An equation with the general form of ax^{2} + bx +c = 0, in which the highest power of the unknown is the second power (square). |
quartic equation hamugeš-e câromik Fr.: équation quartique An equation containing unknowns of the fourth power; the general form: ax^{4} + bx^{3} + cx^{2} + dx + e = 0. From L. quart(us) "fourth" (→ quarter) + → -ic; → equation. hamugeš, → equation; câromân, from cârom "fourth," from câr, cahâr "four" + -om "-th" + -ik, → -ic. |
quintic equation hamugeš-e panjomik 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 |