An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

General: To perceive or show the difference in or between.
Math.: To obtain the differential or the derivative of.

M.L. differentiatus "distinguished," p.p. of differentiare.

Degarsânidan, verbal form of → difference.

A description of a planet's interior which is composed of a rocky, dense inner core and a less dense outer crust.

Differentiated, p.p. of → differentiate; → interior.

A meteorite that has distinctly separated stone, metal, and glass. It is derived from a differentiated parent body and hence not primitive. The parent body accreted surrounding material until it was large enough to start melting in the middle. The denser metals sank to the center and the stones and glasses floated to the top. A differentiated meteorite made completely of metal comes from the center of a parent meteoroid which was broken apart. → undifferenciated meteorite.

Differentiated, p.p. of → differentiate; → meteorite.

1) Math.: The operation of finding the → derivative of a function.
2) Astro.: Process by which an originally homogeneous planetary or asteroidal body is separated into regions of different composition, such as core, mantle, and crust.

Verbal noun of → differentiate.

If N(x,y) is a → function of two → independent variables, then dN = (∂N/∂x)dx + (∂N/∂y)dy is the exact differential.

→ exact; → differential.

A → differential equation composed of → continuous  → differentiable functions for which certain conditions are fulfilled. The equation M(x,y)dx + N(x,y)dy = 0 is called exact if M(x,y) and N(x,y) are continuous differentiable functions for which the following relationship is fulfilled: ∂M/∂y = ∂N/∂x, and ∂M/∂y and ∂N/∂x are continuous in some region.

→ exact; → differential; → equation.

A → differential equation containing only the first → derivative. For example, dy/dx = 3x and 2y(dy/dx) + 3x = 5.

→ first; → order; → differential; → equation.

A → linear differential equation if the right-hand member is zero, Q(x) = 0, on interval I.

→ homogeneous; → linear; → differential; → equation.

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:
f_n(x)y⁽ⁿ⁾ + f_n-1(x)y^(n-1) + ... + f₁(x)y^' + f₀(x)y = Q(x),
where f₀(x), f₁(x), ..., f_n(x) and Q(x) are each continuous functions of x defined on a common interval I and f_n(x)≠ 0 in I. A linear differential equation cannot have, for example, terms such as y² or (y^')^1/2. See also: → homogeneous linear differential equation; → nonhomogeneous linear differential equation.

→ linear; → differential; → equation.

A differential equation that has been derived from an original nonlinear equation.

Linearized, p.p. of → linearize; → differential; → equation.

A → linear differential equation if Q(x)≠ 0 on interval I.

→ nonhomogeneous; → linear; → differential; → equation.

A → differential equation in which the unknown function depends on only one → independent variable, as contrasted with a → partial differential equation.

→ ordinary; → differential; → equation.

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.

The difference of phase (usually expressed as a time or an angle) between two periodic quantities which vary sinusoidally and have the same frequency.

→ phase; → difference.

Between two points, the work done in taking the unit test object from one point to the other. Potential is a scalar quantity.

→ potential; → difference.

A type of meteorite in which the constituting materials (stone, glass, metal) are mixed together in a disorderly mass, in contrast to → differentiated meteorites.

→ un-; → differentiated meteorite.