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

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.

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.