An Etymological Dictionary of Astronomy and Astrophysics

فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory



Number of Results: 11 Search : differential equation
differential equation
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hamugeš-e degarsâneyi

Fr.: équation différentielle   

An equation expressing a relationship between an → independent variable, x, an unknown → function, y = f(x), and its → derivatives. The general form of a differential equation is: F(x, y, y', y'', ..., y(n)) = 0, or F(x,y, dy/dx, d2y/dx2, ..., dny/dxn) = 0. See also: → ordinary differential equation; → partial differential equation; → linear differential equation; → exact differential equation; → first-order differential equation; → homogeneous linear differential equation; → nonhomogeneous linear differential equation; → differential equation with separated variables; → differential equation with separable variables.

differential; → equation.

differential equation with separable variables
  هموگش ِ دگرسانه‌ای با ورتنده‌های ِ جدایی-پذیر   
hamugeš-e degarsâne-yi bâ vartandehhâ-ye jodâyi-pazir

Fr.: équation différentielle à variables séparables   

A → differential equation of the form: M1(x) N1(y) dx + M2(x) N2(y) dy = 0, which can be reduced to a → differential equation with separated variables.

differential; → equation; → separate; → variable.

differential equation with separated variables
  هموگش ِ دگرسانه‌ای با ورتنده‌های ِ جدا   
hamugeš-e degarsâne-yi bâ vartandehhâ-ye jodâ

Fr.: équation différentielle à variables séparées   

A → differentail equation that can be transformed into the form: M(x)dx + N(x)dy = 0.

differential; → equation; → separate; → variable.

exact differential equation
  هموگش ِ دگرسانه‌ای ِ رزین   
hamugeš-e degarsâneyi-ye razin

Fr.: équation différentielle exacte   

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.

first-order differential equation
  هموگش ِ دگرسانه‌ای ِ رایه‌ی ِ نخست   
hamugeš-e degarsâne-yi-ye râye-ye naxost

Fr.: équation différentielle du premier ordre   

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

first; → order; → differential; → equation.

homogeneous linear differential equation
  هموگش ِ دگرسانه‌ای ِ خطی همگن   
hamugeš-e degarsâne-yi-ye xatti hamgen

Fr.: équation différentielle linéaire homogène   

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

homogeneous; → linear; → differential; → equation.

linear differential equation
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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:
fn(x)y(n) + fn-1(x)y(n-1) + ... + f1(x)y' + f0(x)y = Q(x),
where f0(x), f1(x), ..., fn(x) and Q(x) are each continuous functions of x defined on a common interval I and fn(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.

linearized differential equation
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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.

nonhomogeneous linear differential equation
  هموگش ِ دگرسانه‌ای ِ خطی ناهمگن   
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
  هموگش ِ دگرسانه‌ای شونیک   
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.

partial differential equation
  هموگش ِ دگرسانه‌ای با واخنه‌ی ِ پاری   
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.