gradient

/gray"dee euhnt/, n.
1. the degree of inclination, or the rate of ascent or descent, in a highway, railroad, etc.
2. an inclined surface; grade; ramp.
3. Physics.
a. the rate of change with respect to distance of a variable quantity, as temperature or pressure, in the direction of maximum change.
b. a curve representing such a rate of change.
4. Math. a differential operator that, operating upon a function of several variables, results in a vector the coordinates of which are the partial derivatives of the function. Abbr.: grad. Symbolically appearing as a downward pointing triangle.
adj.
5. rising or descending by regular degrees of inclination.
6. progressing by walking; stepping with the feet as animals do.
7. of a type suitable for walking or running, as the feet of certain birds; gressorial.
[1635-45; < L gradient- (s. of gradiens), prp. of gradi to walk, go, equiv. to grad- walk + -i- thematic vowel + -ent- -ENT]

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In mathematics, a differential operator applied to a three-dimensional vector-valued function to yield a vector whose three components are the partial derivatives of the function with respect to its three variables.

The symbol for gradient is ∇. Thus, the gradient of a function f, written grad f, or ∇f, is ∇f = ifx + jfy + kfz where fx, fy, and fz are the first partial derivatives of f and the vectors i, j, and k are the unit vectors of the vector space. If in physics, for example, f is a temperature field (giving the temperature at every point in a space), ∇f is the direction of the heat-flow vector in the field.

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Universalium. 2010.

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  • gradient — [ gradjɑ̃ ] n. m. • 1876; du rad. du lat. gradus « degré », d apr. quotient I ♦ Sc. Taux de variation (d une grandeur physique) en fonction de la distance. 1 ♦ Météor., géogr. Gradient de température : variation de la température en fonction de l …   Encyclopédie Universelle

  • gradient — GRADIÉNT, gradienţi, s.m. Mărime care indică variaţia presiunii barometrice sau a temperaturii în anumite condiţii. [pr.: di ent] – Din fr. gradient. Trimis de gall, 13.09.2007. Sursa: DEX 98  gradiént (mat., fiz., miner. ) s. m. (sil. di ent),… …   Dicționar Român

  • Gradient — Gra di*ent, n. 1. The rate of regular or graded ascent or descent in a road; grade. [1913 Webster] 2. A part of a road which slopes upward or downward; a portion of a way not level; a grade. [1913 Webster] 3. The rate of increase or decrease of a …   The Collaborative International Dictionary of English

  • Gradient — Gra di*ent, a. [L. gradiens, p. pr. of gradi to step, to go. See {Grade}.] 1. Moving by steps; walking; as, gradient automata. Wilkins. [1913 Webster] 2. Rising or descending by regular degrees of inclination; as, the gradient line of a railroad …   The Collaborative International Dictionary of English

  • Gradient — Gradient, barometrischer, ein von der neueren Meteorologie geschaffenes Maß für die Größe des barometrischen Gefälles, der Aenderungen des gleichzeitig herrschenden Luftdruckes von einem Ort zum andern. Da die Isobaren diejenigen Orte verbinden,… …   Lexikon der gesamten Technik

  • Gradiént — (barometrisches Gefälle), die in Millimetern ausgedrückte Zu oder Abnahme des Luftdrucks, die sich ergibt, wenn man von einem Punkt einer Isobare senkrecht zu dieser horizontal um 111 km (die Länge eines Äquatorgrades) fortschreitet. Dabei müssen …   Meyers Großes Konversations-Lexikon

  • Gradiént — Gradiént, barometrischer, oder barometrisches Gefälle, die Richtung und der Betrag der räumlichen horizontalen Unterschiede im Barometerstande, ausgedrückt durch die Zahl der Millimeter, um die sich letzterer ändert, wenn man um einen Äquatorgrad …   Kleines Konversations-Lexikon

  • gradient — (n.) steep slope of a road or railroad, 1835, principally in Amer.Eng., from GRADE (Cf. grade) (n.) by analogy of QUOTIENT (Cf. quotient), etc. It was used 17c. as an adjective, of animals, characterized by walking; in that case probably from L.… …   Etymology dictionary

  • gradient — [n] slope acclivity, angle, bank, cant, declivity, grade, hill, inclination, incline, lean, leaning, pitch, ramp, rise, slant, tilt; concepts 738,757 …   New thesaurus

  • gradient — ► NOUN 1) a sloping part of a road or railway. 2) the degree of a slope, expressed as change of height divided by distance travelled. 3) Physics a change in the magnitude of a property (e.g. temperature) observed in passing from one point or… …   English terms dictionary

  • gradient — [grā′dē ənt] adj. [L gradiens (gen. gradientis), prp. of gradi, to step: see GRADE] ascending or descending with a uniform slope n. 1. a) a slope, as of a road or railroad b) the degree of such slope 2. Biol. a gradation in rate of growth,… …   English World dictionary

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