Слова на English для 'an equation containing differentials of a function'
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verb
- (mathematics) To calculate the differential of a function of multiple variables.
- (mathematics) To calculate the derivative of a function.
- To recognize as different or distinct.
- (transitive, intransitive, often in the passive voice, biology) To (cause to) go through a process of development called differentiation; to make or become different in form or function.
- To modify so as to create a difference or distinction.
- To show or be the difference or distinction between things.
- To perceive the difference between things; to discriminate.
- (education) To teach a lesson in multiple different ways in order to meet the needs of more or less advanced students.
- become distinct and acquire a different character
- evolve so as to lead to a new species or develop in a way most suited to the environment
- be a distinctive feature, attribute, or trait; sometimes in a very positive sense
- mark as different
- calculate a derivative; take the derivative
- become different during development
noun
noun
name
adj
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
adj
- possessing a differential coefficient or derivative
- capable of being perceived as different
- (comparable, of multiple items) able to be differentiated; distinguishable, as for example by differing appearance or measurable characteristics.
- (calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.
adj
- (mathematics, of a differential equation) Able to be brought to a form where all occurrences of the dependent and the independent variable are on opposite sides of the equal sign.
- (abstract algebra, of an algebra over a ring) Satisfying any of several technical conditions on the center of the algebra which generalize the situation of field extensions; see Separable algebra on Wikipedia.Wikipedia
- (of a polynomial) Having no repeated roots (where roots are considered in an algebraic closure)
- Able to be separated.
- (mathematical analysis, of a topological space) Having a countable dense subset.
- (Galois theory, of an algebraic field extension E/F) Such that the minimal polynomial of every element of E is a separable polynomial.
- capable of being divided or dissociated
noun
- (mathematics) A discontinuity arising in the solution of a partial differential equation.
- (figuratively) Something so surprising that it is stunning.
- (physics) A shock wave.
- (medicine) Circulatory shock, a medical emergency characterized by the inability of the circulatory system to supply enough oxygen to meet tissue requirements.
- A sudden, heavy impact.
- (psychology) A sudden or violent mental or emotional disturbance.
- An arrangement of sheaves for drying; a stook.
- A chemical added to a swimming pool to moderate the chlorine levels.
- (medicine) Electric shock, a sudden burst of electrical energy hitting a person or animal.
- (by extension) A tuft or bunch of something, such as hair or grass.
- (psychology) A state of distress following a mental or emotional disturbance, often caused by news or other stimuli.
- (automotive, mechanical engineering) A shock absorber (typically in the suspension of a vehicle).
- a sudden jarring impact
- (pathology) bodily collapse or near collapse caused by inadequate oxygen delivery to the cells; characterized by reduced cardiac output and rapid heartbeat and circulatory insufficiency and pallor
- an instance of agitation of the earth's crust
- an unpleasant or disappointing surprise
- the feeling of distress and disbelief that you have when something bad happens accidentally
- the violent interaction of individuals or groups entering into combat
- a reflex response to the passage of electric current through the body
- a pile of sheaves of grain set on end in a field to dry; stalks of Indian corn set up in a field
- a bushy thick mass (especially hair)
- a mechanical damper; absorbs energy of sudden impulses
adj
verb
- (transitive) To strike with disgust, to offend, scandalize.
- (transitive) To add a chemical to (a swimming pool) to moderate the chlorine levels.
- (transitive) To collect, or make up, into a shock or shocks; to stook.
- (transitive) To subject to a shock wave or violent impact.
- (transitive) To give an electric shock to.
- (transitive) To cause to be emotionally shocked; to cause (someone) to feel greatly surprised or upset.
- (geology, transitive) To deform the crystal structure of a stone by the application of extremely high pressure at moderate temperature, as produced only by hypervelocity impact events, lightning strikes, and nuclear explosions.
- strike with horror or terror
- strike with disgust or revulsion
- collide violently
- inflict a trauma upon
- collect or gather into shocks
- subject to electrical shocks
- surprise greatly; knock someone's socks off
noun
- Any of several generalizations of this concept to functions of several variables or to higher orders: the partial differential, total differential, Gateaux differential, etc.
- (multivariable calculus) The Jacobian matrix of a function of several variables.
- (calculus, of a univariate differentiable function f(x)) A function giving the change in the linear approximation of f at a point x over a small interval Δx or operatorname d!x, the function being called the differential of f and denoted operatorname d!f(x,Δx), operatorname d!f(x), or simply operatorname d!f.
- One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
- The differential gear in an automobile, etc.
- A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
- (differential geometry, of a smooth map ϕ between smooth manifolds) The pushforward or total derivative of ϕ: a linear map from the tangent space at a point x in ϕ's domain to the tangent space at ϕ(x) which is, in a technical sense, the best linear approximation of ϕ at x; denoted operatorname d!ϕₓ.
- (mathematics) Any of several generalizations of the concept(s) above: e.g. the Kähler differential in the setting of schemes, the quadratic differential in the theory of Riemann surfaces, etc.
- (calculus) A quantity representing an infinitesimal change in a variable, now only used as a heuristic aid except in nonstandard analysis but considered rigorous until the 20th century; a fluxion in Newtonian calculus, now usually written in Leibniz's notation as operatorname d!x.
- A qualitative or quantitative difference between similar or comparable things.
- a quality that differentiates between similar things
- a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves
- the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
adj
noun
- (mathematics) a condition specified for the solution to a set of differential equations
- (mathematics) Any of a set of constraints that limit the solutions of a differential equation
- (quantum mechanics) either one of the conditions that the wave function must be continuous and that its derivative must be as well, except in the case of infinite potential
noun
symbol
verb
noun
- (vector calculus) Divergence; a kind of differential operator.
- (UK, Eton College, school slang) A division; a lesson.
- (UK, Ireland, slang) A foolish person; an idiot.
- (military) A division.
- Alternative form of daeva.
- (UK, Winchester College) division; a subject with multidisciplinary scope.
- (UK, Ireland, uncountable, slang) Divinity, as a school subject.
- (web design) A section of a web page, or the div element that represents it in HTML code.
- (mathematics, computing) A function, implemented in many programming languages, that returns the result of a division of two integers.
verb
noun
- (mathematics) Clipping of differential
- (climbing) A difficult route.
- (computing) The output of a diff program, a diff file.
- (slang) Clipping of difference
- (video games, slang) Used to trash-talk an opposing team at the end of a game by pointing out a skill difference between some role and the same role on the other team.
- (automotive) Abbreviation of differential: the differential gear in an automobile.
- (medicine) Abbreviation of differential: differential of types of white blood cell in a complete blood count.
- (computing) Any program which compares two files or sets of files and outputs a description of the differences between them.
- (fandom slang) Clipping of difficulty.
adj
name
verb
- (transitive, computing) To compare two files or other objects, manually or otherwise.
- (transitive, fandom slang) To win (or to be able to win) a fight against another, with a defined level of difficulty. Usually used when power scaling fictional characters.
- (transitive, computing) To run a diff program on (files or items) so as to produce a description of the differences between them, as for a patch file.
adj
- (mathematical analysis) Being defined in terms of objects of differential calculus such as derivatives.
- Of, or relating to division into elements or principles.
- (mathematics, of a function) Being able to be locally represented by convergent power series around every point of the domain.
- (mathematics) Of, or relating to algebra or a similar method of analysis.
- (logic, of a proposition) that follows necessarily by definition; tautologous.
- Of, or relating to any form of analysis, or to analytics.
- (linguistics) Of a language, having a grammar principally dependent on the arrangement of uninflected function words within sentences to indicate meaning.
- Having the ability to analyse.
- using or skilled in using analysis (i.e., separating a whole — intellectual or substantial — into its elemental parts or basic principles)
- using or subjected to a methodology using algebra and calculus
- expressing a grammatical category by using two or more words rather than inflection
- of a proposition that is necessarily true independent of fact or experience
noun
- the mathematical process of obtaining the derivative of a function
- (biology) the structural adaptation of some body part for a particular function
- a discrimination between things as different and distinct on the basis of their characteristics or attributes
- (biology) The process by which the components of multicellular life (cells, organs, etc.) are produced and acquire function, as when a seed develops the root and stem, and the initial stem develops the leaf, branches, and flower buds.
- (biology, evolution) The evolutionary process by which one taxonomic group (species, genus, variety, etc.) becomes distinct from another, or acquires distinct features; the result of such a process: distinctness.
- The act of treating one thing as distinct from another, or of creating such a distinction; of separating a class of things into categories; of describing a thing by illustrating how it is different from something else.
- (geology) The process of separation of cooling magma into various rock types.
- (mathematics, calculus) The process of applying the derivative operator to a function; of calculating a function's derivative.
- The process of developing distinct components.
noun
- (mathematics) The boundary separating two modes of behavior in a differential equation.
- (typography) The proofreader's mark resembling a slash ⟨ / ⟩ or vertical bar ⟨ | ⟩ placed after a note in the margin to indicate that it should replace the item(s) struckthrough in the running text or to separate it from other margin notes.
- A terminator: a line on a partially-illuminated surface separating the lit and shaded regions.
- (typography, historical) The ⟨L⟩ or pipe ⟨|⟩ mark formerly used to divide integers from decimals.
- (physics) The line between regions having different magnetic fields.
- a punctuation mark (‘/’) used to separate related items of information
adj
- (mathematics) of a function of two or more variables in which the ratio of the partial derivatives depends only on the ratio of the variables, not their value
- the relationship of a microcosm to a macrocosm
- (economics) in which the ratio of goods demanded depends only on the ratio of their prices
- (mathematics, geometry) for a geometric figure that is the image of another figure under an homothety.
adj
- (mathematics, of a function) having a single derivative at a point
- producing offspring of only one sex, exhibiting monogeny
- of or relating to monogenesis or to monogenism
- (mathematics, of a semigroup) generated by a set containing only a single element
- (genetics) regulated by a single gene
- of or relating to an inheritable character that is controlled by a single pair of genes
noun
noun
- the part of calculus that deals with integration and its application in the solution of differential equations and in determining areas or volumes etc.
- (calculus) The calculus that generalizes summation to find areas, masses, volumes, sums, and totals of quantities described by continuously varying functions.
noun
- (complex analysis) The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.
- (mathematics, complex analysis, always plural) Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.
noun
- the derivative of a function of two or more variables with respect to a single variable while the other variables are considered to be constant
- a harmonic with a frequency that is a multiple of the fundamental frequency
- (dentistry) dentures that replace only some of the natural teeth
- (bodybuilding) The condition of not exhausting the amplitude during the repetition of an exercise.
- (forensics) An incomplete fingerprint
- (furry fandom) A fursuit that does not fully cover the wearer's body.
- (programming, Internet) A fragment of a template containing markup.
- (mathematics) A partial derivative: a derivative with respect to one independent variable of a function in multiple variables while holding the other variables constant.
- (music) Any of the sine waves which make up a complex tone; often an overtone or harmonic of the fundamental.
adj
- (followed by ‘of’ or ‘to’) having a strong preference or liking for
- being or affecting only a part; not total
- constituting or comprising a part or fraction of a possible whole or entirety
- showing favoritism
- (botany) Subordinate.
- Biased in favor of a person, side, or point of view, especially when dealing with a competition or dispute.
- (crosswording, of a clue) Having a wordplay element, but no definition.
- (followed by the preposition to) Having a predilection for something.
- (computer science) Describing a property that holds only when an algorithm terminates.
- Existing as a part or portion; incomplete.
- (mathematics) Of or relating to a partial derivative or partial differential.
verb
noun
- (calculus) The operation of finding the integral of a function.
- (society) The process of fitting into a community, notably applied to minorities.
- The act or process of making whole or entire.
- (biology) In evolution, the process by which the manifold is compacted into the relatively simple and permanent; supposed to alternate with differentiation as an agent in species' development.
- (US) Ellipsis of racial integration.
- The process of combining with compatible elements in order to incorporate them.
- the action of incorporating a racial or religious group into a community
- the act of combining into an integral whole
- an operation used in the calculus whereby the integral of a function is determined
noun
- (calculus) A function used to define an integral transform.
- (mathematics, category theory, of a morphism f:X→Y in a category with zero morphisms) The equalizer of f and the zero morphism from X to Y, denoted operatorname kerf.
- (botany, US) The stone of certain fruits, such as peaches or plums.
- (botany) A single seed of grain, especially of corn or wheat.
- (computing) The central part of many computer operating systems which manages the system's resources and the communication between hardware and software components.
- (slang) The human clitoris.
- (computing) The core engine of any complex software system.
- (programming) The simplified input to an algorithm that has undergone kernelization.
- A small mass around which other matter is concreted; a nucleus; a concretion or hard lump in the flesh.
- (chemistry) The nucleus and electrons of an atom excluding its valence electrons.
- (botany) The central (usually edible) part of a nut, especially once the hard shell has been removed.
- (mathematics, linear algebra, of a linear transformation f:M→N between modules or vector spaces) The set of elements of M which are mapped to the additive identity 0 of N.
- (mathematics, set theory, of a function f) The set of pairs of elements in the domain of f which are mapped to the same value; the equivalence relation x≡y⟺f(x)=f(y).
- (mathematics, group theory, of a group homomorphism f:G→H between groups) The set of elements of G which are mapped to the identity of H (usually written as 0 in an additive group and as 1 in a multiplicative group).
- (mathematics, fuzzy set theory) The set of members of a fuzzy set that are fully included (i.e., whose grade of membership is 1).
- (mathematics, ring theory, of a ring homomorphism f:R→S between rings) The set of elements of R which are mapped to the additive identity 0 of S.
- (mathematics, category theory) The source of operatorname kerf, denoted operatorname Kerf.
- The core, center, or essence of an object or system.
- a single whole grain of a cereal
- the choicest or most essential or most vital part of some idea or experience
- the inner and usually edible part of a seed or grain or nut or fruit stone
verb
noun
name
noun
- (mathematics) A discontinuity arising in the solution of a partial differential equation.
- (figuratively) Something so surprising that it is stunning.
- (physics) A shock wave.
- (medicine) Circulatory shock, a medical emergency characterized by the inability of the circulatory system to supply enough oxygen to meet tissue requirements.
- A sudden, heavy impact.
- (psychology) A sudden or violent mental or emotional disturbance.
- An arrangement of sheaves for drying; a stook.
- A chemical added to a swimming pool to moderate the chlorine levels.
- (medicine) Electric shock, a sudden burst of electrical energy hitting a person or animal.
- (by extension) A tuft or bunch of something, such as hair or grass.
- (psychology) A state of distress following a mental or emotional disturbance, often caused by news or other stimuli.
- (automotive, mechanical engineering) A shock absorber (typically in the suspension of a vehicle).
- a sudden jarring impact
- (pathology) bodily collapse or near collapse caused by inadequate oxygen delivery to the cells; characterized by reduced cardiac output and rapid heartbeat and circulatory insufficiency and pallor
- an instance of agitation of the earth's crust
- an unpleasant or disappointing surprise
- the feeling of distress and disbelief that you have when something bad happens accidentally
- the violent interaction of individuals or groups entering into combat
- a reflex response to the passage of electric current through the body
- a pile of sheaves of grain set on end in a field to dry; stalks of Indian corn set up in a field
- a bushy thick mass (especially hair)
- a mechanical damper; absorbs energy of sudden impulses
adj
verb
- (transitive) To strike with disgust, to offend, scandalize.
- (transitive) To add a chemical to (a swimming pool) to moderate the chlorine levels.
- (transitive) To collect, or make up, into a shock or shocks; to stook.
- (transitive) To subject to a shock wave or violent impact.
- (transitive) To give an electric shock to.
- (transitive) To cause to be emotionally shocked; to cause (someone) to feel greatly surprised or upset.
- (geology, transitive) To deform the crystal structure of a stone by the application of extremely high pressure at moderate temperature, as produced only by hypervelocity impact events, lightning strikes, and nuclear explosions.
- strike with horror or terror
- strike with disgust or revulsion
- collide violently
- inflict a trauma upon
- collect or gather into shocks
- subject to electrical shocks
- surprise greatly; knock someone's socks off
noun
- Any of several generalizations of this concept to functions of several variables or to higher orders: the partial differential, total differential, Gateaux differential, etc.
- (multivariable calculus) The Jacobian matrix of a function of several variables.
- (calculus, of a univariate differentiable function f(x)) A function giving the change in the linear approximation of f at a point x over a small interval Δx or operatorname d!x, the function being called the differential of f and denoted operatorname d!f(x,Δx), operatorname d!f(x), or simply operatorname d!f.
- One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
- The differential gear in an automobile, etc.
- A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
- (differential geometry, of a smooth map ϕ between smooth manifolds) The pushforward or total derivative of ϕ: a linear map from the tangent space at a point x in ϕ's domain to the tangent space at ϕ(x) which is, in a technical sense, the best linear approximation of ϕ at x; denoted operatorname d!ϕₓ.
- (mathematics) Any of several generalizations of the concept(s) above: e.g. the Kähler differential in the setting of schemes, the quadratic differential in the theory of Riemann surfaces, etc.
- (calculus) A quantity representing an infinitesimal change in a variable, now only used as a heuristic aid except in nonstandard analysis but considered rigorous until the 20th century; a fluxion in Newtonian calculus, now usually written in Leibniz's notation as operatorname d!x.
- A qualitative or quantitative difference between similar or comparable things.
- a quality that differentiates between similar things
- a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves
- the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
adj
noun
- (mathematics) a condition specified for the solution to a set of differential equations
- (mathematics) Any of a set of constraints that limit the solutions of a differential equation
- (quantum mechanics) either one of the conditions that the wave function must be continuous and that its derivative must be as well, except in the case of infinite potential
noun
symbol
verb
noun
- (vector calculus) Divergence; a kind of differential operator.
- (UK, Eton College, school slang) A division; a lesson.
- (UK, Ireland, slang) A foolish person; an idiot.
- (military) A division.
- Alternative form of daeva.
- (UK, Winchester College) division; a subject with multidisciplinary scope.
- (UK, Ireland, uncountable, slang) Divinity, as a school subject.
- (web design) A section of a web page, or the div element that represents it in HTML code.
- (mathematics, computing) A function, implemented in many programming languages, that returns the result of a division of two integers.
verb
noun
- (mathematics) Clipping of differential
- (climbing) A difficult route.
- (computing) The output of a diff program, a diff file.
- (slang) Clipping of difference
- (video games, slang) Used to trash-talk an opposing team at the end of a game by pointing out a skill difference between some role and the same role on the other team.
- (automotive) Abbreviation of differential: the differential gear in an automobile.
- (medicine) Abbreviation of differential: differential of types of white blood cell in a complete blood count.
- (computing) Any program which compares two files or sets of files and outputs a description of the differences between them.
- (fandom slang) Clipping of difficulty.
adj
name
verb
- (transitive, computing) To compare two files or other objects, manually or otherwise.
- (transitive, fandom slang) To win (or to be able to win) a fight against another, with a defined level of difficulty. Usually used when power scaling fictional characters.
- (transitive, computing) To run a diff program on (files or items) so as to produce a description of the differences between them, as for a patch file.
noun
- the mathematical process of obtaining the derivative of a function
- (biology) the structural adaptation of some body part for a particular function
- a discrimination between things as different and distinct on the basis of their characteristics or attributes
- (biology) The process by which the components of multicellular life (cells, organs, etc.) are produced and acquire function, as when a seed develops the root and stem, and the initial stem develops the leaf, branches, and flower buds.
- (biology, evolution) The evolutionary process by which one taxonomic group (species, genus, variety, etc.) becomes distinct from another, or acquires distinct features; the result of such a process: distinctness.
- The act of treating one thing as distinct from another, or of creating such a distinction; of separating a class of things into categories; of describing a thing by illustrating how it is different from something else.
- (geology) The process of separation of cooling magma into various rock types.
- (mathematics, calculus) The process of applying the derivative operator to a function; of calculating a function's derivative.
- The process of developing distinct components.
noun
- (mathematics) The boundary separating two modes of behavior in a differential equation.
- (typography) The proofreader's mark resembling a slash ⟨ / ⟩ or vertical bar ⟨ | ⟩ placed after a note in the margin to indicate that it should replace the item(s) struckthrough in the running text or to separate it from other margin notes.
- A terminator: a line on a partially-illuminated surface separating the lit and shaded regions.
- (typography, historical) The ⟨L⟩ or pipe ⟨|⟩ mark formerly used to divide integers from decimals.
- (physics) The line between regions having different magnetic fields.
- a punctuation mark (‘/’) used to separate related items of information
noun
- the part of calculus that deals with integration and its application in the solution of differential equations and in determining areas or volumes etc.
- (calculus) The calculus that generalizes summation to find areas, masses, volumes, sums, and totals of quantities described by continuously varying functions.
noun
- (complex analysis) The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.
- (mathematics, complex analysis, always plural) Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.
noun
- the derivative of a function of two or more variables with respect to a single variable while the other variables are considered to be constant
- a harmonic with a frequency that is a multiple of the fundamental frequency
- (dentistry) dentures that replace only some of the natural teeth
- (bodybuilding) The condition of not exhausting the amplitude during the repetition of an exercise.
- (forensics) An incomplete fingerprint
- (furry fandom) A fursuit that does not fully cover the wearer's body.
- (programming, Internet) A fragment of a template containing markup.
- (mathematics) A partial derivative: a derivative with respect to one independent variable of a function in multiple variables while holding the other variables constant.
- (music) Any of the sine waves which make up a complex tone; often an overtone or harmonic of the fundamental.
adj
- (followed by ‘of’ or ‘to’) having a strong preference or liking for
- being or affecting only a part; not total
- constituting or comprising a part or fraction of a possible whole or entirety
- showing favoritism
- (botany) Subordinate.
- Biased in favor of a person, side, or point of view, especially when dealing with a competition or dispute.
- (crosswording, of a clue) Having a wordplay element, but no definition.
- (followed by the preposition to) Having a predilection for something.
- (computer science) Describing a property that holds only when an algorithm terminates.
- Existing as a part or portion; incomplete.
- (mathematics) Of or relating to a partial derivative or partial differential.
verb
noun
- (calculus) The operation of finding the integral of a function.
- (society) The process of fitting into a community, notably applied to minorities.
- The act or process of making whole or entire.
- (biology) In evolution, the process by which the manifold is compacted into the relatively simple and permanent; supposed to alternate with differentiation as an agent in species' development.
- (US) Ellipsis of racial integration.
- The process of combining with compatible elements in order to incorporate them.
- the action of incorporating a racial or religious group into a community
- the act of combining into an integral whole
- an operation used in the calculus whereby the integral of a function is determined
noun
- (calculus) A function used to define an integral transform.
- (mathematics, category theory, of a morphism f:X→Y in a category with zero morphisms) The equalizer of f and the zero morphism from X to Y, denoted operatorname kerf.
- (botany, US) The stone of certain fruits, such as peaches or plums.
- (botany) A single seed of grain, especially of corn or wheat.
- (computing) The central part of many computer operating systems which manages the system's resources and the communication between hardware and software components.
- (slang) The human clitoris.
- (computing) The core engine of any complex software system.
- (programming) The simplified input to an algorithm that has undergone kernelization.
- A small mass around which other matter is concreted; a nucleus; a concretion or hard lump in the flesh.
- (chemistry) The nucleus and electrons of an atom excluding its valence electrons.
- (botany) The central (usually edible) part of a nut, especially once the hard shell has been removed.
- (mathematics, linear algebra, of a linear transformation f:M→N between modules or vector spaces) The set of elements of M which are mapped to the additive identity 0 of N.
- (mathematics, set theory, of a function f) The set of pairs of elements in the domain of f which are mapped to the same value; the equivalence relation x≡y⟺f(x)=f(y).
- (mathematics, group theory, of a group homomorphism f:G→H between groups) The set of elements of G which are mapped to the identity of H (usually written as 0 in an additive group and as 1 in a multiplicative group).
- (mathematics, fuzzy set theory) The set of members of a fuzzy set that are fully included (i.e., whose grade of membership is 1).
- (mathematics, ring theory, of a ring homomorphism f:R→S between rings) The set of elements of R which are mapped to the additive identity 0 of S.
- (mathematics, category theory) The source of operatorname kerf, denoted operatorname Kerf.
- The core, center, or essence of an object or system.
- a single whole grain of a cereal
- the choicest or most essential or most vital part of some idea or experience
- the inner and usually edible part of a seed or grain or nut or fruit stone
verb
verb
- (mathematics) To calculate the differential of a function of multiple variables.
- (mathematics) To calculate the derivative of a function.
- To recognize as different or distinct.
- (transitive, intransitive, often in the passive voice, biology) To (cause to) go through a process of development called differentiation; to make or become different in form or function.
- To modify so as to create a difference or distinction.
- To show or be the difference or distinction between things.
- To perceive the difference between things; to discriminate.
- (education) To teach a lesson in multiple different ways in order to meet the needs of more or less advanced students.
- become distinct and acquire a different character
- evolve so as to lead to a new species or develop in a way most suited to the environment
- be a distinctive feature, attribute, or trait; sometimes in a very positive sense
- mark as different
- calculate a derivative; take the derivative
- become different during development
noun
adj
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
adj
- possessing a differential coefficient or derivative
- capable of being perceived as different
- (comparable, of multiple items) able to be differentiated; distinguishable, as for example by differing appearance or measurable characteristics.
- (calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.
adj
- (mathematics, of a differential equation) Able to be brought to a form where all occurrences of the dependent and the independent variable are on opposite sides of the equal sign.
- (abstract algebra, of an algebra over a ring) Satisfying any of several technical conditions on the center of the algebra which generalize the situation of field extensions; see Separable algebra on Wikipedia.Wikipedia
- (of a polynomial) Having no repeated roots (where roots are considered in an algebraic closure)
- Able to be separated.
- (mathematical analysis, of a topological space) Having a countable dense subset.
- (Galois theory, of an algebraic field extension E/F) Such that the minimal polynomial of every element of E is a separable polynomial.
- capable of being divided or dissociated
adj
- (mathematical analysis) Being defined in terms of objects of differential calculus such as derivatives.
- Of, or relating to division into elements or principles.
- (mathematics, of a function) Being able to be locally represented by convergent power series around every point of the domain.
- (mathematics) Of, or relating to algebra or a similar method of analysis.
- (logic, of a proposition) that follows necessarily by definition; tautologous.
- Of, or relating to any form of analysis, or to analytics.
- (linguistics) Of a language, having a grammar principally dependent on the arrangement of uninflected function words within sentences to indicate meaning.
- Having the ability to analyse.
- using or skilled in using analysis (i.e., separating a whole — intellectual or substantial — into its elemental parts or basic principles)
- using or subjected to a methodology using algebra and calculus
- expressing a grammatical category by using two or more words rather than inflection
- of a proposition that is necessarily true independent of fact or experience
adj
- (mathematics) of a function of two or more variables in which the ratio of the partial derivatives depends only on the ratio of the variables, not their value
- the relationship of a microcosm to a macrocosm
- (economics) in which the ratio of goods demanded depends only on the ratio of their prices
- (mathematics, geometry) for a geometric figure that is the image of another figure under an homothety.
adj
- (mathematics, of a function) having a single derivative at a point
- producing offspring of only one sex, exhibiting monogeny
- of or relating to monogenesis or to monogenism
- (mathematics, of a semigroup) generated by a set containing only a single element
- (genetics) regulated by a single gene
- of or relating to an inheritable character that is controlled by a single pair of genes
noun
noun
- Any of several generalizations of this concept to functions of several variables or to higher orders: the partial differential, total differential, Gateaux differential, etc.
- (multivariable calculus) The Jacobian matrix of a function of several variables.
- (calculus, of a univariate differentiable function f(x)) A function giving the change in the linear approximation of f at a point x over a small interval Δx or operatorname d!x, the function being called the differential of f and denoted operatorname d!f(x,Δx), operatorname d!f(x), or simply operatorname d!f.
- One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
- The differential gear in an automobile, etc.
- A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
- (differential geometry, of a smooth map ϕ between smooth manifolds) The pushforward or total derivative of ϕ: a linear map from the tangent space at a point x in ϕ's domain to the tangent space at ϕ(x) which is, in a technical sense, the best linear approximation of ϕ at x; denoted operatorname d!ϕₓ.
- (mathematics) Any of several generalizations of the concept(s) above: e.g. the Kähler differential in the setting of schemes, the quadratic differential in the theory of Riemann surfaces, etc.
- (calculus) A quantity representing an infinitesimal change in a variable, now only used as a heuristic aid except in nonstandard analysis but considered rigorous until the 20th century; a fluxion in Newtonian calculus, now usually written in Leibniz's notation as operatorname d!x.
- A qualitative or quantitative difference between similar or comparable things.
- a quality that differentiates between similar things
- a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves
- the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx