@prefix rdf: . @prefix dbr: . @prefix owl: . dbr:Difference_quotient rdf:type owl:Thing . @prefix rdfs: . dbr:Difference_quotient rdfs:label "\u5DEE\u5206\u5546"@ja , "Coeficiente diferencial"@pt , "Rapporto incrementale"@it , "Differenzenquotient"@de , "Differentiequoti\u00EBnt"@nl , "Difference quotient"@en , "Iloraz r\u00F3\u017Cnicowy"@pl ; rdfs:comment "\u5FAE\u5206\u7A4D\u5206\u5B66\u306B\u304A\u3051\u308B\u5DEE\u5206\u5546\uFF08\u3055\u3076\u3093\u3057\u3087\u3046\u3001\u82F1: difference quotient; \u5DEE\u5546\uFF09\u306F\u3001\u3075\u3064\u3046\u306F\u51FD\u6570 f \u306B\u5BFE\u3059\u308B\u6709\u9650\u5DEE\u5206\u306E\u5546 \u3092\u8A00\u3044\u3001\u3053\u308C\u306F h \u2192 0 \u306E\u6975\u9650\u3067\u5FAE\u5206\u5546\u3068\u306A\u308B\u3002\u5B9F\u969B\u306B\u51FD\u6570\u5024\u306E\u6709\u9650\u5DEE\u5206\u3092\u5BFE\u5FDC\u3059\u308B\u5909\u6570\u306E\u6709\u9650\u5DEE\u5206\u3067\u5272\u3063\u305F\u3082\u306E\u3067\u3042\u308B\u3053\u3068\u306B\u3088\u308A\u3001\u3053\u306E\u540D\u79F0\u304C\u3042\u308B\u3002 \u5DEE\u5206\u5546\u306F\u51FD\u6570 f \u306E\u3042\u308B\u533A\u9593\uFF08\u3044\u307E\u306E\u5834\u5408\u3001\u9577\u3055 h \u306E\u533A\u9593\uFF09\u306B\u304A\u3051\u308B\u300C\u5E73\u5747\u5909\u5316\u7387\u300D(average rate of change) \u3092\u4E0E\u3048\u308B\u3082\u306E\u3067\u3042\u308B\u304B\u3089\u3001\u7279\u306B\u305D\u306E\u6975\u9650\u3068\u3057\u3066\u306E\u5FAE\u5206\u5546\u306F\u300C\u77AC\u9593\u5909\u5316\u7387\u300D\u306B\u5BFE\u5FDC\u3059\u308B\u3068\u8003\u3048\u308B\u3053\u3068\u304C\u3067\u304D\u308B \u3084\u3084\u8A18\u6CD5\u3092\u5909\u66F4\uFF08b \u2254 a + h\uFF09\u3057\u3066\u3001\u533A\u9593 [a, b] \u306B\u5BFE\u3059\u308B\u3001\u5DEE\u5206\u5546 \u3092\u8003\u3048\u308C\u3070\u3001\u3053\u308C\u306F f \u306E\u533A\u9593 [a, b] \u306B\u304A\u3051\u308B\u5FAE\u5206\u4FC2\u6570\u306E\u300C\u5E73\u5747\u5024\u300D\u3092\u8868\u3057\u3066\u3044\u308B\u3068\u8003\u3048\u3089\u308C\u308B\u3002\u3053\u306E\u3053\u3068\u306F\u3001\u53EF\u5FAE\u5206\u51FD\u6570 f \u306B\u5BFE\u3057\u3066 f \u306E\u5FAE\u5206\u4FC2\u6570\u304C\u533A\u9593\u5185\u306E\u9069\u5F53\u306A\u70B9\u306B\u304A\u3044\u3066\u5E73\u5747\u5024\u306B\u5230\u9054\u3059\u308B\u3053\u3068\u3092\u8FF0\u3079\u305F\u5E73\u5747\u5024\u306E\u5B9A\u7406\u306B\u3088\u3063\u3066\u6B63\u5F53\u5316\u3055\u308C\u308B\u3002\u5E7E\u4F55\u5B66\u7684\u306B\u306F\u3001\u3053\u306E\u5DEE\u5206\u5546\u306F\u4E8C\u70B9 (a, f(a)), (b, f(b)) \u3092\u901A\u308B\u5272\u7DDA\u306E\u50BE\u304D\u3092\u6E2C\u308B\u3082\u306E\u3067\u3042\u308B\u3002 \u5DEE\u5206\u5546\u306F\u306B\u304A\u3051\u308B\u8FD1\u4F3C\u306B\u7528\u3044\u3089\u308C\u308B\u304C\u3001\u305D\u308C\u306F\u540C\u6642\u306B\u3053\u306E\u5FDC\u7528\u306B\u304A\u3044\u3066\u6279\u5224\u306E\u4E3B\u984C\u3068\u3082\u306A\u3063\u3066\u3044\u308B \u5DEE\u5206\u5546\u306E\u3053\u3068\u3092\u3001\u30CB\u30E5\u30FC\u30C8\u30F3\u5546\uFF08\u30A2\u30A4\u30B6\u30C3\u30AF\u30FB\u30CB\u30E5\u30FC\u30C8\u30F3\u306B\u7531\u6765\uFF09\u3084\u30D5\u30A7\u30EB\u30DE\u30FC\u306E\u5DEE\u5206\u5546\uFF08\u30D4\u30A8\u30FC\u30EB\u30FB\u30C9\u30FB\u30D5\u30A7\u30EB\u30DE\u30FC\u306B\u7531\u6765\uFF09\u306A\u3069\u3068\u3082\u547C\u3076\u3053\u3068\u304C\u3042\u308B\u3002"@ja , "Iloraz r\u00F3\u017Cnicowy \u2013 wielko\u015B\u0107 opisuj\u0105ca przyrost funkcji na danym przedziale."@pl , "Il rapporto incrementale di una funzione reale di variabile reale \u00E8 un numero che, intuitivamente, misura \"quanto velocemente\" la funzione cresce o decresce al variare della coordinata indipendente attorno a un dato punto. Dal punto di vista geometrico, esso fornisce il valore del coefficiente angolare di una retta secante passante per il dato punto e un altro punto sul grafico della funzione. Il concetto di rapporto incrementale \u00E8 strettamente legato alla nozione di derivata, e pu\u00F2 essere definito per funzioni pi\u00F9 generali, come le funzioni a pi\u00F9 variabili."@it , "Der Differenzenquotient ist ein Begriff aus der Mathematik. Er beschreibt das Verh\u00E4ltnis der Ver\u00E4nderung einer Gr\u00F6\u00DFe zu der Ver\u00E4nderung einer anderen, wobei die erste Gr\u00F6\u00DFe von der zweiten abh\u00E4ngt. In der Analysis verwendet man Differenzenquotienten, um die Ableitung einer Funktion zu definieren. In der numerischen Mathematik werden sie zum L\u00F6sen von Differentialgleichungen und f\u00FCr die n\u00E4herungsweise Bestimmung der Ableitung einer Funktion (numerische Differentiation) benutzt."@de , "Coeficiente diferencial em matem\u00E1tica descreve a altera\u00E7\u00E3o na propor\u00E7\u00E3o de uma grandeza em rela\u00E7\u00E3o a altera\u00E7\u00E3o de outra grandeza, dependente da primeira. Em an\u00E1lise usa-se o coeficiente diferencial, para c\u00E1lculo para definir uma fun\u00E7\u00E3o. Em an\u00E1lise num\u00E9rica s\u00E3o usados para resolver equa\u00E7\u00F5es diferenciais e para a determina\u00E7\u00E3o aproximada da derivada de uma fun\u00E7\u00E3o utilizada."@pt , "In single-variable calculus, the difference quotient is usually the name for the expression which when taken to the limit as h approaches 0 gives the derivative of the function f. The name of the expression stems from the fact that it is the quotient of the difference of values of the function by the difference of the corresponding values of its argument (the latter is (x + h) - x = h in this case). The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of length h). The limit of the difference quotient (i.e., the derivative) is thus the instantaneous rate of change."@en , "Het differentiequoti\u00EBnt is de verhouding van de verandering van de ene grootheid ten opzichte van de verandering van een andere grootheid, waarvan de eerste grootheid afhankelijk is. In de analyse wordt het differentiequoti\u00EBnt gebruikt om de afgeleide van een functie te defini\u00EBren. Differentiequoti\u00EBnten vormen samen met het limietbegrip het theoretische fundament onder de differentiaalrekening. Bij functies wordt in plaats van differentiequoti\u00EBnt ook wel gesproken van gemiddelde verandering van de functiewaarde."@nl . @prefix dcterms: . @prefix dbc: . dbr:Difference_quotient dcterms:subject dbc:Numerical_analysis , dbc:Differential_calculus . @prefix dbo: . dbr:Difference_quotient dbo:wikiPageID 241863 ; dbo:wikiPageRevisionID 1117503568 ; dbo:wikiPageWikiLink dbr:Isaac_Newton , dbr:Multiple_integral , dbr:Differentiable_function , dbr:Newton_polynomial , dbr:Infinitesimal , , , dbr:Temporal_discretization , dbr:Divaricate , dbr:Secant_line , dbr:Mean_value_theorem , dbc:Numerical_analysis , dbr:Finite_difference , dbr:Limit_of_a_function , dbr:Divided_differences , dbr:Pierre_de_Fermat , dbr:Rectangle_method , dbr:Derivative , dbr:Slope , dbc:Differential_calculus , , dbr:Instantaneous , dbr:Leibniz_notation , , dbr:Average , , dbr:Quotient_rule , dbr:ASCII , dbr:Mean_of_a_function , dbr:Fermat_theory , dbr:Quotient , dbr:Symmetric_difference_quotient , dbr:Calculus , dbr:Numerical_differentiation ; dbo:wikiPageExternalLink , , , , , , ; owl:sameAs , . @prefix dbpedia-pt: . dbr:Difference_quotient owl:sameAs dbpedia-pt:Coeficiente_diferencial . @prefix ns8: . dbr:Difference_quotient owl:sameAs ns8:GiTz . @prefix wikidata: . dbr:Difference_quotient owl:sameAs wikidata:Q1224446 , , , . @prefix dbpedia-simple: . dbr:Difference_quotient owl:sameAs dbpedia-simple:Difference_quotient , . @prefix dbpedia-de: . dbr:Difference_quotient owl:sameAs dbpedia-de:Differenzenquotient . @prefix dbpedia-it: . dbr:Difference_quotient owl:sameAs dbpedia-it:Rapporto_incrementale . @prefix dbp: . @prefix dbt: . dbr:Difference_quotient dbp:wikiPageUsesTemplate dbt:Webarchive , dbt:Short_description , dbt:Broader , dbt:Authority_control , dbt:Reflist , dbt:Rp , dbt:Isaac_Newton . @prefix xsd: . dbr:Difference_quotient dbp:date "2005-09-12"^^xsd:date ; dbp:url ; dbo:abstract "Der Differenzenquotient ist ein Begriff aus der Mathematik. Er beschreibt das Verh\u00E4ltnis der Ver\u00E4nderung einer Gr\u00F6\u00DFe zu der Ver\u00E4nderung einer anderen, wobei die erste Gr\u00F6\u00DFe von der zweiten abh\u00E4ngt. In der Analysis verwendet man Differenzenquotienten, um die Ableitung einer Funktion zu definieren. In der numerischen Mathematik werden sie zum L\u00F6sen von Differentialgleichungen und f\u00FCr die n\u00E4herungsweise Bestimmung der Ableitung einer Funktion (numerische Differentiation) benutzt. Das gilt auch f\u00FCr \u00DCbertragungsfunktionen der Systemtheorie, der Steuerungs- und Regelungstechnik f\u00FCr dynamische Systeme mit dem Ausgangs-Eingangsverh\u00E4ltnis der Laplace-transformierten gew\u00F6hnlichen Differenzialgleichungen (mit St\u00F6rfunktion). Sie werden mit der inversen Laplace-Transformation auf gew\u00F6hnliche Differenzialgleichungen zur\u00FCckgef\u00FChrt und k\u00F6nnen mit Hilfe des Differenzenquotienten n\u00E4herungsweise numerisch gel\u00F6st werden."@de , "Het differentiequoti\u00EBnt is de verhouding van de verandering van de ene grootheid ten opzichte van de verandering van een andere grootheid, waarvan de eerste grootheid afhankelijk is. In de analyse wordt het differentiequoti\u00EBnt gebruikt om de afgeleide van een functie te defini\u00EBren. Differentiequoti\u00EBnten vormen samen met het limietbegrip het theoretische fundament onder de differentiaalrekening. Bij functies wordt in plaats van differentiequoti\u00EBnt ook wel gesproken van gemiddelde verandering van de functiewaarde."@nl , "Coeficiente diferencial em matem\u00E1tica descreve a altera\u00E7\u00E3o na propor\u00E7\u00E3o de uma grandeza em rela\u00E7\u00E3o a altera\u00E7\u00E3o de outra grandeza, dependente da primeira. Em an\u00E1lise usa-se o coeficiente diferencial, para c\u00E1lculo para definir uma fun\u00E7\u00E3o. Em an\u00E1lise num\u00E9rica s\u00E3o usados para resolver equa\u00E7\u00F5es diferenciais e para a determina\u00E7\u00E3o aproximada da derivada de uma fun\u00E7\u00E3o utilizada."@pt , "Il rapporto incrementale di una funzione reale di variabile reale \u00E8 un numero che, intuitivamente, misura \"quanto velocemente\" la funzione cresce o decresce al variare della coordinata indipendente attorno a un dato punto. Dal punto di vista geometrico, esso fornisce il valore del coefficiente angolare di una retta secante passante per il dato punto e un altro punto sul grafico della funzione. Il concetto di rapporto incrementale \u00E8 strettamente legato alla nozione di derivata, e pu\u00F2 essere definito per funzioni pi\u00F9 generali, come le funzioni a pi\u00F9 variabili."@it , "In single-variable calculus, the difference quotient is usually the name for the expression which when taken to the limit as h approaches 0 gives the derivative of the function f. The name of the expression stems from the fact that it is the quotient of the difference of values of the function by the difference of the corresponding values of its argument (the latter is (x + h) - x = h in this case). The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of length h). The limit of the difference quotient (i.e., the derivative) is thus the instantaneous rate of change. By a slight change in notation (and viewpoint), for an interval [a, b], the difference quotient is called the mean (or average) value of the derivative of f over the interval [a, b]. This name is justified by the mean value theorem, which states that for a differentiable function f, its derivative f\u2032 reaches its mean value at some point in the interval. Geometrically, this difference quotient measures the slope of the secant line passing through the points with coordinates (a, f(a)) and (b, f(b)). Difference quotients are used as approximations in numerical differentiation, but they have also been subject of criticism in this application. Difference quotients may also find relevance in applications involving Time discretization, where the width of the time step is used for the value of h. The difference quotient is sometimes also called the Newton quotient (after Isaac Newton) or Fermat's difference quotient (after Pierre de Fermat)."@en , "\u5FAE\u5206\u7A4D\u5206\u5B66\u306B\u304A\u3051\u308B\u5DEE\u5206\u5546\uFF08\u3055\u3076\u3093\u3057\u3087\u3046\u3001\u82F1: difference quotient; \u5DEE\u5546\uFF09\u306F\u3001\u3075\u3064\u3046\u306F\u51FD\u6570 f \u306B\u5BFE\u3059\u308B\u6709\u9650\u5DEE\u5206\u306E\u5546 \u3092\u8A00\u3044\u3001\u3053\u308C\u306F h \u2192 0 \u306E\u6975\u9650\u3067\u5FAE\u5206\u5546\u3068\u306A\u308B\u3002\u5B9F\u969B\u306B\u51FD\u6570\u5024\u306E\u6709\u9650\u5DEE\u5206\u3092\u5BFE\u5FDC\u3059\u308B\u5909\u6570\u306E\u6709\u9650\u5DEE\u5206\u3067\u5272\u3063\u305F\u3082\u306E\u3067\u3042\u308B\u3053\u3068\u306B\u3088\u308A\u3001\u3053\u306E\u540D\u79F0\u304C\u3042\u308B\u3002 \u5DEE\u5206\u5546\u306F\u51FD\u6570 f \u306E\u3042\u308B\u533A\u9593\uFF08\u3044\u307E\u306E\u5834\u5408\u3001\u9577\u3055 h \u306E\u533A\u9593\uFF09\u306B\u304A\u3051\u308B\u300C\u5E73\u5747\u5909\u5316\u7387\u300D(average rate of change) \u3092\u4E0E\u3048\u308B\u3082\u306E\u3067\u3042\u308B\u304B\u3089\u3001\u7279\u306B\u305D\u306E\u6975\u9650\u3068\u3057\u3066\u306E\u5FAE\u5206\u5546\u306F\u300C\u77AC\u9593\u5909\u5316\u7387\u300D\u306B\u5BFE\u5FDC\u3059\u308B\u3068\u8003\u3048\u308B\u3053\u3068\u304C\u3067\u304D\u308B \u3084\u3084\u8A18\u6CD5\u3092\u5909\u66F4\uFF08b \u2254 a + h\uFF09\u3057\u3066\u3001\u533A\u9593 [a, b] \u306B\u5BFE\u3059\u308B\u3001\u5DEE\u5206\u5546 \u3092\u8003\u3048\u308C\u3070\u3001\u3053\u308C\u306F f \u306E\u533A\u9593 [a, b] \u306B\u304A\u3051\u308B\u5FAE\u5206\u4FC2\u6570\u306E\u300C\u5E73\u5747\u5024\u300D\u3092\u8868\u3057\u3066\u3044\u308B\u3068\u8003\u3048\u3089\u308C\u308B\u3002\u3053\u306E\u3053\u3068\u306F\u3001\u53EF\u5FAE\u5206\u51FD\u6570 f \u306B\u5BFE\u3057\u3066 f \u306E\u5FAE\u5206\u4FC2\u6570\u304C\u533A\u9593\u5185\u306E\u9069\u5F53\u306A\u70B9\u306B\u304A\u3044\u3066\u5E73\u5747\u5024\u306B\u5230\u9054\u3059\u308B\u3053\u3068\u3092\u8FF0\u3079\u305F\u5E73\u5747\u5024\u306E\u5B9A\u7406\u306B\u3088\u3063\u3066\u6B63\u5F53\u5316\u3055\u308C\u308B\u3002\u5E7E\u4F55\u5B66\u7684\u306B\u306F\u3001\u3053\u306E\u5DEE\u5206\u5546\u306F\u4E8C\u70B9 (a, f(a)), (b, f(b)) \u3092\u901A\u308B\u5272\u7DDA\u306E\u50BE\u304D\u3092\u6E2C\u308B\u3082\u306E\u3067\u3042\u308B\u3002 \u5DEE\u5206\u5546\u306F\u306B\u304A\u3051\u308B\u8FD1\u4F3C\u306B\u7528\u3044\u3089\u308C\u308B\u304C\u3001\u305D\u308C\u306F\u540C\u6642\u306B\u3053\u306E\u5FDC\u7528\u306B\u304A\u3044\u3066\u6279\u5224\u306E\u4E3B\u984C\u3068\u3082\u306A\u3063\u3066\u3044\u308B \u5DEE\u5206\u5546\u306E\u3053\u3068\u3092\u3001\u30CB\u30E5\u30FC\u30C8\u30F3\u5546\uFF08\u30A2\u30A4\u30B6\u30C3\u30AF\u30FB\u30CB\u30E5\u30FC\u30C8\u30F3\u306B\u7531\u6765\uFF09\u3084\u30D5\u30A7\u30EB\u30DE\u30FC\u306E\u5DEE\u5206\u5546\uFF08\u30D4\u30A8\u30FC\u30EB\u30FB\u30C9\u30FB\u30D5\u30A7\u30EB\u30DE\u30FC\u306B\u7531\u6765\uFF09\u306A\u3069\u3068\u3082\u547C\u3076\u3053\u3068\u304C\u3042\u308B\u3002 \u6709\u9650\u5DEE\u5206\u3092\u3068\u308B\u64CD\u4F5C\u3092\u53CD\u5FA9\u9069\u7528\u3057\u3066\u5F97\u3089\u308C\u308B\u3092\u7528\u3044\u308C\u3070\u3001\u9AD8\u968E\u5DEE\u5206\u5546\u3042\u308B\u3044\u306F\uFF08\u5206\u70B9\u304C\u7B49\u9593\u9694\u306E\u5834\u5408\u306E\uFF09\u9AD8\u968E\u5DEE\u5546\u3092\u8003\u3048\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002"@ja , "Iloraz r\u00F3\u017Cnicowy \u2013 wielko\u015B\u0107 opisuj\u0105ca przyrost funkcji na danym przedziale."@pl . @prefix prov: . dbr:Difference_quotient prov:wasDerivedFrom ; dbo:wikiPageLength "21057"^^xsd:nonNegativeInteger . @prefix foaf: . @prefix wikipedia-en: . dbr:Difference_quotient foaf:isPrimaryTopicOf wikipedia-en:Difference_quotient .