| dbo:abstract |
Die Operatorenrechnung nach Heaviside beschreibt eine nach Oliver Heaviside benannte empirische Operatorenrechnung, welche 1887in seinem berühmten Werk „Electromagnetic Theory“ veröffentlicht wurde. (englisch operator calculus oder operational calculus) (de) En mathématiques et plus précisément en analyse fonctionnelle, le calcul opérationnel repose essentiellement sur un astucieux changement de variable basé sur la transformée de Laplace permettant l'algébrisation des symboles de dérivation et d'intégration des expressions mathématiques décrivant les phénomènes linéaires. Certains ingénieurs emploient de préférence la transformation de « Laplace-Carson », une constante ayant comme image la même constante. L'expression : permet d'associer à toute fonction d'une variable dite « fonction origine » une « fonction image » . Ainsi la solution algébrique de l'équation image permet de retrouver, au moyen d'un tableau de correspondance opératoire, la solution de l'équation origine. La transformation directe est notée : image de . La transformation inverse est notée : original de . (fr) Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation. (en) 演算子法（えんざんしほう）とは、解析学の問題、特に微分方程式を、代数的問題（普通は多項式方程式）に変換して解く方法。オリヴァー・ヘヴィサイドの貢献が特に大きいので「ヘヴィサイドの演算子法」とも呼ばれるが、厳密な理論化はその後の数学者たちにより行われた。 (ja) Cálculo operacional, também conhecido como análise operacional, é uma técnica pela qual os problemas em análise, em particular equações diferenciais, são transformados em problemas algébricos, geralmente, o problema de resolver uma equação polinomial. (pt) Операционное исчисление — один из методов математического анализа, позволяющий в ряде случаев с помощью простых средств решать сложные математические задачи. (ru) |
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https://archive.org/details/in.ernet.dli.2015.84683/page/n9 http://projecteuclid.org/euclid.bams/1183486854 https://archive.org/details/operationalmetho029814mbp http://mysite.du.edu/~jcalvert/math/laplace.htm https://web.archive.org/web/20060908015359/http:/ceta.mit.edu/pier/pier26/11.9909172jp.Lindell.pdf https://web.archive.org/web/20110719095509/http:/www.new.dli.ernet.in/cgi-bin/DBscripts/allmetainfo_test.cgi%3Fbarcode=73746 https://web.archive.org/web/20110719095608/http:/www.new.dli.ernet.in/cgi-bin/DBscripts/allmetainfo_test.cgi%3Fbarcode=42240 https://web.archive.org/web/20110719095649/http:/www.new.dli.ernet.in/cgi-bin/DBscripts/allmetainfo_test.cgi%3Fbarcode=2962 http://projecteuclid.org/euclid.bams/1183492106 https://www.embedded.com/electronics-blogs/programmer-s-toolbox/4025617/More-on-the-Rosetta-Stone/ http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/ http://gallica.bnf.fr/ark:/12148/cb37572031d/date https://archive.org/details/theoryoflinearop033341mbp http://ieeexplore.ieee.org/xpl/articleDetails.jsp%3Farnumber=4321749 |
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Die Operatorenrechnung nach Heaviside beschreibt eine nach Oliver Heaviside benannte empirische Operatorenrechnung, welche 1887in seinem berühmten Werk „Electromagnetic Theory“ veröffentlicht wurde. (englisch operator calculus oder operational calculus) (de) Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation. (en) 演算子法（えんざんしほう）とは、解析学の問題、特に微分方程式を、代数的問題（普通は多項式方程式）に変換して解く方法。オリヴァー・ヘヴィサイドの貢献が特に大きいので「ヘヴィサイドの演算子法」とも呼ばれるが、厳密な理論化はその後の数学者たちにより行われた。 (ja) Cálculo operacional, também conhecido como análise operacional, é uma técnica pela qual os problemas em análise, em particular equações diferenciais, são transformados em problemas algébricos, geralmente, o problema de resolver uma equação polinomial. (pt) Операционное исчисление — один из методов математического анализа, позволяющий в ряде случаев с помощью простых средств решать сложные математические задачи. (ru) En mathématiques et plus précisément en analyse fonctionnelle, le calcul opérationnel repose essentiellement sur un astucieux changement de variable basé sur la transformée de Laplace permettant l'algébrisation des symboles de dérivation et d'intégration des expressions mathématiques décrivant les phénomènes linéaires. Certains ingénieurs emploient de préférence la transformation de « Laplace-Carson », une constante ayant comme image la même constante. La transformation directe est notée : image de . La transformation inverse est notée : original de . (fr) |
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Operatorenrechnung nach Heaviside (de) Operational calculus (en) Calcul opérationnel (fr) 演算子法 (ja) Cálculo operacional (pt) Операционное исчисление (ru) |
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