Difference between revisions of "Language/Multiple-languages/Vocabulary/Mathematical-Analysis"
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! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | ! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| || | | || | ||
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| || | | || | ||
|- | |- | ||
| 微积分学 || | | 微积分学 || | ||
| wēijīfēn xué || | | wēijīfēn xué || | ||
| Infinitesimalrechnung [f] || | | Infinitesimalrechnung [f] || | ||
| calcul | | calcul infinitésimal || | ||
| calculus || | |||
| 微分積分学 || | | 微分積分学 || | ||
| び↑ぶんせきぶ↓んがく || | | び↑ぶんせきぶ↓んがく || | ||
| математи́ческий ана́лиз || | | математи́ческий ана́лиз || | ||
|- | |- | ||
| 向量分析,向量微积分 || | | 向量分析,向量微积分 || | ||
| xiàngliàn fēnxī, xiàngliàng wēijīfēn || | | xiàngliàn fēnxī, xiàngliàng wēijīfēn || | ||
| Vektoranalysis [f] || | | Vektoranalysis [f] || | ||
| analyse | | vector calculus, vector analysis || | ||
| analyse vectorielle || | |||
| ベクトル解析 || | | ベクトル解析 || | ||
| ベ↑クトルか↓いせき || | | ベ↑クトルか↓いせき || | ||
| ве́кторный ана́лиз || | | ве́кторный ана́лиз || | ||
|- | |- | ||
| 多元微积分,多变量微积分 || | | 多元微积分,多变量微积分 || | ||
| duōyuán wēijīfēn, duō biànliàng wēijīfēn || | | duōyuán wēijīfēn, duō biànliàng wēijīfēn || | ||
| multivariable Infinitesimalrechnung || | | multivariable Infinitesimalrechnung || | ||
| multivariable calculus, multivariate calculus || | |||
| calcul [m] à plusieurs variables || | | calcul [m] à plusieurs variables || | ||
| 多変数微分積分学, 多変数解析学 || | | 多変数微分積分学, 多変数解析学 || | ||
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| многоме́рный ана́лиз || | | многоме́рный ана́лиз || | ||
|- | |- | ||
| 实分析,实数分析,实变函数论 || | | 实分析,实数分析,实变函数论 || | ||
| shí fēnxī, shíshù fēnxī, shí biàn hánshù lùn || | | shí fēnxī, shíshù fēnxī, shí biàn hánshù lùn || | ||
| reelle Analysis || | | reelle Analysis || | ||
| analyse | | analyse réelle || | ||
| real analysis || | |||
| 実解析, 実関数論 || | | 実解析, 実関数論 || | ||
| じ↑つか↓いせき, じ↑つかんすうろ↓ん || | | じ↑つか↓いせき, じ↑つかんすうろ↓ん || | ||
| тео́рия фу́нкций веще́ственной переме́нной, тео́рия фу́нкций действи́тельного переме́нного || | | тео́рия фу́нкций веще́ственной переме́нной, тео́рия фу́нкций действи́тельного переме́нного || | ||
|- | |- | ||
| 复分析 || | | 复分析 || | ||
| fù fēnxī || | | fù fēnxī || | ||
| Funktionentheorie [f] || | | Funktionentheorie [f] || | ||
| complex analysis || | |||
| analyse [f] complexe || | | analyse [f] complexe || | ||
| 複素解析 || | | 複素解析 || | ||
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| ко́мпле́ксный ана́лиз, тео́рия фу́нкций ко́мпле́ксного переме́нного, тео́рия фу́нкций ко́мпле́ксной переме́нной || | | ко́мпле́ксный ана́лиз, тео́рия фу́нкций ко́мпле́ксного переме́нного, тео́рия фу́нкций ко́мпле́ксной переме́нной || | ||
|- | |- | ||
| 泛函分析 || | | 泛函分析 || | ||
| fànhán fēnxī || | | fànhán fēnxī || | ||
| Funktionalanalysis [f] || | | Funktionalanalysis [f] || | ||
| analyse | | functional analysis || | ||
| analyse fonctionnelle || | |||
| 関数解析学 || | | 関数解析学 || | ||
| か↑んす↓うか↑いせき↓がく || | | か↑んす↓うか↑いせき↓がく || | ||
| функциона́льный ана́лиз || | | функциона́льный ана́лиз || | ||
|- | |- | ||
| 傅里叶分析 || | | 傅里叶分析 || | ||
| Fùlǐyè fēnxī || | | Fùlǐyè fēnxī || | ||
| Fourier-Analysis [f], Fourier-Analyse [f] || | | Fourier-Analysis [f], Fourier-Analyse [f] || | ||
| Fourier analysis || | |||
| analyse [f] de Fourier || | | analyse [f] de Fourier || | ||
| フーリエ解析 || | | フーリエ解析 || | ||
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| ана́лиз Фурье́ || | | ана́лиз Фурье́ || | ||
|- | |- | ||
| 调和分析,谐波分析 || | | 调和分析,谐波分析 || | ||
| tiáohé fēnxī, xiébō fēnxī || | | tiáohé fēnxī, xiébō fēnxī || | ||
| harmonische Analyse, harmonische Analysis || | | harmonische Analyse, harmonische Analysis || | ||
| harmonic analysis || | |||
| analyse [f] harmonique || | | analyse [f] harmonique || | ||
| 調和解析 || | | 調和解析 || | ||
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=== Calculus === | === Calculus === | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 132: | Line 123: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| backward difference || finite difference | |||
| || | | || | ||
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| || | | || | ||
|- | |- | ||
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| || | | || | ||
| || | | || | ||
| central difference || finite difference | |||
| || | | || | ||
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|- | |- | ||
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| continuous function || argument <mathematical logic> | |||
| || | | || | ||
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|- | |- | ||
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| definite integral || second fundamental theorem of calculus | |||
| || | | || | ||
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|- | |- | ||
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| derivative || function of a real variable <algebra> | |||
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|- | |- | ||
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| difference quotient || finite difference | |||
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|- | |- | ||
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| differentiable function || derivative; domain <mathematical logic> | |||
| || | | || | ||
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| || | | || | ||
|- | |- | ||
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| || | | || | ||
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| differentiation || derivative | |||
| || | | || | ||
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|- | |- | ||
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| discontinuous function || argument <mathematical logic> | |||
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|- | |- | ||
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| finite difference || function <mathematical logic> | |||
| || | | || | ||
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|- | |- | ||
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| forward difference || finite difference | |||
| || | | || | ||
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|- | |- | ||
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| indefinite integral || integral; antiderivative | |||
| || | | || | ||
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|- | |- | ||
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| indeterminate form || infinity <number theory> | |||
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|- | |- | ||
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| infinitesimal, infinitesimal number || real number | |||
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|- | |- | ||
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| integral || infinitesimal | |||
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|- | |- | ||
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| Leibniz integral rule || partial derivative | |||
| || | | || | ||
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|- | |- | ||
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| limit || function; sequence | |||
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|- | |- | ||
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| linear approximation || affine transformation <geometry> | |||
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|- | |- | ||
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| Lipschitz continuity || uniform continuity | |||
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|- | |- | ||
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| maximum [pl:maxima] || function | |||
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|- | |- | ||
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| minimum [pl:minima] || function | |||
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|- | |- | ||
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| multiple integral || definite integral | |||
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|- | |- | ||
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| partial derivative || derivative | |||
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|- | |- | ||
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| second derivative, second order derivative || derivative | |||
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|- | |- | ||
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| stationary point || differentiable function; derivative | |||
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|- | |- | ||
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| Taylor polynomial || Taylor's theorem | |||
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|- | |- | ||
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| total derivative || | |||
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{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ differential equation | |+ differential equation | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 396: | Line 387: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| || | | || | ||
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| differential equation || | |||
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|- | |- | ||
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| delay differential equations || derivative | |||
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|- | |- | ||
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| differential-algebraic system of equations || | |||
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|- | |- | ||
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| integro-differential equation || integral; derivative | |||
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|- | |- | ||
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| ordinary differential equation || derivative; independent variable | |||
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Line 450: | Line 441: | ||
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|- | |- | ||
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| partial differential equation || partial derivative; multivariable function | |||
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|- | |- | ||
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| stochastic differential equation || stochastic process <probability theory>; differential equation | |||
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|- | |- | ||
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| stochastic partial differential equation || stochastic process <probability theory>; partial differential equation | |||
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Line 489: | Line 480: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ differentiation rule | |+ differentiation rule | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 498: | Line 489: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| differentiation rule || | |||
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|- | |- | ||
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| chain rule || function composition; differentiable function | |||
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|- | |- | ||
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| general Leibniz rule || product rule | |||
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|- | |- | ||
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| inverse function rule || differentiable function; inverse function | |||
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|- | |- | ||
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| power rule || differentiable function | |||
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|- | |- | ||
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| product rule, Leibniz rule || differentiable function | |||
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|- | |- | ||
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| quotient rule || differentiable function | |||
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|- | |- | ||
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| reciprocal rule || multiplicative inverse; differentiable function | |||
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{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ extremum | |+ extremum | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | ! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
| | |- | ||
| || | | || | ||
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| extremum [pl:extrema] || function <mathematical logic> | |||
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|- | |- | ||
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| absolute maximum, global maximum || maximum; domain <set theory> | |||
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Line 626: | Line 618: | ||
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|- | |- | ||
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| absolute minimum, global minimum || minimum; domain <set theory> | |||
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|- | |- | ||
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| relative maximum, local maximum || maximum; interval <topology> | |||
| || | | || | ||
| || | | || | ||
Line 644: | Line 636: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| relative minimum, local minimum || minimum; interval <topology> | |||
| || | | || | ||
| || | | || | ||
Line 665: | Line 657: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ integral transform | |+ integral transform | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | ! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
| | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| integral transform || | |||
| || | | || | ||
| || | | || | ||
Line 691: | Line 684: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Abel transform || | |||
| || | | || | ||
| || | | || | ||
Line 700: | Line 693: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| associated Legendre transform || | |||
| || | | || | ||
| || | | || | ||
Line 709: | Line 702: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Fourier cosine transform || | |||
| || | | || | ||
| || | | || | ||
Line 718: | Line 711: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Fourier sine transform || | |||
| || | | || | ||
| || | | || | ||
Line 727: | Line 720: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Fourier transform || | |||
| || | | || | ||
| || | | || | ||
Line 736: | Line 729: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Hankel transform || | |||
| || | | || | ||
| || | | || | ||
Line 745: | Line 738: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Hartley transform || | |||
| || | | || | ||
| || | | || | ||
Line 754: | Line 747: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Hermite transform || | |||
| || | | || | ||
| || | | || | ||
Line 763: | Line 756: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Hilbert transform || | |||
| || | | || | ||
| || | | || | ||
Line 772: | Line 765: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Jacobi transform || | |||
| || | | || | ||
| || | | || | ||
Line 781: | Line 774: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Laguerre transform || | |||
| || | | || | ||
| || | | || | ||
Line 790: | Line 783: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Laplace transform || | |||
| || | | || | ||
| || | | || | ||
Line 799: | Line 792: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Legendre transform || | |||
| || | | || | ||
| || | | || | ||
Line 808: | Line 801: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Mellin transform || | |||
| || | | || | ||
| || | | || | ||
Line 817: | Line 810: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Poisson kernel || | |||
| || | | || | ||
| || | | || | ||
Line 826: | Line 819: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Radon transform || | |||
| || | | || | ||
| || | | || | ||
Line 835: | Line 828: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| two-sided Laplace transform, bilateral Laplace transform || | |||
| || | | || | ||
| || | | || | ||
Line 844: | Line 837: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Weierstrass transform || | |||
| || | | || | ||
| || | | || | ||
Line 853: | Line 846: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| X-ray transform, John transform || | |||
| || | | || | ||
| || | | || | ||
Line 874: | Line 867: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ notation for differentiation | |+ notation for differentiation | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | ! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
| | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| notation for differentiation || | |||
| || | | || | ||
| || | | || | ||
Line 900: | Line 894: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Euler's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
Line 909: | Line 903: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Lagrange's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
Line 918: | Line 912: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Leibniz's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
Line 927: | Line 921: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Newton's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
Line 948: | Line 942: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ series | |+ series | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 957: | Line 951: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| series || addition <number theory>; infinity <number theory> | |||
| || | | || | ||
| || | | || | ||
Line 975: | Line 969: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| alternating series || series | |||
| || | | || | ||
| || | | || | ||
Line 984: | Line 978: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| convergent series || limit | |||
| || | | || | ||
| || | | || | ||
Line 993: | Line 987: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| divergent series || limit | |||
| || | | || | ||
| || | | || | ||
Line 1,002: | Line 996: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Fourier series || series; periodic function; sine wave <trigonometry> | |||
| || | | || | ||
| || | | || | ||
Line 1,011: | Line 1,005: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| geometric series || series; ratio | |||
| || | | || | ||
| || | | || | ||
Line 1,020: | Line 1,014: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Gregory's series || Taylor series; inverse trigonometric functions <trigonometry> | |||
| || | | || | ||
| || | | || | ||
Line 1,029: | Line 1,023: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| harmonic series || series | |||
| || | | || | ||
| || | | || | ||
Line 1,038: | Line 1,032: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| partial sum || series; sum <number theory> | |||
| || | | || | ||
| || | | || | ||
Line 1,047: | Line 1,041: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Taylor series || series; derivative | |||
| || | | || | ||
| || | | || | ||
Line 1,056: | Line 1,050: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| telescoping series || series | |||
| || | | || | ||
| || | | || | ||
Line 1,078: | Line 1,072: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ theorem in calculus | |+ theorem in calculus | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,087: | Line 1,081: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| theorem in calculus || | |||
| || | | || | ||
| || | | || | ||
Line 1,105: | Line 1,099: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| extreme value theorem || continuous function; maximum; minimum | |||
| || | | || | ||
| || | | || | ||
Line 1,114: | Line 1,108: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| first fundamental theorem of calculus || continuous function; closed interval <topology>; antiderivative | |||
| || | | || | ||
| || | | || | ||
Line 1,123: | Line 1,117: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| L'Hôpital's rule || limit; indeterminate form | |||
| || | | || | ||
| || | | || | ||
Line 1,132: | Line 1,126: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Rolle's theorem, Rolle's lemma || stationary point | |||
| || | | || | ||
| || | | || | ||
Line 1,141: | Line 1,135: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| second fundamental theorem of calculus || interval <algebra>; antiderivative | |||
| || | | || | ||
| || | | || | ||
Line 1,150: | Line 1,144: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Taylor's theorem || differentiable function; linear appriximation | |||
| || | | || | ||
| || | | || | ||
Line 1,171: | Line 1,165: | ||
==== Vector Calculus ==== | ==== Vector Calculus ==== | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,201: | Line 1,195: | ||
==== Multivariable Calculus ==== | ==== Multivariable Calculus ==== | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,219: | Line 1,213: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| differential operator || operator <algebra>; differentiation | |||
| || | | || | ||
| || | | || | ||
Line 1,228: | Line 1,222: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| triple product rule, cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule || partial derivative | |||
| || | | || | ||
| || | | || | ||
Line 1,249: | Line 1,243: | ||
=== Real Analysis === | === Real Analysis === | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,279: | Line 1,273: | ||
=== Complex Analysis === | === Complex Analysis === | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,297: | Line 1,291: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| complex plane || Cartesian coordinate system <geometry>; complex number <number theory> | |||
| || | | || | ||
| || | | || | ||
Line 1,306: | Line 1,300: | ||
| || | | || | ||
|- | |- | ||
| 虚轴 || | | 虚轴 || | ||
| xū zhóu || | | xū zhóu || | ||
| imaginäre Achse || | | imaginäre Achse || | ||
| imaginary axis || imaginary line | |||
| || | | || | ||
| || | | || | ||
Line 1,315: | Line 1,309: | ||
| || | | || | ||
|- | |- | ||
| 虚数线 || | | 虚数线 || | ||
| xūshù xiàn || | | xūshù xiàn || | ||
| imaginäre Linie || | | imaginäre Linie || | ||
| imaginary line || line <geometry>; point <geometry>; imaginary number <arithmetic> | |||
| || | | || | ||
| || | | || | ||
Line 1,324: | Line 1,318: | ||
| || | | || | ||
|- | |- | ||
| 实轴 || | | 实轴 || | ||
| shí zhóu || | | shí zhóu || | ||
| reelle Achse || | | reelle Achse || | ||
| real axis || real line | |||
| || | | || | ||
| || | | || | ||
Line 1,333: | Line 1,327: | ||
| || | | || | ||
|- | |- | ||
| 实数线 || | | 实数线 || | ||
| shíshù xiàn || | | shíshù xiàn || | ||
| reelle Linie || | | reelle Linie || | ||
| real line || line <geometry>; point <geometry>; real number <arithmetic> | |||
| || | | || | ||
| || | | || | ||
Line 1,354: | Line 1,348: | ||
=== Functional Analysis === | === Functional Analysis === | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,384: | Line 1,378: | ||
=== Numerical Analysis === | === Numerical Analysis === | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,402: | Line 1,396: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| truncation error || | |||
| || | | || | ||
| || | | || | ||
Line 1,423: | Line 1,417: | ||
=== Fourier Analysis === | === Fourier Analysis === | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,453: | Line 1,447: | ||
=== Harmonic Analysis === | === Harmonic Analysis === | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,484: | Line 1,478: | ||
=== Sentence === | === Sentence === | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 语句 !! cmn-Hans-CN: 前提 | |||
! cmn-Hans-CN: | ! cmn-Latn.Pinyin-CN: yǔjù !! cmn-Latn.Pinyin-CN: qiántí | ||
! cmn-Latn.Pinyin-CN: | ! deu-Latn-DE: Satz [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! deu-Latn-DE: | ! eng-Latn-US: sentence !! eng-Latn-US: prerequisite | ||
! fra-Latn-FR: | ! fra-Latn-FR: phrase [f] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: | ! jpn-Jpan-JP: 文章 !! jpn-Jpan-JP: 前提 | ||
! jpn-Hrkt-JP: | ! jpn-Hrkt-JP: ぶ↑んしょ↓う !! jpn-Hrkt-JP: ぜ↑んてい | ||
! rus-Cyrl-RU: | ! rus-Cyrl-RU: фра́за !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| || | | || | ||
Line 1,515: | Line 1,509: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! symbol | ! symbol | ||
! cmn-Hans-CN: 概念 | ! cmn-Hans-CN: 概念 | ||
! cmn-Latn.Pinyin-CN: gàiniàn | ! cmn-Latn.Pinyin-CN: gàiniàn | ||
! deu-Latn-DE: Begriff [m] | ! deu-Latn-DE: Begriff [m] | ||
! eng-Latn-US: concept | |||
! fra-Latn-FR: concept [m] | ! fra-Latn-FR: concept [m] | ||
! jpn-Jpan-JP: 概念 | ! jpn-Jpan-JP: 概念 | ||
Line 1,547: | Line 1,541: | ||
=== Process === | === Process === | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 过程 !! cmn-Hans-CN: 构件 | ! cmn-Hans-CN: 过程 !! cmn-Hans-CN: 构件 | ||
! cmn-Latn.Pinyin-CN: guòchéng !! cmn-Latn.Pinyin-CN: gòujiàn | ! cmn-Latn.Pinyin-CN: guòchéng !! cmn-Latn.Pinyin-CN: gòujiàn | ||
! deu-Latn-DE: Prozess [m] !! deu-Latn-DE: Bestandteil [m] | ! deu-Latn-DE: Prozess [m] !! deu-Latn-DE: Bestandteil [m] | ||
! eng-Latn-US: process !! eng-Latn-US: constituent | |||
! fra-Latn-FR: procès [m] !! fra-Latn-FR: composant [m] | ! fra-Latn-FR: procès [m] !! fra-Latn-FR: composant [m] | ||
! jpn-Jpan-JP: 過程 !! jpn-Jpan-JP: 構材 | ! jpn-Jpan-JP: 過程 !! jpn-Jpan-JP: 構材 |
Revision as of 08:19, 26 March 2022
Hello polyglots, 😀
On this page you will find a part of the Sci–Tech Index, a project for science and technology learners.
eng-Latn-US: concept | eng-Latn-US: prerequaisite | cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
微积分学 | wēijīfēn xué | Infinitesimalrechnung [f] | calcul infinitésimal | calculus | 微分積分学 | び↑ぶんせきぶ↓んがく | математи́ческий ана́лиз | ||||||||
向量分析,向量微积分 | xiàngliàn fēnxī, xiàngliàng wēijīfēn | Vektoranalysis [f] | vector calculus, vector analysis | analyse vectorielle | ベクトル解析 | ベ↑クトルか↓いせき | ве́кторный ана́лиз | ||||||||
多元微积分,多变量微积分 | duōyuán wēijīfēn, duō biànliàng wēijīfēn | multivariable Infinitesimalrechnung | multivariable calculus, multivariate calculus | calcul [m] à plusieurs variables | 多変数微分積分学, 多変数解析学 | た↑へ↓んすうび↑ぶんせきぶ↓んがく, た↑へ↓んすうか↑いせき↓がく | многоме́рный ана́лиз | ||||||||
实分析,实数分析,实变函数论 | shí fēnxī, shíshù fēnxī, shí biàn hánshù lùn | reelle Analysis | analyse réelle | real analysis | 実解析, 実関数論 | じ↑つか↓いせき, じ↑つかんすうろ↓ん | тео́рия фу́нкций веще́ственной переме́нной, тео́рия фу́нкций действи́тельного переме́нного | ||||||||
复分析 | fù fēnxī | Funktionentheorie [f] | complex analysis | analyse [f] complexe | 複素解析 | ふ↑くそか↓いせき | ко́мпле́ксный ана́лиз, тео́рия фу́нкций ко́мпле́ксного переме́нного, тео́рия фу́нкций ко́мпле́ксной переме́нной | ||||||||
泛函分析 | fànhán fēnxī | Funktionalanalysis [f] | functional analysis | analyse fonctionnelle | 関数解析学 | か↑んす↓うか↑いせき↓がく | функциона́льный ана́лиз | ||||||||
傅里叶分析 | Fùlǐyè fēnxī | Fourier-Analysis [f], Fourier-Analyse [f] | Fourier analysis | analyse [f] de Fourier | フーリエ解析 | フ↓ーリエかいせき | ана́лиз Фурье́ | ||||||||
调和分析,谐波分析 | tiáohé fēnxī, xiébō fēnxī | harmonische Analyse, harmonische Analysis | harmonic analysis | analyse [f] harmonique | 調和解析 | ちょ↑うわか↓いせき | гармони́ческий ана́лиз | ||||||||
Main
Calculus
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
backward difference | finite difference | ||||||||||||||
central difference | finite difference | ||||||||||||||
continuous function | argument <mathematical logic> | ||||||||||||||
definite integral | second fundamental theorem of calculus | ||||||||||||||
derivative | function of a real variable <algebra> | ||||||||||||||
difference quotient | finite difference | ||||||||||||||
differentiable function | derivative; domain <mathematical logic> | ||||||||||||||
differentiation | derivative | ||||||||||||||
discontinuous function | argument <mathematical logic> | ||||||||||||||
finite difference | function <mathematical logic> | ||||||||||||||
forward difference | finite difference | ||||||||||||||
indefinite integral | integral; antiderivative | ||||||||||||||
indeterminate form | infinity <number theory> | ||||||||||||||
infinitesimal, infinitesimal number | real number | ||||||||||||||
integral | infinitesimal | ||||||||||||||
Leibniz integral rule | partial derivative | ||||||||||||||
limit | function; sequence | ||||||||||||||
linear approximation | affine transformation <geometry> | ||||||||||||||
Lipschitz continuity | uniform continuity | ||||||||||||||
maximum [pl:maxima] | function | ||||||||||||||
minimum [pl:minima] | function | ||||||||||||||
multiple integral | definite integral | ||||||||||||||
partial derivative | derivative | ||||||||||||||
second derivative, second order derivative | derivative | ||||||||||||||
stationary point | differentiable function; derivative | ||||||||||||||
Taylor polynomial | Taylor's theorem | ||||||||||||||
total derivative | |||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
differential equation | |||||||||||||||
delay differential equations | derivative | ||||||||||||||
differential-algebraic system of equations | |||||||||||||||
integro-differential equation | integral; derivative | ||||||||||||||
ordinary differential equation | derivative; independent variable | ||||||||||||||
partial differential equation | partial derivative; multivariable function | ||||||||||||||
stochastic differential equation | stochastic process <probability theory>; differential equation | ||||||||||||||
stochastic partial differential equation | stochastic process <probability theory>; partial differential equation | ||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
differentiation rule | |||||||||||||||
chain rule | function composition; differentiable function | ||||||||||||||
general Leibniz rule | product rule | ||||||||||||||
inverse function rule | differentiable function; inverse function | ||||||||||||||
power rule | differentiable function | ||||||||||||||
product rule, Leibniz rule | differentiable function | ||||||||||||||
quotient rule | differentiable function | ||||||||||||||
reciprocal rule | multiplicative inverse; differentiable function | ||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
extremum [pl:extrema] | function <mathematical logic> | ||||||||||||||
absolute maximum, global maximum | maximum; domain <set theory> | ||||||||||||||
absolute minimum, global minimum | minimum; domain <set theory> | ||||||||||||||
relative maximum, local maximum | maximum; interval <topology> | ||||||||||||||
relative minimum, local minimum | minimum; interval <topology> | ||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
integral transform | |||||||||||||||
Abel transform | |||||||||||||||
associated Legendre transform | |||||||||||||||
Fourier cosine transform | |||||||||||||||
Fourier sine transform | |||||||||||||||
Fourier transform | |||||||||||||||
Hankel transform | |||||||||||||||
Hartley transform | |||||||||||||||
Hermite transform | |||||||||||||||
Hilbert transform | |||||||||||||||
Jacobi transform | |||||||||||||||
Laguerre transform | |||||||||||||||
Laplace transform | |||||||||||||||
Legendre transform | |||||||||||||||
Mellin transform | |||||||||||||||
Poisson kernel | |||||||||||||||
Radon transform | |||||||||||||||
two-sided Laplace transform, bilateral Laplace transform | |||||||||||||||
Weierstrass transform | |||||||||||||||
X-ray transform, John transform | |||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
notation for differentiation | |||||||||||||||
Euler's notation | differentiation | ||||||||||||||
Lagrange's notation | differentiation | ||||||||||||||
Leibniz's notation | differentiation | ||||||||||||||
Newton's notation | differentiation | ||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
series | addition <number theory>; infinity <number theory> | ||||||||||||||||
alternating series | series | ||||||||||||||||
convergent series | limit | ||||||||||||||||
divergent series | limit | ||||||||||||||||
Fourier series | series; periodic function; sine wave <trigonometry> | ||||||||||||||||
geometric series | series; ratio | ||||||||||||||||
Gregory's series | Taylor series; inverse trigonometric functions <trigonometry> | ||||||||||||||||
harmonic series | series | ||||||||||||||||
partial sum | series; sum <number theory> | ||||||||||||||||
Taylor series | series; derivative | ||||||||||||||||
telescoping series | series | ||||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
theorem in calculus | |||||||||||||||
extreme value theorem | continuous function; maximum; minimum | ||||||||||||||
first fundamental theorem of calculus | continuous function; closed interval <topology>; antiderivative | ||||||||||||||
L'Hôpital's rule | limit; indeterminate form | ||||||||||||||
Rolle's theorem, Rolle's lemma | stationary point | ||||||||||||||
second fundamental theorem of calculus | interval <algebra>; antiderivative | ||||||||||||||
Taylor's theorem | differentiable function; linear appriximation | ||||||||||||||
Vector Calculus
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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Multivariable Calculus
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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differential operator | operator <algebra>; differentiation | ||||||||||||||
triple product rule, cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule | partial derivative | ||||||||||||||
Real Analysis
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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Complex Analysis
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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complex plane | Cartesian coordinate system <geometry>; complex number <number theory> | ||||||||||||||
虚轴 | xū zhóu | imaginäre Achse | imaginary axis | imaginary line | |||||||||||
虚数线 | xūshù xiàn | imaginäre Linie | imaginary line | line <geometry>; point <geometry>; imaginary number <arithmetic> | |||||||||||
实轴 | shí zhóu | reelle Achse | real axis | real line | |||||||||||
实数线 | shíshù xiàn | reelle Linie | real line | line <geometry>; point <geometry>; real number <arithmetic> | |||||||||||
Functional Analysis
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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Numerical Analysis
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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truncation error | |||||||||||||||
Fourier Analysis
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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Harmonic Analysis
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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Appendix
Sentence
cmn-Hans-CN: 语句 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: yǔjù | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Satz [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: sentence | eng-Latn-US: prerequisite | fra-Latn-FR: phrase [f] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 文章 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: ぶ↑んしょ↓う | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: фра́за | rus-Cyrl-RU: предпосы́лка |
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Symbol
symbol | cmn-Hans-CN: 概念 | cmn-Latn.Pinyin-CN: gàiniàn | deu-Latn-DE: Begriff [m] | eng-Latn-US: concept | fra-Latn-FR: concept [m] | jpn-Jpan-JP: 概念 | jpn-Hrkt-JP: が↓いねん | rus-Cyrl-RU: конце́пция |
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Process
cmn-Hans-CN: 过程 | cmn-Hans-CN: 构件 | cmn-Latn.Pinyin-CN: guòchéng | cmn-Latn.Pinyin-CN: gòujiàn | deu-Latn-DE: Prozess [m] | deu-Latn-DE: Bestandteil [m] | eng-Latn-US: process | eng-Latn-US: constituent | fra-Latn-FR: procès [m] | fra-Latn-FR: composant [m] | jpn-Jpan-JP: 過程 | jpn-Jpan-JP: 構材 | jpn-Hrkt-JP: か↑てい | jpn-Hrkt-JP: こ↑うざい | rus-Cyrl-RU: проце́сс | rus-Cyrl-RU: соста́вная часть |
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Resource under a Public License
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