Difference between revisions of "Language/Multiple-languages/Vocabulary/Mathematical-Analysis"
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{{Sci-Tech-Index-Intro}} | |||
{| class="wikitable sortable" | |||
! cmn-Hans-CN: 科目 | |||
! cmn-Latn.Pinyin-CN: kēmù | |||
! deu-Latn-DE: Fach [n] | |||
! eng-Latn-US: subject | |||
! fra-Latn-FR: matière [f] | |||
! jpn-Jpan-JP: 科目 | |||
! jpn-Hrkt-JP: か↑もく | |||
! rus-Cyrl-RU: предме́т | |||
|- | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
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|- | |||
| 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 [f pl] | |||
| 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 | |||
|- | |||
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|} | |||
== 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 | ||
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| || | | || | ||
|- | |- | ||
| mathematical | | || | ||
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| | | backward difference || finite difference | ||
| | | || | ||
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|- | |||
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| central difference || finite difference | |||
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|- | |||
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| constant of integration || constant term <algebra>; antiderivative | |||
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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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| 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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|- | |||
| 变限积分 || | |||
| biànxiàn jīfēn || | |||
| Integral [n] mit variablen Grenzen [f pl] || | |||
| integral with variable limits || integral; limit; variable <mathematical logic> | |||
| intégrale [f] avec limites [f pl] variables || | |||
| 可変限界との積分 || | |||
| か↑へんげ↓んかいとのせ↑きぶん || | |||
| интегра́л с переме́нными преде́лами || | |||
|- | |||
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| integration by substitution, u-substitution, reverse chain rule, change of variables || integral; antiderivative | |||
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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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| 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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| | | separation of variables, Fourier method || ordinary differential equation; partial differential equation | ||
| | | || | ||
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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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Line 114: | Line 411: | ||
|} | |} | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ 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 | ! 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 equation || | |||
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| delay differential equations || derivative | |||
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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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|- | |||
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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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|- | |||
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|} | |||
{| class="wikitable sortable" | |||
|+ 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 | ||
! 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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| differentiation rule || | |||
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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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| 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" | |||
|+ extremum | |||
! 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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| extremum [pl:extrema] || function <mathematical logic> | |||
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| absolute maximum, global maximum || maximum; domain <set theory> | |||
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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> | |||
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|- | |- | ||
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| relative minimum, local minimum || minimum; interval <topology> | |||
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|- | |- | ||
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|} | |||
{| class="wikitable sortable" | |||
|+ integral 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 | |||
|- | |||
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| integral transform || | |||
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| Abel transform || | |||
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|- | |- | ||
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| associated Legendre transform || | |||
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Line 242: | Line 737: | ||
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|- | |- | ||
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| Fourier cosine transform || | |||
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Line 251: | Line 746: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Fourier sine transform || | |||
| || | | || | ||
| || | | || | ||
Line 260: | Line 755: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Fourier transform || | |||
| || | | || | ||
| || | | || | ||
Line 269: | Line 764: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Hankel transform || | |||
| || | | || | ||
| || | | || | ||
Line 278: | Line 773: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Hartley transform || | |||
| || | | || | ||
| || | | || | ||
Line 287: | Line 782: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Hermite transform || | |||
| || | | || | ||
| || | | || | ||
Line 296: | Line 791: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Hilbert transform || | |||
| || | | || | ||
| || | | || | ||
Line 305: | Line 800: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Jacobi transform || | |||
| || | | || | ||
| || | | || | ||
Line 314: | Line 809: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Laguerre transform || | |||
| || | | || | ||
| || | | || | ||
Line 323: | Line 818: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Laplace transform || | |||
| || | | || | ||
| || | | || | ||
Line 332: | Line 827: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Legendre transform || | |||
| || | | || | ||
| || | | || | ||
Line 341: | Line 836: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Mellin transform || | |||
| || | | || | ||
| || | | || | ||
Line 350: | Line 845: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Poisson kernel || | |||
| || | | || | ||
| || | | || | ||
Line 359: | Line 854: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Radon transform || | |||
| || | | || | ||
| || | | || | ||
Line 368: | Line 863: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| two-sided Laplace transform, bilateral Laplace transform || | |||
| || | | || | ||
| || | | || | ||
Line 377: | Line 872: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Weierstrass transform || | |||
| || | | || | ||
| || | | || | ||
Line 386: | Line 881: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| X-ray transform, John transform || | |||
| || | | || | ||
| || | | || | ||
Line 406: | Line 901: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ 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 434: | Line 929: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Euler's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
Line 443: | Line 938: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Lagrange's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
Line 452: | Line 947: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Leibniz's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
Line 461: | Line 956: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Newton's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
Line 479: | Line 974: | ||
| || | | || | ||
|} | |} | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ 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 | ||
! 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 | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| series || addition <number theory>; infinity <number theory> | |||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | |||
| || | |||
| || | |||
| alternating series || series | |||
| || | | || | ||
| || | | || | ||
Line 502: | Line 1,014: | ||
|- | |- | ||
| || | | || | ||
| || | |||
| || | |||
| convergent series || limit | |||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| divergent series || limit | |||
| || | | || | ||
| || | | || | ||
Line 510: | Line 1,031: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Fourier series || series; periodic function; sine wave <trigonometry> | |||
| || | | || | ||
| || | | || | ||
Line 519: | Line 1,040: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| geometric series || series; ratio | |||
| || | | || | ||
| || | | || | ||
Line 528: | Line 1,049: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Gregory's series || Taylor series; inverse trigonometric functions <trigonometry> | |||
| || | | || | ||
| || | | || | ||
Line 537: | Line 1,058: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| harmonic series || series | |||
| || | | || | ||
| || | | || | ||
Line 546: | Line 1,067: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| partial sum || series; sum <number theory> | |||
| || | | || | ||
| || | | || | ||
Line 555: | Line 1,076: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Taylor series || series; derivative | |||
| || | | || | ||
| || | | || | ||
Line 567: | Line 1,088: | ||
| || | | || | ||
| || | | || | ||
| telescoping series || series | |||
| || | | || | ||
| || | | || | ||
Line 583: | Line 1,105: | ||
|} | |} | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ 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 595: | Line 1,117: | ||
|- | |- | ||
| || | | || | ||
| || | |||
| || | |||
| theorem in calculus || | |||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| extreme value theorem || continuous function; maximum; minimum | |||
| || | | || | ||
| || | | || | ||
Line 604: | Line 1,144: | ||
|- | |- | ||
| || | | || | ||
| || | |||
| || | |||
| 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 | |||
| || | | || | ||
| || | | || | ||
Line 633: | Line 1,179: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Taylor's theorem || differentiable function; linear appriximation | |||
| || | | || | ||
| || | | || | ||
Line 652: | Line 1,198: | ||
|} | |} | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ mean value theorem | |||
! 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 | ||
|- | |||
| 中值定理 || | |||
| zhōngzhí dìnglǐ || | |||
| Mittelwertsatz [m] || | |||
| mean value theorem || | |||
| théorème [m pl] des accroissements [m pl] finis || | |||
| 平均値の定理 || | |||
| へ↑いき↓んちの↑て↓いり || | |||
| || | |||
|- | |- | ||
| || | | || | ||
Line 671: | Line 1,226: | ||
| || | | || | ||
| || | | || | ||
|- | |||
| 柯西中值定理 || | |||
| Kēxī zhōngzhí dìnglǐ || | |||
| cauchy'scher Mittelwertsatz || | |||
| Cauchy's mean value theorem, extended mean value theorem || | |||
| théorème [m] de la moyenne de Cauchy || | |||
| コーシーの平均値定理 || | |||
| コ↓ーシーのへ↑いきんちて↓いり || | |||
| теоре́ма Коши́ о сре́днем значе́нии || | |||
|- | |||
| 积分第一中值定理 || | |||
| jīfēn dìyī zhōngzhí dìnglǐ || | |||
| erster Mittelwertsatz der Integralrechnung || | |||
| first mean value theorem for integrals || | |||
| première formule [f] de la moyenne || | |||
| 積分の第一平均値定理 || | |||
| せ↑きぶんのだ↓いい↑ちへいきんちて↓いり || | |||
| пе́рвая теоре́ма о сре́днем || | |||
|- | |||
| 拉格朗日中值定理 || | |||
| Lǎgélǎngrì zhǒngzhí dìnglǐ || | |||
| Mittelwertsatz [m] von Lagrange || | |||
| Lagrange's mean value theorem || | |||
| théorème [m] de la valeur moyenne de Lagrange || | |||
| ラグランジュの平均値の定理 || | |||
| ラ↑グラ↓ンジュのへ↑いき↓んちの↑て↓いり || | |||
| Фо́рмула коне́чных прираще́ний, теоре́ма Лагра́нжа о сре́днем значе́нии || | |||
|- | |||
| 积分第二中值定理 || | |||
| jīfēn dì'èr zhōngzhí dìnglǐ || | |||
| zweiter Mittelwertsatz der Integralrechnung || | |||
| second mean value theorem for integrals || | |||
| deuxième formule [f] de la moyenne || | |||
| 積分の第二平均値定理 || | |||
| せ↑きぶんのだ↓いにへ↑いきんちて↓いり || | |||
| Втора́я теоре́ма о сре́днем || | |||
|- | |||
| 罗尔定理 || | |||
| Luó'ěr dìnglǐ || | |||
| Satz [m] von Rolle || | |||
| Rolle's theorem, Rolle's lemma || | |||
| théorème [m] de Rolle, lemme [m] de Rolle || | |||
| ロルの定理 || | |||
| ロ↑ル↓の↑て↓いり || | |||
| теоре́ма Ро́лля || | |||
|- | |- | ||
| || | | || | ||
Line 682: | Line 1,282: | ||
|} | |} | ||
== | === 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 702: | Line 1,302: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | |||
| || | |||
| || | |||
| || | |||
|} | |||
=== Multivariable Calculus === | |||
{| class="wikitable sortable" | |||
! 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 | |||
|- | |- | ||
| | | || | ||
| | | || | ||
| | | || | ||
| | | || | ||
| || | | || | ||
| || | | || | ||
Line 720: | Line 1,332: | ||
| || | | || | ||
|- | |- | ||
| | | || | ||
| | | || | ||
| | | || | ||
| | | differential operator || operator <algebra>; differentiation | ||
| || | | || | ||
| || | | || | ||
Line 729: | Line 1,341: | ||
| || | | || | ||
|- | |- | ||
| | | || | ||
| | | || | ||
| | | || | ||
| | | triple product rule, cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule || partial derivative | ||
| || | | || | ||
| || | | || | ||
Line 748: | Line 1,360: | ||
|} | |} | ||
== | == 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 778: | Line 1,390: | ||
|} | |} | ||
== | == 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 798: | Line 1,410: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| 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> | |||
| || | | || | ||
| || | | || | ||
Line 817: | Line 1,465: | ||
|} | |} | ||
== | == 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 847: | Line 1,495: | ||
|} | |} | ||
== 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 863: | Line 1,510: | ||
| || | | || | ||
| || | | || | ||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | |||
| || | |||
| || | |||
| truncation error || | |||
| || | | || | ||
| || | | || | ||
Line 878: | Line 1,534: | ||
|} | |} | ||
== 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 911: | Line 1,564: | ||
|} | |} | ||
== | == Harmonic Analysis == | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | |||
! cmn-Hans-CN: | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! cmn-Latn.Pinyin-CN: gàiniàn | ! eng-Latn-US: concept !! eng-Latn-US: prerequisite | ||
! deu-Latn-DE: Begriff [m] | ! 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 | |||
! eng-Latn-US: | |||
! fra-Latn-FR: | |||
! jpn-Jpan-JP: | |||
! jpn-Hrkt-JP: | |||
! rus-Cyrl-RU: | |||
|- | |- | ||
| || | | || | ||
Line 974: | Line 1,594: | ||
|} | |} | ||
<center> | |||
https://upload.wikimedia.org/wikipedia/commons/f/f5/LeibnizInfinitesimalTriangle.png | |||
</center> | |||
{{Sci-Tech-Index-Menu}} | {{Sci-Tech-Index-Menu}} | ||
==Other Lessons== | |||
* [[Language/Multiple-languages/Vocabulary/Love-in-many-languages|Love in many languages]] | |||
* [[Language/Multiple-languages/Vocabulary/Unit-of-Measurement|Unit of Measurement]] | |||
* [[Language/Multiple-languages/Vocabulary/False-Friends|False Friends]] | |||
* [[Language/Multiple-languages/Vocabulary/Collocations-with-Save|Collocations with Save]] | |||
* [[Language/Multiple-languages/Vocabulary/Chaos-Theory|Chaos Theory]] | |||
* [[Language/Multiple-languages/Vocabulary/Thermodynamics|Thermodynamics]] | |||
* [[Language/Multiple-languages/Vocabulary/Computer-Science|Computer Science]] | |||
* [[Language/Multiple-languages/Vocabulary/Collocations-with-take|Collocations with take]] | |||
* [[Language/Multiple-languages/Vocabulary/Common-Han-Characters-with-⼀|Common Han Characters with ⼀]] | |||
* [[Language/Multiple-languages/Vocabulary/Cell-Biology|Cell Biology]] | |||
* [[Language/Multiple-languages/Vocabulary/I-love-you-in-all-languages|I love you in all languages]] | |||
* [[Language/Multiple-languages/Vocabulary/Cinema-in-many-languages|Cinema in many languages]] | |||
* [[Language/Multiple-languages/Vocabulary/Greetings-Where-have-you-come-from|Greetings Where have you come from]] | |||
* [[Language/Multiple-languages/Vocabulary/Number-Theory|Number Theory]] | |||
* [[Language/Multiple-languages/Vocabulary/Metalworking|Metalworking]] | |||
<span links></span> |
Latest revision as of 13:52, 27 March 2023
Hello polyglots, 😀
On this page you will find a part of the Sci–Tech Index, a project for science and technology learners.
cmn-Hans-CN: 科目 | cmn-Latn.Pinyin-CN: kēmù | deu-Latn-DE: Fach [n] | eng-Latn-US: subject | fra-Latn-FR: matière [f] | jpn-Jpan-JP: 科目 | jpn-Hrkt-JP: か↑もく | rus-Cyrl-RU: предме́т |
---|---|---|---|---|---|---|---|
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 [f pl] | 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 |
Calculus[edit | edit source]
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 | ||||||||||||||
constant of integration | constant term <algebra>; antiderivative | ||||||||||||||
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 | ||||||||||||||
变限积分 | biànxiàn jīfēn | Integral [n] mit variablen Grenzen [f pl] | integral with variable limits | integral; limit; variable <mathematical logic> | intégrale [f] avec limites [f pl] variables | 可変限界との積分 | か↑へんげ↓んかいとのせ↑きぶん | интегра́л с переме́нными преде́лами | |||||||
integration by substitution, u-substitution, reverse chain rule, change of variables | integral; antiderivative | ||||||||||||||
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 | ||||||||||||||
separation of variables, Fourier method | ordinary differential equation; partial differential equation | ||||||||||||||
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 | ||||||||||||||
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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中值定理 | zhōngzhí dìnglǐ | Mittelwertsatz [m] | mean value theorem | théorème [m pl] des accroissements [m pl] finis | 平均値の定理 | へ↑いき↓んちの↑て↓いり | |||||||||
柯西中值定理 | Kēxī zhōngzhí dìnglǐ | cauchy'scher Mittelwertsatz | Cauchy's mean value theorem, extended mean value theorem | théorème [m] de la moyenne de Cauchy | コーシーの平均値定理 | コ↓ーシーのへ↑いきんちて↓いり | теоре́ма Коши́ о сре́днем значе́нии | ||||||||
积分第一中值定理 | jīfēn dìyī zhōngzhí dìnglǐ | erster Mittelwertsatz der Integralrechnung | first mean value theorem for integrals | première formule [f] de la moyenne | 積分の第一平均値定理 | せ↑きぶんのだ↓いい↑ちへいきんちて↓いり | пе́рвая теоре́ма о сре́днем | ||||||||
拉格朗日中值定理 | Lǎgélǎngrì zhǒngzhí dìnglǐ | Mittelwertsatz [m] von Lagrange | Lagrange's mean value theorem | théorème [m] de la valeur moyenne de Lagrange | ラグランジュの平均値の定理 | ラ↑グラ↓ンジュのへ↑いき↓んちの↑て↓いり | Фо́рмула коне́чных прираще́ний, теоре́ма Лагра́нжа о сре́днем значе́нии | ||||||||
积分第二中值定理 | jīfēn dì'èr zhōngzhí dìnglǐ | zweiter Mittelwertsatz der Integralrechnung | second mean value theorem for integrals | deuxième formule [f] de la moyenne | 積分の第二平均値定理 | せ↑きぶんのだ↓いにへ↑いきんちて↓いり | Втора́я теоре́ма о сре́днем | ||||||||
罗尔定理 | Luó'ěr dìnglǐ | Satz [m] von Rolle | Rolle's theorem, Rolle's lemma | théorème [m] de Rolle, lemme [m] de Rolle | ロルの定理 | ロ↑ル↓の↑て↓いり | теоре́ма Ро́лля | ||||||||
Vector Calculus[edit | edit source]
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
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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Other Lessons[edit | edit source]
- Love in many languages
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