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[[Category:Sci–Tech_Index]] | |||
This is a part of the [https://polyglotclub.com/wiki/Language/Multiple-languages/Culture/Introduction-to-Sci%E2%80%93Tech-Index Sci–Tech Index], a project for science and technology learners. | |||
In progress. | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequaisite | |||
! 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] | ||
! 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 | ||
|- | |||
| mathematical analysis || | |||
| 数学分析 || | |||
| shùxué fēnxî || | |||
| Analysis [f] || | |||
| analyse [f] || | |||
| 解析学 || | |||
| か↑いせき↓がく || | |||
| ана́лиз [м] || | |||
|- | |- | ||
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Line 122: | Line 32: | ||
| || | | || | ||
|- | |- | ||
| | | calculus || | ||
| | | 微积分学 || | ||
| | | wēijīfēn xué || | ||
| | | Infinitesimalrechnung [f] || | ||
| | | calcul [m] infinitésimal || | ||
| | | 微分積分学 || | ||
| | | び↑ぶんせきぶ↓んがく || | ||
| | | математи́ческий ана́лиз || | ||
|- | |- | ||
| | | vector calculus, vector analysis || | ||
| | | 向量分析,向量微积分 || | ||
| | | xiàngliàn fēnxī, xiàngliàng wēijīfēn || | ||
| | | Vektoranalysis [f] || | ||
| | | analyse [f] vectorielle || | ||
| | | ベクトル解析 || | ||
| | | ベ↑クトルか↓いせき || | ||
| | | ве́кторный ана́лиз || | ||
|- | |- | ||
| | | multivariable calculus, multivariate calculus || | ||
| | | 多元微积分,多变量微积分 || | ||
| | | duōyuán wēijīfēn, duō biànliàng wēijīfēn || | ||
| | | multivariable Infinitesimalrechnung || | ||
| | | 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 || | ||
|- | |- | ||
| | | real analysis || | ||
| | | 实分析,实数分析,实变函数论 || | ||
| | | shí fēnxī, shíshù fēnxī, shí biàn hánshù lùn || | ||
| | | reelle Analysis || | ||
| | | analyse [f] réelle || | ||
| | | 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 || | ||
|- | |- | ||
| | | complex analysis || | ||
| | | 复分析 || | ||
| | | fù fēnxī || | ||
| | | Funktionentheorie [f] || | ||
| | | analyse [f] complexe || | ||
| | | 複素解析 || | ||
| | | ふ↑くそか↓いせき || | ||
| | | ко́мпле́ксный ана́лиз, тео́рия фу́нкций ко́мпле́ксного переме́нного, тео́рия фу́нкций ко́мпле́ксной переме́нной || | ||
|- | |- | ||
| | | functional analysis || | ||
| | | 泛函分析 || | ||
| | | fànhán fēnxī || | ||
| | | Funktionalanalysis [f] || | ||
| | | analyse [f] fonctionnelle || | ||
| | | 関数解析学 || | ||
| | | か↑んす↓うか↑いせき↓がく || | ||
| | | функциона́льный ана́лиз || | ||
|- | |- | ||
| | | Fourier analysis || | ||
| | | 傅里叶分析 || | ||
| | | Fùlǐyè fēnxī || | ||
| | | Fourier-Analysis [f], Fourier-Analyse [f] || | ||
| | | analyse [f] de Fourier || | ||
| | | フーリエ解析 || | ||
| | | フ↓ーリエかいせき || | ||
| | | ана́лиз Фурье́ || | ||
|- | |- | ||
| | | harmonic analysis || | ||
| | | 调和分析,谐波分析 || | ||
| | | tiáohé fēnxī, xiébō fēnxī || | ||
| | | harmonische Analyse, harmonische 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" | |||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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 | |||
|- | |- | ||
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| backward difference || finite difference | |||
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| central difference || finite difference | |||
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| continuous function || argument <mathematical logic> | |||
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| definite integral || second fundamental theorem of calculus | |||
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| derivative || function of a real variable <algebra> | |||
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| difference quotient || finite difference | |||
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| differentiable function || derivative; domain <mathematical logic> | |||
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| differentiation || derivative | |||
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| discontinuous function || argument <mathematical logic> | |||
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| finite difference || function <mathematical logic> | |||
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| forward difference || finite difference | |||
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| indefinite integral || integral; antiderivative | |||
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| indeterminate form || infinity <number theory> | |||
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| infinitesimal, infinitesimal number || real number | |||
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| integral || infinitesimal | |||
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| Leibniz integral rule || partial derivative | |||
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| limit || function; sequence | |||
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| linear approximation || affine transformation <geometry> | |||
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| Lipschitz continuity || uniform continuity | |||
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| | | maxima [pl:maxima] || function | ||
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| minimum [pl:minima] || function | |||
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| multiple integral || definite integral | |||
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| partial derivative || derivative | |||
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| second derivative, second order derivative || derivative | |||
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| stationary point || differentiable function; derivative | |||
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| Taylor polynomial || Taylor's theorem | |||
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| total derivative || | |||
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{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ differentiation rule | |+ differentiation rule | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 524: | Line 398: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| differentiation rule || | |||
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| chain rule || function composition; differentiable function | |||
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| general Leibniz rule || product rule | |||
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| inverse function rule || differentiable function; inverse function | |||
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| power rule || differentiable function | |||
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| product rule, Leibniz rule || differentiable function | |||
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| quotient rule || differentiable function | |||
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| reciprocal rule || multiplicative inverse; differentiable function | |||
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Line 626: | Line 500: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ extremum | |+ extremum | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 | ||
| | | extremum [pl:extrema] || function <mathematical logic> | ||
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| absolute maximum, global maximum || maximum; domain <set theory> | |||
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Line 653: | Line 526: | ||
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| absolute minimum, global minimum || minimum; domain <set theory> | |||
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| relative maximum, local maximum || maximum; interval <topology> | |||
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Line 671: | Line 544: | ||
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| relative minimum, local minimum || minimum; interval <topology> | |||
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Line 692: | Line 565: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ integral transform | |+ integral transform | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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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Line 728: | Line 582: | ||
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| Fourier transform || | | Fourier transform || | ||
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{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 | ||
| notation for differentiation || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 929: | Line 683: | ||
| || | | || | ||
|- | |- | ||
| Euler's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 938: | Line 692: | ||
| || | | || | ||
|- | |- | ||
| Lagrange's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 947: | Line 701: | ||
| || | | || | ||
|- | |- | ||
| Leibniz's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 956: | Line 710: | ||
| || | | || | ||
|- | |- | ||
| Newton's notation || differentiation | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 977: | Line 731: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ series | |+ series | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 986: | Line 740: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| series || addition <number theory>; infinity <number theory> | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,004: | Line 758: | ||
| || | | || | ||
|- | |- | ||
| alternating series || series | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,013: | Line 767: | ||
| || | | || | ||
|- | |- | ||
| convergent series || limit | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,022: | Line 776: | ||
| || | | || | ||
|- | |- | ||
| divergent series || limit | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,031: | Line 785: | ||
| || | | || | ||
|- | |- | ||
| Fourier series || series; periodic function; sine wave <trigonometry> | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,040: | Line 794: | ||
| || | | || | ||
|- | |- | ||
| geometric series || series; ratio | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,049: | Line 803: | ||
| || | | || | ||
|- | |- | ||
| Gregory's series || Taylor series; inverse trigonometric functions <trigonometry> | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,058: | Line 812: | ||
| || | | || | ||
|- | |- | ||
| harmonic series || series | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,067: | Line 821: | ||
| || | | || | ||
|- | |- | ||
| partial sum || series; sum <number theory> | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,076: | Line 830: | ||
| || | | || | ||
|- | |- | ||
| Taylor series || series; derivative | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,085: | Line 839: | ||
| || | | || | ||
|- | |- | ||
| telescoping series || series | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,107: | Line 861: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ theorem in calculus | |+ theorem in calculus | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 1,116: | Line 870: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| theorem in calculus || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,134: | Line 888: | ||
| || | | || | ||
|- | |- | ||
| extreme value theorem || continuous function; maximum; minimum | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,143: | Line 897: | ||
| || | | || | ||
|- | |- | ||
| first fundamental theorem of calculus || continuous function; closed interval <topology>; antiderivative | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,152: | Line 906: | ||
| || | | || | ||
|- | |- | ||
| L'Hôpital's rule || limit; indeterminate form | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,161: | Line 915: | ||
| || | | || | ||
|- | |- | ||
| Rolle's theorem, Rolle's lemma || stationary point | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,170: | Line 924: | ||
| || | | || | ||
|- | |- | ||
| second fundamental theorem of calculus || interval <algebra>; antiderivative | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,179: | Line 933: | ||
| || | | || | ||
|- | |- | ||
| Taylor's theorem || differentiable function; linear appriximation | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,198: | Line 952: | ||
|} | |} | ||
=== Vector Calculus, Vector Analysis === | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 | ||
|- | |- | ||
| || | | || | ||
Line 1,226: | Line 971: | ||
| || | | || | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
Line 1,282: | Line 982: | ||
|} | |} | ||
=== | === Multivariable Calculus, Multivariate Calculus === | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | ! eng-Latn-US: concept !! eng-Latn-US: prerequisite | ||
! 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] | ||
! 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 1,332: | Line 1,002: | ||
| || | | || | ||
|- | |- | ||
| differential operator || operator <algebra>; differentiation | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,341: | Line 1,011: | ||
| || | | || | ||
|- | |- | ||
| triple product rule, cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule || partial derivative | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,362: | Line 1,032: | ||
== Real Analysis == | == Real Analysis == | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 1,392: | Line 1,062: | ||
== Complex Analysis == | == Complex Analysis == | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 1,410: | Line 1,080: | ||
| || | | || | ||
|- | |- | ||
| complex plane || Cartesian coordinate system <geometry>; complex number <number theory> | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,419: | Line 1,089: | ||
| || | | || | ||
|- | |- | ||
| imaginary axis || imaginary line | |||
| 虚轴 || | | 虚轴 || | ||
| xū zhóu || | | xū zhóu || | ||
| imaginäre Achse || | | imaginäre Achse || | ||
| || | | || | ||
| || | | || | ||
Line 1,428: | Line 1,098: | ||
| || | | || | ||
|- | |- | ||
| imaginary line || line <geometry>; point <geometry>; imaginary number <arithmetic> | |||
| 虚数线 || | | 虚数线 || | ||
| xūshù xiàn || | | xūshù xiàn || | ||
| imaginäre Linie || | | imaginäre Linie || | ||
| || | | || | ||
| || | | || | ||
Line 1,437: | Line 1,107: | ||
| || | | || | ||
|- | |- | ||
| real axis || real line | |||
| 实轴 || | | 实轴 || | ||
| shí zhóu || | | shí zhóu || | ||
| reelle Achse || | | reelle Achse || | ||
| || | | || | ||
| || | | || | ||
Line 1,446: | Line 1,116: | ||
| || | | || | ||
|- | |- | ||
| real line || line <geometry>; point <geometry>; real number <arithmetic> | |||
| 实数线 || | | 实数线 || | ||
| shíshù xiàn || | | shíshù xiàn || | ||
| reelle Linie || | | reelle Linie || | ||
| || | | || | ||
| || | | || | ||
Line 1,467: | Line 1,137: | ||
== Functional Analysis == | == Functional Analysis == | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 1,497: | Line 1,167: | ||
== Numerical Analysis == | == Numerical Analysis == | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 1,515: | Line 1,185: | ||
| || | | || | ||
|- | |- | ||
| truncation error || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
Line 1,536: | Line 1,206: | ||
== Fourier Analysis == | == Fourier Analysis == | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 1,566: | Line 1,236: | ||
== Harmonic Analysis == | == Harmonic Analysis == | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! 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] | ||
! 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 | |||
|- | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
|- | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
| || | |||
|} | |||
[[File:432px-Fourier_Series.svg.png]] | |||
== * Appendix * == | |||
=== Adjective & Adjective Phrase; Verb & Verb Phrase === | |||
{| class="wikitable sortable" | |||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | ! eng-Latn-US: concept !! eng-Latn-US: prerequisite | ||
! 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] | ! 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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=== Symbol === | |||
{| class="wikitable sortable" | |||
! symbol | |||
! eng-Latn-US: concept | |||
! cmn-Hans-CN: 概念 | |||
! cmn-Latn.Pinyin-CN: gàiniàn | |||
! deu-Latn-DE: Begriff [m] | |||
! 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 === | |||
{| class="wikitable sortable" | |||
! eng-Latn-US: process !! eng-Latn-US: constituent | |||
! 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] | |||
! 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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=== Related Free Educational Resources === | |||
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! public license | |||
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{{Sci-Tech-Index-Menu}} | {{Sci-Tech-Index-Menu}} | ||