Difference between revisions of "Language/Multiple-languages/Vocabulary/Mathematical-Analysis"

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[[Category:Sci–Tech_Index]]
{{Sci-Tech-Index-Intro}}
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"
! 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 ==
{| 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]
! 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 23: Line 122:
|  ||  
|  ||  
|-
|-
| mathematical analysis ||  
| ||  
| 数学分析 ||  
| ||  
| shùxué fēnxî ||  
| ||  
| Analysis [f] ||  
| backward difference || finite difference
| analyse [f] ||  
| ||  
| 解析学 ||  
| ||  
| か↑いせき↓がく ||  
| ||  
| ана́лиз [м] ||  
| ||
|-
|  ||
|  ||
|  ||
| central difference || finite difference
|  ||
|  ||
|  ||
|  ||  
|-
|-
| calculus ||  
| ||  
| 微积分学 ||  
| ||  
| wēijīfēn xué ||  
| ||  
| Infinitesimalrechnung [f] ||  
| constant of integration || constant term <algebra>; antiderivative
| 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] ||  
| continuous function || argument <mathematical logic>
| 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 ||  
| definite integral || second fundamental theorem of 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 ||  
| ||  
|-
|-
| real analysis ||  
| ||  
| 实分析, 实数分析, 实变函数论 ||  
| ||  
| shí fēnxī, shíshù fēnxī, shí biàn hánshù lùn ||  
| ||  
| reelle Analysis ||  
| derivative || function of a real variable <algebra>
| 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] ||  
| difference quotient || finite difference
| 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] ||  
| differentiable function || derivative; domain <mathematical logic>
| 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] ||  
| differentiation || derivative
| 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 ||  
| discontinuous function || argument <mathematical logic>
| analyse [f] harmonique ||  
| ||  
| 調和解析 ||  
| ||  
| ちょ↑うわか↓いせき ||  
| ||  
| гармони́ческий ана́лиз ||  
| ||  
|-
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| finite difference || function <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||  
|  ||  
|  ||
|  ||
| forward difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
== 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
|-
|-
|  ||  
|  ||  
|  ||
|  ||
| indefinite integral || integral; antiderivative
|  ||
|  ||
|  ||
|  ||
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| indeterminate form || infinity <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 134: Line 248:
|  ||  
|  ||  
|-
|-
| backward difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| infinitesimal, infinitesimal number || real number
|  ||  
|  ||  
|  ||  
|  ||  
Line 143: Line 257:
|  ||  
|  ||  
|-
|-
| central difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| integral || infinitesimal
|  ||  
|  ||  
|  ||  
|  ||  
Line 152: Line 266:
|  ||  
|  ||  
|-
|-
| continuous function || argument <mathematical logic>
| 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
|  ||  
|  ||  
|  ||  
|  ||  
Line 161: Line 284:
|  ||  
|  ||  
|-
|-
| definite integral || second fundamental theorem of calculus
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Leibniz integral rule || partial derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 170: Line 293:
|  ||  
|  ||  
|-
|-
| derivative || function of a real variable <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| limit || function; sequence
|  ||  
|  ||  
|  ||  
|  ||  
Line 179: Line 302:
|  ||  
|  ||  
|-
|-
| difference quotient || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| linear approximation || affine transformation <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 188: Line 311:
|  ||  
|  ||  
|-
|-
| differentiable function || derivative; domain <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Lipschitz continuity || uniform continuity
|  ||  
|  ||  
|  ||  
|  ||  
Line 197: Line 320:
|  ||  
|  ||  
|-
|-
| differentiation || derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| maximum [pl:maxima] || function
|  ||  
|  ||  
|  ||  
|  ||  
Line 206: Line 329:
|  ||  
|  ||  
|-
|-
| discontinuous function || argument <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| minimum [pl:minima] || function
|  ||  
|  ||  
|  ||  
|  ||  
Line 215: Line 338:
|  ||  
|  ||  
|-
|-
| finite difference || function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| multiple integral || definite integral
|  ||  
|  ||  
|  ||  
|  ||  
Line 224: Line 347:
|  ||  
|  ||  
|-
|-
| forward difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| partial derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 233: Line 356:
|  ||  
|  ||  
|-
|-
| indefinite integral || integral; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| second derivative, second order derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 242: Line 365:
|  ||  
|  ||  
|-
|-
| indeterminate form || infinity <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| separation of variables, Fourier method || ordinary differential equation; partial differential equation
|  ||  
|  ||  
|  ||  
|  ||  
Line 251: Line 374:
|  ||  
|  ||  
|-
|-
| infinitesimal, infinitesimal number || real number
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| stationary point || differentiable function; derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 260: Line 383:
|  ||  
|  ||  
|-
|-
| integral || infinitesimal
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Taylor polynomial || Taylor's theorem
|  ||  
|  ||  
|  ||  
|  ||  
Line 269: Line 392:
|  ||  
|  ||  
|-
|-
| Leibniz integral rule || partial derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| total derivative ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 278: Line 401:
|  ||  
|  ||  
|-
|-
| limit || function; sequence
|  ||  
|  ||  
|  ||  
|  ||  
Line 286: Line 408:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|}
{| 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
! 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
|-
|-
| linear approximation || affine transformation <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| differential equation ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 296: Line 431:
|  ||  
|  ||  
|-
|-
| maxima [pl:maxima] || function
| ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 305: Line 440:
|  ||  
|  ||  
|-
|-
| minimum [pl:minima] || function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| delay differential equations || derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 314: Line 449:
|  ||  
|  ||  
|-
|-
| multiple integral || definite integral
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| differential-algebraic system of equations ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 323: Line 458:
|  ||  
|  ||  
|-
|-
| partial derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| integro-differential equation || integral; derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 332: Line 467:
|  ||  
|  ||  
|-
|-
| second derivative, second order derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| ordinary differential equation || derivative; independent variable
|  ||  
|  ||  
|  ||  
|  ||  
Line 341: Line 476:
|  ||  
|  ||  
|-
|-
| stationary point || differentiable function; derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| partial differential equation || partial derivative; multivariable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 350: Line 485:
|  ||  
|  ||  
|-
|-
| Taylor polynomial || Taylor's theorem
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| stochastic differential equation || stochastic process <probability theory>; differential equation
|  ||  
|  ||  
|  ||  
|  ||  
Line 359: Line 494:
|  ||  
|  ||  
|-
|-
| total derivative ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| stochastic partial differential equation || stochastic process <probability theory>; partial differential equation
|  ||  
|  ||  
|  ||  
|  ||  
Line 379: Line 514:


{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
|+ 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
|+ differentiation rule
|-
| differentiation rule ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| differentiation rule ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 406: Line 542:
|  ||  
|  ||  
|-
|-
| chain rule || function composition; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| chain rule || function composition; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 415: Line 551:
|  ||  
|  ||  
|-
|-
| general Leibniz rule || product rule
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| general Leibniz rule || product rule
|  ||  
|  ||  
|  ||  
|  ||  
Line 424: Line 560:
|  ||  
|  ||  
|-
|-
| inverse function rule || differentiable function; inverse function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| inverse function rule || differentiable function; inverse function
|  ||  
|  ||  
|  ||  
|  ||  
Line 433: Line 569:
|  ||  
|  ||  
|-
|-
| power rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| power rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 442: Line 578:
|  ||  
|  ||  
|-
|-
| product rule, Leibniz rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| product rule, Leibniz rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 451: Line 587:
|  ||  
|  ||  
|-
|-
| quotient rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| quotient rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 460: Line 596:
|  ||  
|  ||  
|-
|-
| reciprocal rule || multiplicative inverse; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| reciprocal rule || multiplicative inverse; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 489: Line 625:


{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
|+ 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
|+ extremum
|-
| extremum [pl:extrema] || function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| extremum [pl:extrema] || function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 507: Line 644:
|  ||  
|  ||  
|-
|-
| absolute maximum, global maximum || maximum; domain <set theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| absolute maximum, global maximum || maximum; domain <set theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 516: Line 653:
|  ||  
|  ||  
|-
|-
| absolute minimum, global minimum || minimum; domain <set theory>>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| absolute minimum, global minimum || minimum; domain <set theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 525: Line 662:
|  ||  
|  ||  
|-
|-
| relative maximum, local maximum || maximum; interval <topology>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| relative maximum, local maximum || maximum; interval <topology>
|  ||  
|  ||  
|  ||  
|  ||  
Line 534: Line 671:
|  ||  
|  ||  
|-
|-
| relative minimum, local minimum || minimum; interval <topology>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| relative minimum, local minimum || minimum; interval <topology>
|  ||  
|  ||  
|  ||  
|  ||  
Line 554: Line 691:


{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
|+ 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
|-
|  ||
|  ||
|  ||
| integral transform ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| Abel transform ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| associated Legendre transform ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| Fourier cosine transform ||
|  ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||
|  ||
| Fourier sine transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 572: Line 755:
|  ||  
|  ||  
|-
|-
|  ||
|  ||
|  ||
| Fourier transform ||  
| Fourier transform ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|-
|  ||
|  ||
|  ||
| Hankel transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 582: Line 774:
|-
|-
|  ||  
|  ||  
|  ||
|  ||
| Hartley transform ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Hermite transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 591: Line 792:
|-
|-
|  ||  
|  ||  
|  ||
|  ||
| Hilbert transform ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Jacobi transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 602: Line 812:
|  ||  
|  ||  
|  ||  
|  ||  
| Laguerre transform ||
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| Laplace transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 611: Line 830:
|  ||  
|  ||  
|  ||  
|  ||  
| Legendre transform ||
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| Mellin transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 620: Line 848:
|  ||  
|  ||  
|  ||  
|  ||  
| Poisson kernel ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||  
|  ||  
|  ||
|  ||
| Radon transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 627: Line 864:
|-
|-
|  ||  
|  ||  
|  ||
|  ||
| two-sided Laplace transform, bilateral Laplace transform ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| Weierstrass transform ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| X-ray transform, John transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 646: Line 901:


{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
|+ 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
|-
| notation for differentiation ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| notation for differentiation ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 673: Line 929:
|  ||  
|  ||  
|-
|-
| Euler's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Euler's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
Line 682: Line 938:
|  ||  
|  ||  
|-
|-
| Lagrange's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Lagrange's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
Line 691: Line 947:
|  ||  
|  ||  
|-
|-
| Leibniz's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Leibniz's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
Line 700: Line 956:
|  ||  
|  ||  
|-
|-
| Newton's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Newton's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
Line 720: Line 976:


{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
|+ 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
|+ theorem in calculus
|-
|-
| theorem in calculus ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| series || addition <number theory>; infinity <number theory>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| alternating series || series
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| convergent series || limit
|  ||  
|  ||  
|  ||  
|  ||  
Line 742: Line 1,025:
|  ||  
|  ||  
|  ||  
|  ||  
| divergent series || limit
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| Fourier series || series; periodic function; sine wave <trigonometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 748: Line 1,040:
|  ||  
|  ||  
|-
|-
| extreme value theorem || continuous function; maximum; minimum
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| geometric series || series; ratio
|  ||  
|  ||  
|  ||  
|  ||  
Line 757: Line 1,049:
|  ||  
|  ||  
|-
|-
| first fundamental theorem of calculus || continuous function; closed interval <topology>; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Gregory's series || Taylor series; inverse trigonometric functions <trigonometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 766: Line 1,058:
|  ||  
|  ||  
|-
|-
| L'Hôpital's rule || limit; indeterminate form
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| harmonic series || series
|  ||  
|  ||  
|  ||  
|  ||  
Line 775: Line 1,067:
|  ||  
|  ||  
|-
|-
| Rolle's theorem, Rolle's lemma || stationary point
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| partial sum || series; sum <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 784: Line 1,076:
|  ||  
|  ||  
|-
|-
| second fundamental theorem of calculus || interval <algebra>; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Taylor series || series; derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 793: Line 1,085:
|  ||  
|  ||  
|-
|-
| Taylor's theorem || differentiable function; linear appriximation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
| telescoping series || series
|  ||  
|  ||  
|  ||  
|  ||  
Line 812: Line 1,105:
|}
|}


=== Vector Calculus, Vector Analysis ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
|+ 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 825: Line 1,118:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
| theorem in calculus ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
| extreme value theorem || continuous function; maximum; minimum
|  ||  
|  ||  
|  ||  
|  ||  
Line 835: Line 1,146:
|  ||  
|  ||  
|  ||  
|  ||  
| first fundamental theorem of calculus || continuous function; closed interval <topology>; antiderivative
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| L'Hôpital's rule || limit; indeterminate form
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
=== Multivariable Calculus, Multivariate 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
|-
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Rolle's theorem, Rolle's lemma || stationary point
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| second fundamental theorem of calculus || interval <algebra>; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 862: Line 1,179:
|  ||  
|  ||  
|-
|-
| triple product rule, cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule || partial derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Taylor's theorem || differentiable function; linear appriximation
|  ||  
|  ||  
|  ||  
|  ||  
Line 881: Line 1,198:
|}
|}


== Real Analysis ==
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
|+ 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 900: 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 911: Line 1,282:
|}
|}


== Complex Analysis ==
=== Vector Calculus ===
{| 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]
! 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 931: Line 1,302:
|  ||  
|  ||  
|-
|-
| imaginary axis || imaginary line
| 虚轴 ||
| xū zhóu ||
| imaginäre Achse ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||
|}
=== 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
|-
|-
| imaginary line || line <geometry>; point <geometry>; imaginary number <arithmetic>
| ||  
| 虚数线 ||  
| ||  
| xūshù xiàn ||  
| ||  
| imaginäre Linie ||  
| ||  
|  ||  
|  ||  
|  ||  
|  ||  
Line 949: Line 1,332:
|  ||  
|  ||  
|-
|-
| real axis || real line
| ||  
| 实轴 ||  
| ||  
| shí zhóu ||  
| ||  
| reelle Achse ||  
| differential operator || operator <algebra>; differentiation
|  ||  
|  ||  
|  ||  
|  ||  
Line 958: Line 1,341:
|  ||  
|  ||  
|-
|-
| real line || line <geometry>; point <geometry>; real number <arithmetic>
| ||  
| 实数线 ||  
| ||  
| shíshù xiàn ||  
| ||  
| reelle Linie ||  
| triple product rule, cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule || partial derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 977: Line 1,360:
|}
|}


== Functional 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]
! 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 1,007: Line 1,390:
|}
|}


== Numerical 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]
! 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 1,027: Line 1,410:
|  ||  
|  ||  
|-
|-
| truncation error ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| 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 1,046: Line 1,465:
|}
|}


== Fourier 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]
! 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 1,076: Line 1,495:
|}
|}


 
== Numerical 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]
! 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 1,092: Line 1,510:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| truncation error ||
|  ||  
|  ||  
|  ||  
|  ||  
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|}
|}


[[File:432px-Fourier_Series.svg.png]]
== Fourier Analysis ==
 
== * Appendix * ==
=== Adjective & Adjective Phrase; Verb & Verb Phrase ===
{| 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]
! 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 1,140: Line 1,564:
|}
|}


=== Symbol ===
== Harmonic Analysis ==
{| class="wikitable sortable"
{| class="wikitable sortable"
! symbol
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! eng-Latn-US: concept
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Hans-CN: 概念
! 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]
! fra-Latn-FR: concept [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! jpn-Hrkt-JP: が↓いねん
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция
|-
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|}
 
=== 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
|-
|-
|  ||  
|  ||  
Line 1,203: Line 1,594:
|}
|}


=== Related Free Educational Resources ===
<center>
{| class="wikitable sortable"
https://upload.wikimedia.org/wikipedia/commons/f/f5/LeibnizInfinitesimalTriangle.png
! branch
</center>
! name
! link
! language
! public license
|-
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{{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
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
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
differentiation rule
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
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
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>
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
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
notation for 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
notation for differentiation
Euler's notation differentiation
Lagrange's notation differentiation
Leibniz's notation differentiation
Newton's notation differentiation
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
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
theorem in 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
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
mean value theorem
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
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

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
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

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
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

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
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

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

LeibnizInfinitesimalTriangle.png

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Other Lessons[edit | edit source]

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