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

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{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequaisite
! cmn-Hans-CN: 科目
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: kēmù
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Fach [n]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: subject
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: matière [f]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 科目
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! jpn-Hrkt-JP: か↑もく
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: предме́т
|-
|-
| mathematical analysis ||  
|  
| 数学分析 ||  
|  
| shùxué fēnxî ||  
|  
| Analysis [f] ||  
|  
| analyse [f] ||  
|  
| 解析学 ||  
|  
| か↑いせき↓がく ||  
|  
| ана́лиз [м] ||  
|  
|-
|-
| ||
| 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
|-
|-
| calculus ||
| 向量分析，向量微积分
| 微积分学 ||
| xiàngliàn fēnxī, xiàngliàng wēijīfēn
| wēijīfēn xué ||
| Vektoranalysis [f]
| Infinitesimalrechnung [f] ||
| vector calculus, vector analysis
| calcul [m] infinitésimal ||
| analyse vectorielle
| 微分積分学 ||
| ベクトル解析
| び↑ぶんせきぶ↓んがく ||
| ベ↑クトルか↓いせき
| математи́ческий ана́лиз ||
| ве́кторный ана́лиз
|-
|-
| vector calculus, vector analysis ||
| 多元微积分，多变量微积分
| 向量分析，向量微积分 ||
| duōyuán wēijīfēn, duō biànliàng wēijīfēn
| xiàngliàn fēnxī, xiàngliàng wēijīfēn ||
| multivariable Infinitesimalrechnung
| Vektoranalysis [f] ||
| multivariable calculus, multivariate calculus
| analyse [f] vectorielle ||
| calcul [m] à plusieurs variables [f pl]
| ベクトル解析 ||
| 多変数微分積分学，多変数解析学
| ベ↑クトルか↓いせき ||
| 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
| ве́кторный ана́лиз ||
| многоме́рный ана́лиз
|-
|-
| multivariable calculus, multivariate calculus ||
| 实分析，实数分析，实变函数论
| 多元微积分，多变量微积分 ||
| shí fēnxī, shíshù fēnxī, shí biàn hánshù lùn
| duōyuán wēijīfēn, duō biànliàng wēijīfēn ||
| reelle Analysis
| multivariable Infinitesimalrechnung ||
| analyse réelle
| calcul [m] à plusieurs variables ||
| real analysis
| 多変数微分積分学, 多変数解析学 ||
| 実解析，実関数論
| 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 ||
| じ↑つか↓いせき，じ↑つかんすうろ↓ん
| многоме́рный ана́лиз ||
| тео́рия фу́нкций веще́ственной переме́нной, тео́рия фу́нкций действи́тельного переме́нного
|-
|-
| real analysis ||
| 复分析
| 实分析，实数分析，实变函数论 ||
| fù fēnxī
| shí fēnxī, shíshù fēnxī, shí biàn hánshù lùn ||
| Funktionentheorie [f]
| reelle Analysis ||
| complex analysis
| analyse [f] réelle ||  
| analyse [f] complexe
| 実解析, 実関数論 ||
| 複素解析
| じ↑つか↓いせき, じ↑つかんすうろ↓ん ||
| ふ↑くそか↓いせき
| тео́рия фу́нкций веще́ственной переме́нной, тео́рия фу́нкций действи́тельного переме́нного ||
| ко́мпле́ксный ана́лиз, тео́рия фу́нкций ко́мпле́ксного переме́нного, тео́рия фу́нкций ко́мпле́ксной переме́нной
|-
|-
| complex analysis ||
| 泛函分析
| 复分析 ||
| fànhán fēnxī
| fù fēnxī ||
| Funktionalanalysis [f]
| Funktionentheorie [f] ||
| functional analysis
| analyse [f] complexe ||
| analyse fonctionnelle
| 複素解析 ||
| 関数解析学
| ふ↑くそか↓いせき ||
| か↑んす↓うか↑いせき↓がく
| ко́мпле́ксный ана́лиз, тео́рия фу́нкций ко́мпле́ксного переме́нного, тео́рия фу́нкций ко́мпле́ксной переме́нной ||
| функциона́льный ана́лиз
|-
|-
| functional analysis ||
| 傅里叶分析
| 泛函分析 ||
| Fùlǐyè fēnxī
| fànhán fēnxī ||
| Fourier-Analysis [f], Fourier-Analyse [f]
| Funktionalanalysis [f] ||
| Fourier analysis
| analyse [f] fonctionnelle ||
| analyse [f] de Fourier
| 関数解析学 ||
| フーリエ解析
| か↑んす↓うか↑いせき↓がく ||
| フ↓ーリエかいせき
| функциона́льный ана́лиз ||
| ана́лиз Фурье́
|-
|-
| Fourier analysis ||
| 调和分析，谐波分析
| 傅里叶分析 ||
| tiáohé fēnxī, xiébō fēnxī
| Fùlǐyè fēnxī ||
| harmonische Analyse, harmonische Analysis
| Fourier-Analysis [f], Fourier-Analyse [f] ||  
| harmonic analysis
| analyse [f] de Fourier ||
| analyse [f] harmonique
| フーリエ解析 ||
| 調和解析
| フ↓ーリエかいせき ||
| ちょ↑うわか↓いせき
| ана́лиз Фурье́ ||
| гармони́ческий ана́лиз
|-
|-
| 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 ||  
|  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||  
|}
|}


== Main ==
== Calculus ==
=== 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 132: Line 122:
|  ||  
|  ||  
|-
|-
| backward difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| backward difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| central difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| central difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| continuous function || argument <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| constant of integration || constant term <algebra>; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| definite integral || second fundamental theorem of calculus
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| continuous function || argument <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| derivative || function of a real variable <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| definite integral || second fundamental theorem of calculus
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| difference quotient || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| derivative || function of a real variable <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| differentiable function || derivative; domain <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| difference quotient || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| differentiation || derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| differentiable function || derivative; domain <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| discontinuous function || argument <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| differentiation || derivative
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| finite difference || function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| discontinuous function || argument <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| forward difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| finite difference || function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| indefinite integral || integral; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| forward difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| indeterminate form || infinity <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| indefinite integral || integral; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| infinitesimal, infinitesimal number || real number
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| indeterminate form || infinity <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| integral || infinitesimal
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| infinitesimal, infinitesimal number || real number
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| Leibniz integral rule || partial derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| integral || infinitesimal
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| limit || function; sequence
| 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
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| linear approximation || affine transformation <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Leibniz integral rule || partial derivative
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| Lipschitz continuity || uniform continuity
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| limit || function; sequence
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|-
|-
| maximum [pl:maxima] || function
|  ||  
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|  ||  
|  ||  
|  ||  
|  ||  
| linear approximation || affine transformation <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
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|-
|-
| minimum [pl:minima] || function
|  ||  
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|  ||  
|  ||  
|  ||  
|  ||  
| Lipschitz continuity || uniform continuity
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| multiple integral || definite integral
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| maximum [pl:maxima] || function
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| partial derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| minimum [pl:minima] || function
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| second derivative, second order derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| multiple integral || definite integral
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| stationary point || differentiable function; derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| partial derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| Taylor polynomial || Taylor's theorem
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| second derivative, second order derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| total derivative ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| separation of variables, Fourier method || ordinary differential equation; partial differential equation
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|  ||  
|  ||  
| stationary point || differentiable function; derivative
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| Taylor polynomial || Taylor's theorem
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
{| class="wikitable sortable"
|+ differential equation
! 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
|-
|-
| differential equation ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| total derivative ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 413: Line 409:
|  ||  
|  ||  
|  ||  
|  ||  
|}
{| 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
|-
|-
| delay differential equations || derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| differential equation ||
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| differential-algebraic system of equations ||  
| ||  
|  ||  
|  ||  
|  ||  
|  ||  
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|  ||  
|  ||  
|-
|-
| integro-differential equation || integral; derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| delay differential equations || derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 441: Line 449:
|  ||  
|  ||  
|-
|-
| ordinary differential equation || derivative; independent variable
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| differential-algebraic system of equations ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 450: Line 458:
|  ||  
|  ||  
|-
|-
| partial differential equation || partial derivative; multivariable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| integro-differential equation || integral; derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 459: Line 467:
|  ||  
|  ||  
|-
|-
| stochastic differential equation || stochastic process <probability theory>; differential equation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| ordinary differential equation || derivative; independent variable
|  ||  
|  ||  
|  ||  
|  ||  
Line 468: Line 476:
|  ||  
|  ||  
|-
|-
| stochastic partial differential equation || stochastic process <probability theory>; partial differential equation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| partial differential equation || partial derivative; multivariable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 478: Line 486:
|-
|-
|  ||  
|  ||  
|  ||
|  ||
| stochastic differential equation || stochastic process <probability theory>; differential equation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
| stochastic partial differential equation || stochastic process <probability theory>; partial differential equation
 
|  ||
{| class="wikitable sortable"
|  ||
|+ differentiation rule
|  ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
 
{| 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
Line 498: Line 524:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| differentiation rule ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| differentiation rule ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 516: Line 542:
|  ||  
|  ||  
|-
|-
| chain rule || function composition; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| chain rule || function composition; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 525: Line 551:
|  ||  
|  ||  
|-
|-
| general Leibniz rule || product rule
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| general Leibniz rule || product rule
|  ||  
|  ||  
|  ||  
|  ||  
Line 534: Line 560:
|  ||  
|  ||  
|-
|-
| inverse function rule || differentiable function; inverse function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| inverse function rule || differentiable function; inverse function
|  ||  
|  ||  
|  ||  
|  ||  
Line 543: Line 569:
|  ||  
|  ||  
|-
|-
| power rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| power rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 552: Line 578:
|  ||  
|  ||  
|-
|-
| product rule, Leibniz rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| product rule, Leibniz rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 561: Line 587:
|  ||  
|  ||  
|-
|-
| quotient rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| quotient rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 570: Line 596:
|  ||  
|  ||  
|-
|-
| reciprocal rule || multiplicative inverse; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| reciprocal rule || multiplicative inverse; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 600: Line 626:
{| 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]
! 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 [pl:extrema] || function <mathematical logic>
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| extremum [pl:extrema] || function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 617: Line 644:
|  ||  
|  ||  
|-
|-
| absolute maximum, global maximum || maximum; domain <set theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| absolute maximum, global maximum || maximum; domain <set theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 626: Line 653:
|  ||  
|  ||  
|-
|-
| absolute minimum, global minimum || minimum; domain <set theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| absolute minimum, global minimum || minimum; domain <set theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 635: Line 662:
|  ||  
|  ||  
|-
|-
| relative maximum, local maximum || maximum; interval <topology>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| relative maximum, local maximum || maximum; interval <topology>
|  ||  
|  ||  
|  ||  
|  ||  
Line 644: Line 671:
|  ||  
|  ||  
|-
|-
| relative minimum, local minimum || minimum; interval <topology>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| relative minimum, local minimum || minimum; interval <topology>
|  ||  
|  ||  
|  ||  
|  ||  
Line 665: Line 692:
{| 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]
! 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 ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 691: Line 719:
|  ||  
|  ||  
|-
|-
| Abel transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Abel transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 700: Line 728:
|  ||  
|  ||  
|-
|-
| associated Legendre transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| associated Legendre transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 709: Line 737:
|  ||  
|  ||  
|-
|-
| Fourier cosine transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Fourier cosine transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 718: Line 746:
|  ||  
|  ||  
|-
|-
| Fourier sine transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Fourier sine transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 727: Line 755:
|  ||  
|  ||  
|-
|-
| Fourier transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Fourier transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 736: Line 764:
|  ||  
|  ||  
|-
|-
| Hankel transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Hankel transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 745: Line 773:
|  ||  
|  ||  
|-
|-
| Hartley transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Hartley transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 754: Line 782:
|  ||  
|  ||  
|-
|-
| Hermite transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Hermite transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 763: Line 791:
|  ||  
|  ||  
|-
|-
| Hilbert transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Hilbert transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 772: Line 800:
|  ||  
|  ||  
|-
|-
| Jacobi transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Jacobi transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 781: Line 809:
|  ||  
|  ||  
|-
|-
| Laguerre transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Laguerre transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 790: Line 818:
|  ||  
|  ||  
|-
|-
| Laplace transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Laplace transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 799: Line 827:
|  ||  
|  ||  
|-
|-
| Legendre transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Legendre transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 808: Line 836:
|  ||  
|  ||  
|-
|-
| Mellin transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Mellin transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 817: Line 845:
|  ||  
|  ||  
|-
|-
| Poisson kernel ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Poisson kernel ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 826: Line 854:
|  ||  
|  ||  
|-
|-
| Radon transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Radon transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 835: Line 863:
|  ||  
|  ||  
|-
|-
| two-sided Laplace transform, bilateral Laplace transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| two-sided Laplace transform, bilateral Laplace transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 844: Line 872:
|  ||  
|  ||  
|-
|-
| Weierstrass transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Weierstrass transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 853: Line 881:
|  ||  
|  ||  
|-
|-
| X-ray transform, John transform ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| X-ray transform, John transform ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 873: 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 900: Line 929:
|  ||  
|  ||  
|-
|-
| Euler's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Euler's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
Line 909: Line 938:
|  ||  
|  ||  
|-
|-
| Lagrange's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Lagrange's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
Line 918: Line 947:
|  ||  
|  ||  
|-
|-
| Leibniz's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Leibniz's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
Line 927: Line 956:
|  ||  
|  ||  
|-
|-
| Newton's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Newton's notation || differentiation
|  ||  
|  ||  
|  ||  
|  ||  
Line 948: Line 977:
{| 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]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 957: Line 986:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| series || addition <number theory>; infinity <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| series || addition <number theory>; infinity <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 975: Line 1,004:
|  ||  
|  ||  
|-
|-
| alternating series || series
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| alternating series || series
|  ||  
|  ||  
|  ||  
|  ||  
Line 984: Line 1,013:
|  ||  
|  ||  
|-
|-
| convergent series || limit
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| convergent series || limit
|  ||  
|  ||  
|  ||  
|  ||  
Line 993: Line 1,022:
|  ||  
|  ||  
|-
|-
| divergent series || limit
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| divergent series || limit
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,002: Line 1,031:
|  ||  
|  ||  
|-
|-
| Fourier series || series; periodic function; sine wave <trigonometry>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Fourier series || series; periodic function; sine wave <trigonometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,011: Line 1,040:
|  ||  
|  ||  
|-
|-
| geometric series || series; ratio
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| geometric series || series; ratio
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,020: Line 1,049:
|  ||  
|  ||  
|-
|-
| Gregory's series || Taylor series; inverse trigonometric functions <trigonometry>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Gregory's series || Taylor series; inverse trigonometric functions <trigonometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,029: Line 1,058:
|  ||  
|  ||  
|-
|-
| harmonic series || series
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| harmonic series || series
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,038: Line 1,067:
|  ||  
|  ||  
|-
|-
| partial sum || series; sum <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| partial sum || series; sum <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,047: Line 1,076:
|  ||  
|  ||  
|-
|-
| Taylor series || series; derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Taylor series || series; derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,056: Line 1,085:
|  ||  
|  ||  
|-
|-
| telescoping series || series
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| telescoping series || series
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,078: Line 1,107:
{| 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]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 1,087: Line 1,116:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| theorem in calculus ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| theorem in calculus ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,105: Line 1,134:
|  ||  
|  ||  
|-
|-
| extreme value theorem || continuous function; maximum; minimum
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| extreme value theorem || continuous function; maximum; minimum
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,114: Line 1,143:
|  ||  
|  ||  
|-
|-
| first fundamental theorem of calculus || continuous function; closed interval <topology>; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| first fundamental theorem of calculus || continuous function; closed interval <topology>; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,123: Line 1,152:
|  ||  
|  ||  
|-
|-
| L'Hôpital's rule || limit; indeterminate form
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| L'Hôpital's rule || limit; indeterminate form
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,132: Line 1,161:
|  ||  
|  ||  
|-
|-
| Rolle's theorem, Rolle's lemma || stationary point
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Rolle's theorem, Rolle's lemma || stationary point
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,141: Line 1,170:
|  ||  
|  ||  
|-
|-
| second fundamental theorem of calculus || interval <algebra>; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| second fundamental theorem of calculus || interval <algebra>; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,150: Line 1,179:
|  ||  
|  ||  
|-
|-
| Taylor's theorem || differentiable function; linear appriximation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Taylor's theorem || differentiable function; linear appriximation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,169: Line 1,198:
|}
|}


==== Vector Calculus, Vector 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 1,188: 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 1,199: Line 1,282:
|}
|}


==== Multivariable Calculus, Multivariate Calculus ====
=== 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 1,211: Line 1,294:
|-
|-
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
| differential operator || operator <algebra>; differentiation
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
| triple product rule, cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule || partial derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,247: Line 1,312:
|}
|}


=== Real Analysis ===
=== Multivariable 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 1,270: Line 1,335:
|  ||  
|  ||  
|  ||  
|  ||  
| differential operator || operator <algebra>; differentiation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|}
|  ||
 
|  ||
=== Complex Analysis ===
| triple product rule, cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule || partial derivative
{| class="wikitable sortable"
|  ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
 
== Real Analysis ==
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 1,297: Line 1,380:
|  ||  
|  ||  
|-
|-
| complex plane || Cartesian coordinate system <geometry>; complex number <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
| imaginary axis || imaginary line
| 虚轴 ||
| xū zhóu ||
| imaginäre Achse ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
== Complex Analysis ==
{| 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 ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
| real axis || real line
| 实轴 ||
| shí zhóu ||
| reelle Achse ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,333: Line 1,410:
|  ||  
|  ||  
|-
|-
| real line || line <geometry>; point <geometry>; real number <arithmetic>
| 实数线 ||
| shíshù xiàn ||
| reelle Linie ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| complex plane || Cartesian coordinate system <geometry>; complex number <number theory>
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
| 虚轴 ||
| xū zhóu ||
| imaginäre Achse ||
| imaginary axis || imaginary line
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|}
=== Functional Analysis ===
{| 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
|-
|-
| 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 1,382: Line 1,465:
|}
|}


=== Numerical 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 1,394: Line 1,477:
|-
|-
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
| truncation error ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,421: Line 1,495:
|}
|}


=== Fourier 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]
! 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 1,443: Line 1,517:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
| truncation error ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|}
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}


=== Harmonic 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]
! 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 1,481: Line 1,564:
|}
|}


== Appendix ==
== Harmonic Analysis ==
=== Sentence ===
{| 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 1,512: Line 1,594:
|}
|}


=== Symbol ===
<center>
{| class="wikitable sortable"
https://upload.wikimedia.org/wikipedia/commons/f/f5/LeibnizInfinitesimalTriangle.png
! symbol
</center>
! eng-Latn-US: concept
 
! cmn-Hans-CN: 概念
{{Sci-Tech-Index-Menu}}
! 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
|-
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|}


=== Process ===
==Other Lessons==
{| class="wikitable sortable"
* [[Language/Multiple-languages/Vocabulary/Love-in-many-languages|Love in many languages]]
! eng-Latn-US: process !! eng-Latn-US: constituent
* [[Language/Multiple-languages/Vocabulary/Unit-of-Measurement|Unit of Measurement]]
! cmn-Hans-CN: 过程 !! cmn-Hans-CN: 构件
* [[Language/Multiple-languages/Vocabulary/False-Friends|False Friends]]
! cmn-Latn.Pinyin-CN: guòchéng !! cmn-Latn.Pinyin-CN: gòujiàn
* [[Language/Multiple-languages/Vocabulary/Collocations-with-Save|Collocations with Save]]
! deu-Latn-DE: Prozess [m] !! deu-Latn-DE: Bestandteil [m]
* [[Language/Multiple-languages/Vocabulary/Chaos-Theory|Chaos Theory]]
! fra-Latn-FR: procès [m] !! fra-Latn-FR: composant [m]
* [[Language/Multiple-languages/Vocabulary/Thermodynamics|Thermodynamics]]
! jpn-Jpan-JP: 過程 !! jpn-Jpan-JP: 構材
* [[Language/Multiple-languages/Vocabulary/Computer-Science|Computer Science]]
! jpn-Hrkt-JP: か↑てい !! jpn-Hrkt-JP: こ↑うざい
* [[Language/Multiple-languages/Vocabulary/Collocations-with-take|Collocations with take]]
! rus-Cyrl-RU: проце́сс !! rus-Cyrl-RU: соста́вная часть
* [[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]]
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* [[Language/Multiple-languages/Vocabulary/Number-Theory|Number Theory]]
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* [[Language/Multiple-languages/Vocabulary/Metalworking|Metalworking]]
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{{Sci-Tech-Index-Menu}}

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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