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{{Sci-Tech-Index-Intro}}
[[Category:Sci–Tech_Index]]
This is a part of the [https://polyglotclub.com/wiki/Language/Multiple-languages/Culture/Introduction-to-Sci%E2%80%93Tech-Index Sci–Tech Index], a project for science and technology learners.


{| class="wikitable sortable"
In progress.
! 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 122: Line 23:
|  ||  
|  ||  
|-
|-
| ||  
| mathematical analysis ||  
| ||  
| 数学分析 ||  
| ||  
| shùxué fēnxî ||  
| backward difference || finite difference
| Analysis [f] ||  
| ||  
| analyse [f] ||  
| ||  
| 解析学 ||  
| ||  
| か↑いせき↓がく ||  
| ||  
| ана́лиз [м] ||  
|-
|-
| ||  
| calculus ||  
| ||  
| 微积分学 ||  
| ||  
| wēijīfēn xué ||  
| central difference || finite difference
| Infinitesimalrechnung [f] ||  
| ||  
| calcul [m] infinitésimal ||  
| ||  
| 微分積分学 ||  
| ||  
| び↑ぶんせきぶ↓んがく ||  
| ||  
| математи́ческий ана́лиз ||  
|-
|-
| ||  
| vector calculus, vector analysis ||  
| ||  
| 向量分析, 向量微积分 ||  
| ||  
| xiàngliàn fēnxī, xiàngliàng wēijīfēn ||  
| constant of integration || constant term <algebra>; antiderivative
| Vektoranalysis [f] ||  
| ||  
| analyse [f] vectorielle ||  
| ||  
| ベクトル解析 ||  
| ||  
| ベ↑クトルか↓いせき ||  
| ||  
| ве́кторный ана́лиз ||  
|-
|-
| ||  
| multivariable calculus, multivariate calculus ||  
| ||  
| 多元微积分, 多变量微积分 ||  
| ||  
| duōyuán wēijīfēn, duō biànliàng wēijīfēn ||  
| continuous function || argument <mathematical logic>
| multivariable Infinitesimalrechnung ||  
| ||  
| calcul [m] à plusieurs variables ||  
| ||  
| 多変数微分積分学, 多変数解析学 ||  
| ||  
| た↑へ↓んすうび↑ぶんせきぶ↓んがく, た↑へ↓んすうか↑いせき↓がく ||  
| ||  
| многоме́рный ана́лиз ||  
|-
|-
| ||  
| real analysis ||  
| ||  
| 实分析, 实数分析, 实变函数论 ||  
| ||  
| shí fēnxī, shíshù fēnxī, shí biàn hánshù lùn ||  
| definite integral || second fundamental theorem of calculus
| reelle Analysis ||  
| ||  
| analyse [f] réelle ||  
| ||  
| 実解析, 実関数論 ||  
| ||  
| じ↑つか↓いせき, じ↑つかんすうろ↓ん ||  
| ||  
| тео́рия фу́нкций веще́ственной переме́нной, тео́рия фу́нкций действи́тельного переме́нного ||  
|-
|-
| ||  
| complex analysis ||  
| ||  
| 复分析 ||  
| ||  
| fù fēnxī ||  
| derivative || function of a real variable <algebra>
| Funktionentheorie [f] ||  
| ||  
| analyse [f] complexe ||  
| ||  
| 複素解析 ||  
| ||  
| ふ↑くそか↓いせき ||  
| ||  
| ко́мпле́ксный ана́лиз, тео́рия фу́нкций ко́мпле́ксного переме́нного, тео́рия фу́нкций ко́мпле́ксной переме́нной ||  
|-
|-
| ||  
| functional analysis ||  
| ||  
| 泛函分析 ||  
| ||  
| fànhán fēnxī ||  
| difference quotient || finite difference
| Funktionalanalysis [f] ||  
| ||  
| analyse [f] fonctionnelle ||  
| ||  
| 関数解析学 ||  
| ||  
| か↑んす↓うか↑いせき↓がく ||  
| ||  
| функциона́льный ана́лиз ||  
|-
|-
| ||  
| Fourier analysis ||  
| ||  
| 傅里叶分析 ||  
| ||  
| Fùlǐyè fēnxī ||  
| differentiable function || derivative; domain <mathematical logic>
| Fourier-Analysis [f], Fourier-Analyse [f] ||  
| ||  
| analyse [f] de Fourier ||  
| ||  
| フーリエ解析 ||  
| ||  
| フ↓ーリエかいせき ||  
| ||  
| ана́лиз Фурье́ ||  
|-
|-
| ||  
| harmonic analysis ||  
| ||  
| 调和分析, 谐波分析 ||  
| ||  
| tiáohé fēnxī, xiébō fēnxī ||  
| differentiation || derivative
| harmonische Analyse, harmonische Analysis ||  
| ||  
| analyse [f] harmonique ||  
| ||  
| 調和解析 ||  
| ||  
| ちょ↑うわか↓いせき ||  
| ||  
| гармони́ческий ана́лиз ||  
|-
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| discontinuous function || argument <mathematical logic>
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| finite difference || function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
== 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
|-
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| forward difference || finite difference
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| indefinite integral || integral; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 239: Line 134:
|  ||  
|  ||  
|-
|-
| backward difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| indeterminate form || infinity <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 248: Line 143:
|  ||  
|  ||  
|-
|-
| central difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| infinitesimal, infinitesimal number || real number
|  ||  
|  ||  
|  ||  
|  ||  
Line 257: Line 152:
|  ||  
|  ||  
|-
|-
| continuous function || argument <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| integral || infinitesimal
|  ||  
|  ||  
|  ||  
|  ||  
Line 266: Line 161:
|  ||  
|  ||  
|-
|-
| 变限积分 ||
| definite integral || second fundamental theorem of calculus
| 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 284: Line 170:
|  ||  
|  ||  
|-
|-
| derivative || function of a real variable <algebra>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Leibniz integral rule || partial derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 293: Line 179:
|  ||  
|  ||  
|-
|-
| difference quotient || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| limit || function; sequence
|  ||  
|  ||  
|  ||  
|  ||  
Line 302: Line 188:
|  ||  
|  ||  
|-
|-
| differentiable function || derivative; domain <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| linear approximation || affine transformation <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 311: Line 197:
|  ||  
|  ||  
|-
|-
| differentiation || derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Lipschitz continuity || uniform continuity
|  ||  
|  ||  
|  ||  
|  ||  
Line 320: Line 206:
|  ||  
|  ||  
|-
|-
| discontinuous function || argument <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| maximum [pl:maxima] || function
|  ||  
|  ||  
|  ||  
|  ||  
Line 329: Line 215:
|  ||  
|  ||  
|-
|-
| finite difference || function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| minimum [pl:minima] || function
|  ||  
|  ||  
|  ||  
|  ||  
Line 338: Line 224:
|  ||  
|  ||  
|-
|-
| forward difference || finite difference
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| multiple integral || definite integral
|  ||  
|  ||  
|  ||  
|  ||  
Line 347: Line 233:
|  ||  
|  ||  
|-
|-
| indefinite integral || integral; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| partial derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 356: Line 242:
|  ||  
|  ||  
|-
|-
| indeterminate form || infinity <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| second derivative, second order derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 365: Line 251:
|  ||  
|  ||  
|-
|-
| infinitesimal, infinitesimal number || real number
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| separation of variables, Fourier method || ordinary differential equation; partial differential equation
|  ||  
|  ||  
|  ||  
|  ||  
Line 374: Line 260:
|  ||  
|  ||  
|-
|-
| integral || infinitesimal
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| stationary point || differentiable function; derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 383: Line 269:
|  ||  
|  ||  
|-
|-
| Leibniz integral rule || partial derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Taylor polynomial || Taylor's theorem
|  ||  
|  ||  
|  ||  
|  ||  
Line 392: Line 278:
|  ||  
|  ||  
|-
|-
| limit || function; sequence
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| total derivative ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 401: Line 287:
|  ||  
|  ||  
|-
|-
| linear approximation || affine transformation <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 408: Line 295:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|}
{| 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
|-
|-
| maxima [pl:maxima] || function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| differential equation ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 431: Line 305:
|  ||  
|  ||  
|-
|-
| ||  
| minimum [pl:minima] || function
|  ||  
|  ||  
|  ||  
|  ||  
Line 440: Line 314:
|  ||  
|  ||  
|-
|-
| multiple integral || definite integral
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| delay differential equations || derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 449: Line 323:
|  ||  
|  ||  
|-
|-
| partial derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| differential-algebraic system of equations ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 458: Line 332:
|  ||  
|  ||  
|-
|-
| second derivative, second order derivative || derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| integro-differential equation || integral; derivative
|  ||  
|  ||  
|  ||  
|  ||  
Line 467: Line 341:
|  ||  
|  ||  
|-
|-
| stationary point || differentiable function; derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| ordinary differential equation || derivative; independent variable
|  ||  
|  ||  
|  ||  
|  ||  
Line 476: Line 350:
|  ||  
|  ||  
|-
|-
| Taylor polynomial || Taylor's theorem
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| partial differential equation || partial derivative; multivariable function
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| stochastic differential equation || stochastic process <probability theory>; differential equation
|  ||  
|  ||  
|  ||  
|  ||  
Line 494: Line 359:
|  ||  
|  ||  
|-
|-
| total derivative ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| stochastic partial differential equation || stochastic process <probability theory>; partial differential equation
|  ||  
|  ||  
|  ||  
|  ||  
Line 514: Line 379:


{| class="wikitable sortable"
{| class="wikitable sortable"
|+ differentiation rule
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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 542: Line 406:
|  ||  
|  ||  
|-
|-
| chain rule || function composition; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| chain rule || function composition; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 551: Line 415:
|  ||  
|  ||  
|-
|-
| general Leibniz rule || product rule
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| general Leibniz rule || product rule
|  ||  
|  ||  
|  ||  
|  ||  
Line 560: Line 424:
|  ||  
|  ||  
|-
|-
| inverse function rule || differentiable function; inverse function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| inverse function rule || differentiable function; inverse function
|  ||  
|  ||  
|  ||  
|  ||  
Line 569: Line 433:
|  ||  
|  ||  
|-
|-
| power rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| power rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 578: Line 442:
|  ||  
|  ||  
|-
|-
| product rule, Leibniz rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| product rule, Leibniz rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 587: Line 451:
|  ||  
|  ||  
|-
|-
| quotient rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| quotient rule || differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 596: Line 460:
|  ||  
|  ||  
|-
|-
| reciprocal rule || multiplicative inverse; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| reciprocal rule || multiplicative inverse; differentiable function
|  ||  
|  ||  
|  ||  
|  ||  
Line 625: Line 489:


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


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


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


{| class="wikitable sortable"
{| class="wikitable sortable"
|+ 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
! 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>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,004: Line 748:
|  ||  
|  ||  
|-
|-
| extreme value theorem || continuous function; maximum; minimum
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| alternating series || series
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,013: Line 757:
|  ||  
|  ||  
|-
|-
| first fundamental theorem of calculus || continuous function; closed interval <topology>; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| convergent series || limit
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,022: Line 766:
|  ||  
|  ||  
|-
|-
| L'Hôpital's rule || limit; indeterminate form
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| divergent series || limit
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,031: Line 775:
|  ||  
|  ||  
|-
|-
| Rolle's theorem, Rolle's lemma || stationary point
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Fourier series || series; periodic function; sine wave <trigonometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,040: Line 784:
|  ||  
|  ||  
|-
|-
| second fundamental theorem of calculus || interval <algebra>; antiderivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| geometric series || series; ratio
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,049: Line 793:
|  ||  
|  ||  
|-
|-
| Taylor's theorem || differentiable function; linear appriximation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Gregory's series || Taylor series; inverse trigonometric functions <trigonometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,061: Line 805:
|  ||  
|  ||  
|  ||  
|  ||  
| harmonic series || series
|  ||  
|  ||  
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| partial sum || series; sum <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
=== Vector Calculus, Vector 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
|-
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Taylor series || series; derivative
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| telescoping series || series
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,105: Line 842:
|}
|}


=== Multivariable Calculus, Multivariate Calculus ===
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ 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
! 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 ||
|  ||
|  ||
|  ||
|  ||
|-
|-
|  ||  
|  ||  
Line 1,134: Line 862:
|  ||  
|  ||  
|-
|-
| triple product rule, cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule || partial derivative
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| 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
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,198: Line 881:
|}
|}


== Real Analysis ==
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ mean value theorem
! 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
|-
| 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 1,226: Line 900:
|  ||  
|  ||  
|  ||  
|  ||  
|-
| 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 1,282: Line 911:
|}
|}


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


== Real 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 1,390: Line 1,007:
|}
|}


== Complex 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 1,410: Line 1,027:
|  ||  
|  ||  
|-
|-
| 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 1,465: Line 1,046:
|}
|}


== Functional 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 1,495: Line 1,076:
|}
|}


== 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 1,510: Line 1,092:
|  ||  
|  ||  
|  ||  
|  ||  
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| truncation error ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,534: Line 1,107:
|}
|}


== Fourier Analysis ==
[[File:432px-Fourier_Series.svg.png]]
 
== * 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 1,564: Line 1,140:
|}
|}


== Harmonic Analysis ==
=== Symbol ===
{| class="wikitable sortable"
! symbol
! eng-Latn-US: concept
! cmn-Hans-CN: 概念
! cmn-Latn.Pinyin-CN: gàiniàn
! deu-Latn-DE: Begriff [m]
! fra-Latn-FR: concept [m]
! jpn-Jpan-JP: 概念
! jpn-Hrkt-JP: が↓いねん
! rus-Cyrl-RU: конце́пция
|-
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|}
 
=== Process ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! eng-Latn-US: process !! eng-Latn-US: constituent
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Hans-CN: 过程 !! cmn-Hans-CN: 构件
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! cmn-Latn.Pinyin-CN: guòchéng !! cmn-Latn.Pinyin-CN: gòujiàn
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! deu-Latn-DE: Prozess [m] !! deu-Latn-DE: Bestandteil [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: procès [m] !! fra-Latn-FR: composant [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 過程 !! jpn-Jpan-JP: 構材
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! jpn-Hrkt-JP: か↑てい !! jpn-Hrkt-JP: こ↑うざい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: проце́сс !! rus-Cyrl-RU: соста́вная часть
|-
|-
|  ||  
|  ||  
Line 1,594: Line 1,203:
|}
|}


<center>
=== Related Free Educational Resources ===
https://upload.wikimedia.org/wikipedia/commons/f/f5/LeibnizInfinitesimalTriangle.png
{| class="wikitable sortable"
</center>
! branch
! name
! link
! language
! public license
|-
|
|
|
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|
|-
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|
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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>

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