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

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


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


{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequaisite
|+ integral transform
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 14: Line 701:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| mathematical analysis ||  
| ||  
| 数学分析 ||  
| ||  
| shùxué fēnxî ||  
| ||  
| Analysis [f] ||  
| integral transform ||  
| analyse [f] ||  
| ||  
| 解析学 ||  
| ||  
| か↑いせき↓がく ||  
| ||  
| ана́лиз [м] ||  
| ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| 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 ||
|  ||
|  ||
|  ||
|  ||  
|-
|-
| calculus ||  
| ||  
| 微积分学 ||  
| ||  
| wēijīfēn xué ||  
| ||  
| Infinitesimalrechnung [f] ||  
| Laplace transform ||  
| calcul [m] infinitésimal ||  
| ||  
| 微分積分学 ||  
| ||  
| び↑ぶんせきぶ↓んがく ||  
| ||  
| математи́ческий ана́лиз ||  
| ||  
|-
|-
| vector calculus, vector analysis ||  
| ||  
| 向量分析, 向量微积分 ||  
| ||  
| xiàngliàn fēnxī, xiàngliàng wēijīfēn ||  
| ||  
| Vektoranalysis [f] ||  
| Legendre transform ||  
| analyse [f] vectorielle ||  
| ||  
| ベクトル解析 ||  
| ||  
| ベ↑クトルか↓いせき ||  
| ||  
| ве́кторный ана́лиз ||  
| ||  
|-
|-
| multivariable calculus, multivariate calculus ||  
| ||  
| 多元微积分, 多变量微积分 ||  
| ||  
| duōyuán wēijīfēn, duō biànliàng wēijīfēn ||  
| ||  
| multivariable Infinitesimalrechnung ||  
| Mellin transform ||  
| calcul [m] à plusieurs variables ||  
| ||  
| 多変数微分積分学, 多変数解析学 ||  
| ||  
| た↑へ↓んすうび↑ぶんせきぶ↓んがく, た↑へ↓んすうか↑いせき↓がく ||  
| ||  
| многоме́рный ана́лиз ||  
| ||  
|-
|-
| real analysis ||  
| ||  
| 实分析, 实数分析, 实变函数论 ||  
| ||  
| shí fēnxī, shíshù fēnxī, shí biàn hánshù lùn ||  
| ||  
| reelle Analysis ||  
| Poisson kernel ||  
| analyse [f] réelle ||  
| ||  
| 実解析, 実関数論 ||  
| ||  
| じ↑つか↓いせき, じ↑つかんすうろ↓ん ||  
| ||  
| тео́рия фу́нкций веще́ственной переме́нной, тео́рия фу́нкций действи́тельного переме́нного ||  
| ||  
|-
|-
| complex analysis ||  
| ||  
| 复分析 ||  
| ||  
| fù fēnxī ||  
| ||  
| Funktionentheorie [f] ||  
| Radon transform ||  
| analyse [f] complexe ||  
| ||  
| 複素解析 ||  
| ||  
| ふ↑くそか↓いせき ||  
| ||  
| ко́мпле́ксный ана́лиз, тео́рия фу́нкций ко́мпле́ксного переме́нного, тео́рия фу́нкций ко́мпле́ксной переме́нной ||  
| ||  
|-
|-
| functional analysis ||  
| ||  
| 泛函分析 ||  
| ||  
| fànhán fēnxī ||  
| ||  
| Funktionalanalysis [f] ||  
| two-sided Laplace transform, bilateral Laplace transform ||  
| analyse [f] fonctionnelle ||  
| ||  
| 関数解析学 ||  
| ||  
| か↑んす↓うか↑いせき↓がく ||  
| ||  
| функциона́льный ана́лиз ||  
| ||  
|-
|-
| Fourier analysis ||  
| ||  
| 傅里叶分析 ||  
| ||  
| Fùlǐyè fēnxī ||  
| ||  
| Fourier-Analysis [f], Fourier-Analyse [f] ||  
| Weierstrass transform ||  
| analyse [f] de Fourier ||  
| ||  
| フーリエ解析 ||  
| ||  
| フ↓ーリエかいせき ||  
| ||  
| ана́лиз Фурье́ ||  
| ||  
|-
|-
| harmonic analysis ||  
| ||  
| 调和分析, 谐波分析 ||  
| ||  
| tiáohé fēnxī, xiébō fēnxī ||  
| ||  
| harmonische Analyse, harmonische Analysis ||  
| X-ray transform, John transform ||  
| analyse [f] harmonique ||  
| ||  
| 調和解析 ||  
| ||  
| ちょ↑うわか↓いせき ||  
| ||  
| гармони́ческий ана́лиз ||  
| ||  
|-
|-
|  ||  
|  ||  
Line 105: Line 900:
|}
|}


== Calculus ==
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ 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
! 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
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
{| class="wikitable sortable"
|+ series
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
|  ||
|  ||
| series || addition <number theory>; infinity <number theory>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| alternating series || series
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| 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
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|-
|  ||  
|  ||  
Line 126: Line 1,105:
|}
|}


=== Vector Calculus / Vector Analysis ===
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ 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
! 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
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
{| class="wikitable sortable"
|+ mean value theorem
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
| 中值定理 ||
| zhōngzhí dìnglǐ ||
| Mittelwertsatz [m] ||
| mean value theorem ||
| théorème [m pl] des accroissements [m pl] finis ||
| 平均値の定理 ||
| へ↑いき↓んちの↑て↓いり ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
| 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 147: Line 1,282:
|}
|}


=== Multivariable Calculus / Multivariate Calculus ===
=== Vector Calculus ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
=== Multivariable Calculus ===
{| 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
! 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
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| differential operator || operator <algebra>; differentiation
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| triple product rule, cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule || partial derivative
|  ||
|  ||
|  ||
|  ||
|-
|-
|  ||  
|  ||  
Line 170: Line 1,362:
== Real Analysis ==
== Real Analysis ==
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|-
|  ||  
|  ||  
Line 191: Line 1,392:
== Complex Analysis ==
== Complex Analysis ==
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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 200: Line 1,401:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| imaginary axis || imaginary line
| ||  
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| complex plane || Cartesian coordinate system <geometry>; complex number <number theory>
|  ||
|  ||
|  ||
|  ||
|-
| 虚轴 ||  
| 虚轴 ||  
| xū zhóu ||  
| xū zhóu ||  
| imaginäre Achse ||  
| imaginäre Achse ||  
| imaginary axis || imaginary line
|  ||  
|  ||  
|  ||  
|  ||  
Line 209: Line 1,428:
|  ||  
|  ||  
|-
|-
| imaginary line || line <geometry>; point <geometry>; imaginary number <arithmetic>
| 虚数线 ||  
| 虚数线 ||  
| xūshù xiàn ||  
| xūshù xiàn ||  
| imaginäre Linie ||  
| imaginäre Linie ||  
| imaginary line || line <geometry>; point <geometry>; imaginary number <arithmetic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 218: Line 1,437:
|  ||  
|  ||  
|-
|-
| real axis || real line
| 实轴 ||  
| 实轴 ||  
| shí zhóu ||  
| shí zhóu ||  
| reelle Achse ||  
| reelle Achse ||  
| real axis || real line
|  ||  
|  ||  
|  ||  
|  ||  
Line 227: Line 1,446:
|  ||  
|  ||  
|-
|-
| real line || line <geometry>; point <geometry>; real number <arithmetic>
| 实数线 ||  
| 实数线 ||  
| shíshù xiàn ||  
| shíshù xiàn ||  
| reelle Linie ||  
| reelle Linie ||  
| real line || line <geometry>; point <geometry>; real number <arithmetic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 248: Line 1,467:
== Functional Analysis ==
== Functional Analysis ==
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|-
|  ||  
|  ||  
Line 267: Line 1,495:
|}
|}


 
== Numerical 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
! 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
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| truncation error ||
|  ||
|  ||
|  ||
|  ||
|-
|-
|  ||  
|  ||  
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== Fourier 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
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
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== Harmonic 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
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|}
=== Symbol ===
{| class="wikitable sortable"
! symbol
! eng-Latn-US: concept
! cmn-Hans-CN: 概念
! cmn-Latn.Pinyin-CN: gàiniàn
! deu-Latn-DE: Begriff [m]
! fra-Latn-FR: concept [m]
! jpn-Jpan-JP: 概念
! jpn-Hrkt-JP: が↓いねん
! rus-Cyrl-RU: конце́пция
|-
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|}
=== Process ===
{| class="wikitable sortable"
! eng-Latn-US: process !! eng-Latn-US: constituent
! cmn-Hans-CN: 过程 !! cmn-Hans-CN: 构件
! cmn-Latn.Pinyin-CN: guòchéng !! cmn-Latn.Pinyin-CN: gòujiàn
! deu-Latn-DE: Prozess [m] !! deu-Latn-DE: Bestandteil [m]
! fra-Latn-FR: procès [m] !! fra-Latn-FR: composant [m]
! jpn-Jpan-JP: 過程 !! jpn-Jpan-JP: 構材
! jpn-Hrkt-JP: か↑てい !! jpn-Hrkt-JP: こ↑うざい
! rus-Cyrl-RU: проце́сс !! rus-Cyrl-RU: соста́вная часть
|-
|-
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=== Related Free Educational Resources ===
<center>
{| class="wikitable sortable"
https://upload.wikimedia.org/wikipedia/commons/f/f5/LeibnizInfinitesimalTriangle.png
! branch
</center>
! name
! link
! language
! public license
|-
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{{Sci-Tech-Index-Menu}}
{{Sci-Tech-Index-Menu}}
==Other Lessons==
* [[Language/Multiple-languages/Vocabulary/Love-in-many-languages|Love in many languages]]
* [[Language/Multiple-languages/Vocabulary/Unit-of-Measurement|Unit of Measurement]]
* [[Language/Multiple-languages/Vocabulary/False-Friends|False Friends]]
* [[Language/Multiple-languages/Vocabulary/Collocations-with-Save|Collocations with Save]]
* [[Language/Multiple-languages/Vocabulary/Chaos-Theory|Chaos Theory]]
* [[Language/Multiple-languages/Vocabulary/Thermodynamics|Thermodynamics]]
* [[Language/Multiple-languages/Vocabulary/Computer-Science|Computer Science]]
* [[Language/Multiple-languages/Vocabulary/Collocations-with-take|Collocations with take]]
* [[Language/Multiple-languages/Vocabulary/Common-Han-Characters-with-⼀|Common Han Characters with ⼀]]
* [[Language/Multiple-languages/Vocabulary/Cell-Biology|Cell Biology]]
* [[Language/Multiple-languages/Vocabulary/I-love-you-in-all-languages|I love you in all languages]]
* [[Language/Multiple-languages/Vocabulary/Cinema-in-many-languages|Cinema in many languages]]
* [[Language/Multiple-languages/Vocabulary/Greetings-Where-have-you-come-from|Greetings Where have you come from]]
* [[Language/Multiple-languages/Vocabulary/Number-Theory|Number Theory]]
* [[Language/Multiple-languages/Vocabulary/Metalworking|Metalworking]]
<span links></span>

Latest revision as of 13:52, 27 March 2023

Hello polyglots, 😀

On this page you will find a part of the Sci–Tech Index, a project for science and technology learners.

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

Calculus[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
backward difference finite difference
central difference finite difference
constant of integration constant term <algebra>; antiderivative
continuous function argument <mathematical logic>
definite integral second fundamental theorem of calculus
derivative function of a real variable <algebra>
difference quotient finite difference
differentiable function derivative; domain <mathematical logic>
differentiation derivative
discontinuous function argument <mathematical logic>
finite difference function <mathematical logic>
forward difference finite difference
indefinite integral integral; antiderivative
indeterminate form infinity <number theory>
infinitesimal, infinitesimal number real number
integral infinitesimal
变限积分 biànxiàn jīfēn Integral [n] mit variablen Grenzen [f pl] integral with variable limits integral; limit; variable <mathematical logic> intégrale [f] avec limites [f pl] variables 可変限界との積分 か↑へんげ↓んかいとのせ↑きぶん интегра́л с переме́нными преде́лами
integration by substitution, u-substitution, reverse chain rule, change of variables integral; antiderivative
Leibniz integral rule partial derivative
limit function; sequence
linear approximation affine transformation <geometry>
Lipschitz continuity uniform continuity
maximum [pl:maxima] function
minimum [pl:minima] function
multiple integral definite integral
partial derivative derivative
second derivative, second order derivative derivative
separation of variables, Fourier method ordinary differential equation; partial differential equation
stationary point differentiable function; derivative
Taylor polynomial Taylor's theorem
total derivative
differential equation
cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
differential equation
delay differential equations derivative
differential-algebraic system of equations
integro-differential equation integral; derivative
ordinary differential equation derivative; independent variable
partial differential equation partial derivative; multivariable function
stochastic differential equation stochastic process <probability theory>; differential equation
stochastic partial differential equation stochastic process <probability theory>; partial differential equation
differentiation rule
cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
differentiation rule
chain rule function composition; differentiable function
general Leibniz rule product rule
inverse function rule differentiable function; inverse function
power rule differentiable function
product rule, Leibniz rule differentiable function
quotient rule differentiable function
reciprocal rule multiplicative inverse; differentiable function
extremum
cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
extremum [pl:extrema] function <mathematical logic>
absolute maximum, global maximum maximum; domain <set theory>
absolute minimum, global minimum minimum; domain <set theory>
relative maximum, local maximum maximum; interval <topology>
relative minimum, local minimum minimum; interval <topology>
integral transform
cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
integral transform
Abel transform
associated Legendre transform
Fourier cosine transform
Fourier sine transform
Fourier transform
Hankel transform
Hartley transform
Hermite transform
Hilbert transform
Jacobi transform
Laguerre transform
Laplace transform
Legendre transform
Mellin transform
Poisson kernel
Radon transform
two-sided Laplace transform, bilateral Laplace transform
Weierstrass transform
X-ray transform, John transform
notation for differentiation
cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
notation for differentiation
Euler's notation differentiation
Lagrange's notation differentiation
Leibniz's notation differentiation
Newton's notation differentiation
series
cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
series addition <number theory>; infinity <number theory>
alternating series series
convergent series limit
divergent series limit
Fourier series series; periodic function; sine wave <trigonometry>
geometric series series; ratio
Gregory's series Taylor series; inverse trigonometric functions <trigonometry>
harmonic series series
partial sum series; sum <number theory>
Taylor series series; derivative
telescoping series series
theorem in calculus
cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
theorem in calculus
extreme value theorem continuous function; maximum; minimum
first fundamental theorem of calculus continuous function; closed interval <topology>; antiderivative
L'Hôpital's rule limit; indeterminate form
Rolle's theorem, Rolle's lemma stationary point
second fundamental theorem of calculus interval <algebra>; antiderivative
Taylor's theorem differentiable function; linear appriximation
mean value theorem
cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
中值定理 zhōngzhí dìnglǐ Mittelwertsatz [m] mean value theorem théorème [m pl] des accroissements [m pl] finis 平均値の定理 へ↑いき↓んちの↑て↓いり
柯西中值定理 Kēxī zhōngzhí dìnglǐ cauchy'scher Mittelwertsatz Cauchy's mean value theorem, extended mean value theorem théorème [m] de la moyenne de Cauchy コーシーの平均値定理 コ↓ーシーのへ↑いきんちて↓いり теоре́ма Коши́ о сре́днем значе́нии
积分第一中值定理 jīfēn dìyī zhōngzhí dìnglǐ erster Mittelwertsatz der Integralrechnung first mean value theorem for integrals première formule [f] de la moyenne 積分の第一平均値定理 せ↑きぶんのだ↓いい↑ちへいきんちて↓いり пе́рвая теоре́ма о сре́днем
拉格朗日中值定理 Lǎgélǎngrì zhǒngzhí dìnglǐ Mittelwertsatz [m] von Lagrange Lagrange's mean value theorem théorème [m] de la valeur moyenne de Lagrange ラグランジュの平均値の定理 ラ↑グラ↓ンジュのへ↑いき↓んちの↑て↓いり Фо́рмула коне́чных прираще́ний, теоре́ма Лагра́нжа о сре́днем значе́нии
积分第二中值定理 jīfēn dì'èr zhōngzhí dìnglǐ zweiter Mittelwertsatz der Integralrechnung second mean value theorem for integrals deuxième formule [f] de la moyenne 積分の第二平均値定理 せ↑きぶんのだ↓いにへ↑いきんちて↓いり Втора́я теоре́ма о сре́днем
罗尔定理 Luó'ěr dìnglǐ Satz [m] von Rolle Rolle's theorem, Rolle's lemma théorème [m] de Rolle, lemme [m] de Rolle ロルの定理 ロ↑ル↓の↑て↓いり теоре́ма Ро́лля

Vector Calculus[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка

Multivariable Calculus[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
differential operator operator <algebra>; differentiation
triple product rule, cyclic chain rule, cyclic relation, cyclical rule, Euler's chain rule partial derivative

Real Analysis[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка

Complex Analysis[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
complex plane Cartesian coordinate system <geometry>; complex number <number theory>
虚轴 xū zhóu imaginäre Achse imaginary axis imaginary line
虚数线 xūshù xiàn imaginäre Linie imaginary line line <geometry>; point <geometry>; imaginary number <arithmetic>
实轴 shí zhóu reelle Achse real axis real line
实数线 shíshù xiàn reelle Linie real line line <geometry>; point <geometry>; real number <arithmetic>

Functional Analysis[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка

Numerical Analysis[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
truncation error

Fourier Analysis[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка

Harmonic Analysis[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка

LeibnizInfinitesimalTriangle.png

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Other Lessons[edit | edit source]

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