常微分方程中的英文單詞和短語

1、常微分方程OrdinaryDifferentialEqutions第一章基本概念Chapter1BasicConcepts常微分方程ordinarydifferentialequation/ode階order線性linear非線性nonlinear偏微分方程partialdifferentialequation/pde通解generalsolution特解particularsolution初值條件initialvaluecondition初值問題initialvalueproblem柯西問題Cauchyproblem幾何解釋geometryexplanation積分曲線integralcur

2、ve線素lineelement線素場fieldoflineelement方向場directionfield等斜線isocline對稱形式symmetricform奇異點(diǎn)singularity通積分generalintegral第二章初等積分法Chapter2ElementaryIntegrationMethods恰當(dāng)方程exactequation可微函數(shù)differentiablefunction全微分totalderivative偏導(dǎo)數(shù)partialderivative隱函數(shù)implicitfunction原函數(shù)primitivefunction變量可分離的方程equationofsepar

3、ablevariables一階線性方程first-orderlinearequation齊次homogeneous非齊次non-homogeneous積分因子法methodofintegrationfactor常數(shù)變易法methodofconstantsvariation初等變換法elementarymethodoftransformation齊次方程homogeneousequation伯努利方程Bernoulliequation利卡提方程Riccatiequation第三章存在和唯一性定理Chapter3ExistenceandUniquenessTheorems皮卡存在和唯一性定理Pic

4、ardtheoremofexistenceanduniqueness李普希茲條件Lipschitzcondition逐次迭代法successiveiterativemethod皮卡序列Picardsequence一致收斂uniformconvergence奧斯古德唯一性條件Osgooduniquenesscondition皮亞諾存在定理Peanoexistencetheorem歐拉折線Eulerspolygonalarc函數(shù)序列functionsequence一致有界uniformbound等度連續(xù)equicontinuous子序列sub-sequence歐拉序列Eulersequence矩形

5、區(qū)域rectangulararea解的延伸extensionofsolution有界閉區(qū)域boundedclosedregion最大存在區(qū)間maximumintervalofexistence邊界boundary有限閉區(qū)間finiteclosedinterval開集openset有限半開區(qū)間finitesemi-openinterval拉格朗日公式Lagrangeformula局部local有限覆蓋定理finitecoveringtheorem條形域bararea單調(diào)遞減monotonedecreasing扇形區(qū)域sectorialarea比較定理comparabilitysolution最小

6、解minimumsolution最大解maximumsolution斜率slope第四章奇解Chapter4SingularSolutions一階隱式微分方程first-orderimplicitdifferentialequation微分法differentiation克萊羅方程Clairautequation參數(shù)parameter奇解singularsolutionP-判別式p-testformulaP-判別曲線p-testcurve包絡(luò)envelope曲線族curvefamily相切tangencyC-判別式c-testformula非退化nonsingular切向量tangentvec

7、tor第五章高階微分方程Chapter5Higher-OrderDifferentialEquations軌線trajectory相平面phaseplane相圖phasediagram首次積分firstintefral自變量independent-variable未知函數(shù)unknownfunction拓?fù)渥儞Qtopologicaltransform逆變換inversetransform鄰域neighborhood開區(qū)域openregionn維線性空間n-dimensionallinearspacen維向量值函數(shù)n-dimensionalvector-valuedfunction函數(shù)組funct

8、iongroup標(biāo)準(zhǔn)微分方程normaldifferentialequation歐氏模Eulermodule解對初值的連續(xù)continuousdependenceofsolutionc依賴性initialvalue變分方程variationalequation第六章線性微分方程組Chapter6LinearDifferentialEquations存在和唯一性定理existenceanduniquenesstheorem齊次線性微分方homogeneouslineardifferential程組equations基本解組basicsolutions朗斯基行列式Wronskiandetermin

9、ant劉維爾公式Liouvilleformula解矩陣solutionmatrix基解矩陣basicsolutionmatrix常數(shù)矩陣constantmatrix非齊次線性微分non-homogeneouslineardifferential方程組equations常數(shù)列向量constantarrangevector常數(shù)變異公式formulaofvariationofconstant計(jì)算公式computingformula結(jié)構(gòu)公式frameworkformula常系數(shù)線性微分constantcoefficientlineardifferential方程組equations矩陣指數(shù)函數(shù)expo

10、nentialfunctionofmatrix標(biāo)準(zhǔn)基解矩陣normalbasicsolutionmatrix若爾當(dāng)標(biāo)準(zhǔn)型Jordannormalform矩陣函數(shù)matrixfunction實(shí)值解real-valuedfunction復(fù)值解complex-valuefunction代數(shù)余子式algebraiccofactor特征方程characteristicequation算子式operatormethod算子多項(xiàng)式operatorpolynomial拉普拉斯逆變換Laplaceinversetransform第七章微分方程的冪級數(shù)解法Chapter7PowerSeriesSolutionso

11、fDifferentialEquations柯西定理Cauchytheorem解析解analyticsolution優(yōu)級數(shù)excellentseries優(yōu)函數(shù)excellentfunction強(qiáng)函數(shù)strongfunction冪級數(shù)powerseries冪級數(shù)解法methodofpowerseries奇點(diǎn)singularity勒讓德方程Legendreequation勒讓德多項(xiàng)式Legendrepolynomial羅德里格斯公式Rodriguesformula正交orthogonal廣義傅里葉級數(shù)generalizedFourierseries廣義冪級數(shù)generalizedpowerseri

12、es指標(biāo)index正則奇點(diǎn)regularsingularpoint指標(biāo)方程indexequation共軛復(fù)根conjugatecomplexroot貝塞爾方程Besselequation第一類貝塞爾函數(shù)Besselfunctionofthefirstkind漸進(jìn)式asymptoticexpression第八章定性理論與分支理論Chapter8QualitativeTheoryandBifurcationTheory動力系統(tǒng)dynamicalsystem相空間phasespace增廣相空間augmentedphasespace速度場velocityfield向量場vectorfield拓?fù)浣Y(jié)構(gòu)圖

13、topologicalstructuregraph相圖phasediagram幾何理論geometricaltheory平衡點(diǎn)equilibriumpoint奇點(diǎn)singularpoint閉軌closedorbit軌線的唯一性uniquenessoforbit抽象動力系統(tǒng)abstractdynamicalsystem拓?fù)鋭恿ο到y(tǒng)topologicaldynamicalsystem微分動力系統(tǒng)differentialdynamicalsystem解的穩(wěn)定性stabilityofsolution利亞普諾夫穩(wěn)定性Liapunovstability漸近穩(wěn)定asymptoticstability漸近穩(wěn)定

14、域asymptoticstabilityfield吸引域attractiondomain全局漸近穩(wěn)定globeasymptoticstability線性近似linearapproximate臨界情形criticalstate利亞普諾夫第一方法firstmethodofLiapunov直接方法directmethod李雅普諾夫函數(shù)Liapunovfunction正定函數(shù)positivedefinitefunction負(fù)定函數(shù)negativedefinitefunction平面上的動力系統(tǒng)dynamicalsystemonplane極限環(huán)limitcycle常點(diǎn)constantpoint初等奇點(diǎn)e

15、lementarysingularpoint高階奇點(diǎn)higher-ordersingularpoint星形結(jié)點(diǎn)starnode臨界結(jié)點(diǎn)criticalnode鞍點(diǎn)saddlepoint單向結(jié)點(diǎn)one-waypoint退化結(jié)點(diǎn)impropernode穩(wěn)定結(jié)點(diǎn)stablefocus不穩(wěn)定結(jié)點(diǎn)unstablefocus中心點(diǎn)centerpoint拓?fù)涞葍r(jià)topologicalequivalence雙曲奇點(diǎn)hyperbolicsingularity穩(wěn)定極限環(huán)stablelimitcycle不穩(wěn)定極限環(huán)unstablelimitcycle半穩(wěn)定極限環(huán)semi-stablelimitcycle軌道穩(wěn)定性s

16、tabilityoforbit龐加萊-班迪克Poincare-Bendixsonannulustheorem環(huán)域定理oftheorem李納方程Lienardequation李納作圖法Lienardconstruction李納映射Lienardmapping后繼函數(shù)法subsequencefunctionmethod單極限環(huán)singlelimitcycleK重極限環(huán)k-foldlimitcycle鞍-結(jié)點(diǎn)saddle-node霍普夫分支Hopfbifurcation龐加萊分支Poincarebifurcation開折unfolding普適開折universalunfolding第九章邊值問題Chapter9BoundaryV