常微分方程中的英文单词和短语

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1、常微分方程中的英文单词和短语常微分方程OrdinaryDifferentialEqutions第一章基本概念Chapter1BasicConcepts常微分方程ordinarydifferentialequation/ode阶order线性linear非线性nonlinear偏微分方程partialdifferentialequation/pde通解generalsolution特解particularsolution初值条件initialvaluecondition初值问题initialvalueproblem柯西问题Cauchyproblem

2、几何解释geometryexplanation积分曲线integralcurve线素lineelement线素场fieldoflineelement方向场directionfield等斜线isocline对称形式symmetricform奇异点singularity通积分generalintegral第二章初等积分法Chapter2ElementaryIntegrationMethods恰当方程exactequation可微函数differentiablefunction全微分totalderivative偏导数partialderivative

3、隐函数implicitfunction原函数primitivefunction变量可分离的方程equationofseparablevariables一阶线性方程first-orderlinearequation齐次homogeneous非齐次non-homogeneous积分因子法methodofintegrationfactor常数变易法methodofconstantsvariation初等变换法elementarymethodoftransformation齐次方程homogeneousequation伯努利方程Bernoulliequa

4、tion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Picardtheoremofexistenceanduniqueness李普希兹条件Lipschitzcondition逐次迭代法successiveiterativemethod皮卡序列Picardsequence一致收敛uniformconvergence奥斯古德唯一性条件Osgooduniquenesscondition皮亚诺存在定理Peanoexistencetheorem

5、欧拉折线Euler’spolygonalarc函数序列functionsequence一致有界uniformbound等度连续equicontinuous子序列sub-sequence欧拉序列Eulersequence矩形区域rectangulararea解的延伸extensionofsolution有界闭区域boundedclosedregion最大存在区间maximumintervalofexistence边界boundary有限闭区间finiteclosedinterval开集openset有限半开区间finitesemi-openinte

6、rval拉格朗日公式Lagrangeformula局部local有限覆盖定理finitecoveringtheorem条形域bararea单调递减monotonedecreasing扇形区域sectorialarea比较定理comparabilitysolution最小解minimumsolution最大解maximumsolution斜率slope第一章奇解Chapter4SingularSolutions一阶隐式微分方程first-orderimplicitdifferentialequation微分法differentiation克莱罗方程

7、Clairautequation参数parameter奇解singularsolutionP-判别式p-testformulaP-判别曲线p-testcurve包络envelope曲线族curvefamily相切tangencyc-判别式c-testformula非退化nonsingular切向量tangentvector第二章高阶微分方程Chapter5Higher-OrderDifferentialEquations轨线trajectory相平面phaseplane相图phasediagram首次积分firstintefral自变量indep

8、endent-variable未知函数unknownfunction拓扑变换topologicaltransform逆变换inverse