数学分析中的英文单词和短语

发布时间：2023-04-12 12:40:05

数学分析中的英文单词和短语
有序完备集order-completeset

实数的完备性
completenessofrealnumberscompleteorderedfieldaxiomofcompletenessDedekindcutDedekindpropertyconstantandvariablequantitiesdefinitionoffunctiondomainrangeindependentvariabledependentvariableintermediatevariablemonotonicityelementaryfunctionconstantfunctionpowerfunctionexponentialfunctionlogarithmicfunctiontrigonometricfunctioninversetrigonometricfunctioninversefunctioncompoundfunctionmappinginversemappingimageprimaryimagepiecewisefunctionsignfunctionDirichletfunctionRiemannfunctionboundedfunctionmonotonefunctionmonotoneincreasingfunctionstrictlymonotonefunctionodd(evenfunctionminimalpositiveperiodabsolutevaluefunctionidentityfunctionpolynomialfunctionlinearfunctionquadraticfunctionrationalfunction全序域完备性公理戴德金分割
第一章实数集和函数
Chapter1
SetofRealNumbersandFunctions实数及其性质有理数无理数定义命题加减乘除
绝对值和不等式三角不等式反三角不等式伯努利不等式确界原理开区间闭区间半开区间半闭区间有限区间无限区间邻域去心邻域和差积商数轴封闭性阿基米德性稠密性上界和下届有界集无界集存在域上确界下确界
realnumbeanditspropertiesrationalnumberirrationalnumberdefinitionpropositionplusminusmultipliedby/timesover/isto/dividedbyabsolutevalueandinequalitytriangleinequalityinversetriangleinequalityBernoulliinequalityprinciplesofsupremumandinfimumclosedintervalclosedintervalsemi-openintervalsemi-closedintervalfiniteintervalinfiniteintervalneighborhooddeletedneighborhoodsumdifferenceproductquotientnumberaxis/numberlineclosenessArchimedeanpropertydensityupperandlowerboundsboundedsetunboundedsetexistencedomainsupremuminfimum戴德金性质常量和变量函数的定义定义域值域自变量因变量中间变量单调性初等函数常量函数幂函数指数函数对数函数三角函数反三角函数反函数复合函数映射逆映射像原像分段函数符号函数狄利克雷函数黎曼函数有界函数单调函数单调增函数严格单调函数奇（偶）函数最小正周期绝对值函数恒等函数多项式函数线性函数二次函数有理函数

双曲正弦双曲余弦三角恒等式奇偶恒等式余函数恒等式毕达哥拉斯恒等式半角恒等式积恒等式和恒等式加法恒等式倍角恒等式
hyperbolicsinehyperboliccosinetrigonometricidentityodd-evenidentitycofunctionidentityPythagoreanidentityhalf-angleidentityproductidentitysumidentityadditionidentitydouble-angleidentity函数极限的性质局部有界性海涅定理无穷大量无穷小量的阶高（低）阶无穷小量同阶无穷小量等价无穷小量k-阶无穷小量垂直渐近线斜渐近线水平渐近线
propertyoflimitoffunctionlocalboundednessHeinetheoreminfinityorderofinfinitesimalinfinitesimalofhigher(lowerorderinfinitesimalofsameorderequivalentinfinitesimalk-orderinfinitesimalverticalasymptoteobliqueasymptotehorizontalasymptote第二章数列极限
Chapter2
LimitsofSequences数列极限发散数列无穷小数列收敛数列唯一性定理有界性定理保序性保不等式性子列严格递增单调递增数列单调递减数列严格递增必要条件充分条件夹逼定理柯西收敛准则
limitofsequencedivergentsequenceinfinitesimalsequenceconvergentsequenceuniquenesstheoremboundednesstheoreminheritingorderpropertiesinheritinginequalitysubsequencestrictlyincreasingmonotoneincreasingsequencemonotonedecreasingsequencestrictlydecreasingnecessaryconditionsufficientconditionsqueezeprincipleCauchyconvergencecritterion第四章函数的连续性
Chapter4
ContinuityofFunctions自变量的增量函数的增量右（左）连续间断点及其分类可去间断点跳跃间断点第一类间断点第二类间断点连续函数的局部性质连续函数的复合性质闭区间上连续函数的性质极值定理
最大值和最小值定理介值性定理零点定理一致连续性定理
incrementofindependentvariableincrementoffunctionright(leftcontinuousdiscontinuitypointanditsclassificationremovablediscontinuityjumpdiscontinuitydiscontinuityofthefirstkinddiscontinuityofthesecondkindlocalpropertiesofcontinuousfunctioncompositionpropertiesofcontinuousfunctionpropertiesofcontinuousfunctionoverclosedintervalextremevaluetheoremmaximumandminimumvaluetheoremintermediatevaluetheoremzero-pointtheoremuniformcontinuitytheoremcontinuityofinversefunctionlocalinheritingorderpropertycontinuityofelementaryfunction第三章函数极限
Chapter3
LimitsofFunctions函数极限无穷极限单侧极限右（左）极限
limitoffunctioninfinitelimitone-sidedlimitright(leftlimit/right(lefthandlimit反函数的连续性局部保号性初等函数的连续性
第五章导数和微分
Chapter5
DerivativesandDifferentials

数学分析中的英文单词和短语

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