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ciyu£ü|gaodengshuxueyingwenshuyuduizhao2021-04-08 06:56¡¤fanyijiaoxueyuyanjiubenwenzhuanzi£ºyijiangAdvanced Mathematical VocabularygaodengshuxueshuxuecihuiyinghanduizhaobiaoAabscissa, X-coordinate hengzuobiaoabsolute value jueduizhiabsolute convergence jueduishoulianacceleration jiasuduaccumulating point judianaccuracy jingduaddition, add, sum, summation he£¬qiuhe£¬jiafaadjugate matrix zhuanzhibansuizhenalgebra daishualgorithm suanfaangle jiaoantiderivative, primitive function fandaoshu£¬yuanhanshuapproach qujinarc huarea of a plane region pingmiantuxingdemianjiarea of a plane region bounded by curves youqumianweichengdepingmiantuxingdemianjiarea of surface qumianmianjiassume, assumption jiasheasteroid xingxingxianasymptote jianjinxianx-axis, y-axis x zhou£¬y zhouauxiliary equation, characteristic equation fuzhufangcheng£¬tezhengfangchengBbasis jiboundary bianjiebounded by bei¡­suoweichengboundedness youjiexingCcalculus weijifencardioid xinzangxiancenter of gravity zhongxincenter of mass zhixincentroid xingxinchain rule lianshifazecharacteristic root tezhenggenchord xiancircle yuancoefficient xishucofactor daishuyuzishicolumn lie£¬elementary column transformation (operation) chudengliebianhuancombination zuhecomparison test bijiaopanbiefacomplex number fushucomposition of functions fuhehanshuconcave, concavity ao£¬aoxingcondition tiaojian£¬conditionally convergent tiaojianshoulianconfidence interval zhixinqujiancone zhuimianconj ugate gongzuoconjugate complex number gongzuofushuconjugate c urve gongzuoquxianconsistent xiangrongconstant changshucontinuous lianxudecontour, level line dengzhixian£¬denggaoxiancontradiction maodun£¬by contradiction fanzhengfaconvergence, convergent shoulian£¬convergence test shoulianxingpanbiefaconvex, convexity tu£¬tuxingcoordinate system zuobiaoxi£¬rectangular/cylindrical/spherical coordinate system zhijiao/zhumian/qiumianzuobiaoxi£¬polar coordinate system jizuobiaoxicoordinates of vector xiangliangdezuobiaocorollary tuilunCramer¡¯s Rule kelamofazecross product (or outer product, vector product) chaji£¨huowaiji¡¢xiangliangji£©cumulant jileiliangcumulant generating function jileiliangmuhanshucurve qumiancylinder zhumianD(is) defined to be dingyiweidefinite integral dingjifendefinite integral with variable upper limit jifenshangxianhanshudefinition dingyidenominator fenmudenote, denote to be, denoted by biaoshiweidependent variable yinbianliangderivative daoshudeterminant xinglieshidiagonal duijiaoxian£¬diagonalization of a marix juzhendeduijiaohuadiameter zhijingdimension wei£¬weishudirectional angle fangxiangjiaodirectional cosines fangxiangyuxiandiscrete lisandedisk yuanpan£¬yuanpanbiquyudivergent, divergence fasandisplacement weiyifirst/second/nth derivative yijie/erjie/n jiedaoshuright-hand (left-hand) derivative you£¨zuo£©daoshudifference, subtraction, subtract cha£¬jianfa£¬xiangjiandifferentiable kedaode£¬keweidedifferential weifen£¬differential calculus weifenxuediscontinuity jianduan£¬point of discontinuity jianduandiandistribution fenbunormal distribution zhengtaifenbuBernoulli distribution bonulifenbubinomial distribution erxiangfenbuPoisson distribution bosongfenbunegative binomial distribution fuerxiangfenbugeometric distribution jihefenbuhypergeometric distribution chaojihefenbuuniform distribution junyunfenbuexponential distribution zhishufenbuGamma distribution zuomafenbuWeibull distribution weiboerfenbulognormal distribution duishuzhengtaifenbuchi-distribution kafangfenbustudent t-distribution xueshengt fenbuF-distribution F fenbudivision, divide, quotient chufa£¬xiangchu£¬shangdomain, natural domain dingyiyu£¬zirandingyiyudot product (or inner product, scalar product) dianji£¨huoneiji¡¢shuliangji£©double product erzhongjifenEeigenvalue, eigenvector tezhengzhi£¬tezhengxiangliangelement yuansuelementary transformation chudengbianhuanellipse tuoyuanellipsoid tuoqiumianelliptic cylinder tuoyuanzhumianentry xiangliangdefenliang£¬yuansuequal, be equal to xiangdeng£¬equation dengshiequilibrium pinghengeven function ouhanshuexclusive huchidemutually exclusive wanquanhuchiexpansion zhankaishiexpectation (expected value) qiwangexponential function zhishuhanshuexpression biaodashi£¬express y in terms of x jiangy biaoshiweix deyigeshiziexterior point waidianabsolute/global extreme values zuidazuixiaozhirelative/local extreme values jizhiFfactorial jiechengfind, compute, evaluate jisuanfirst-order linear differential equation yijiexianxingweifenfangchengfirst-order separable differential equation yijiekefenlibianliangweifenfangchengfocus jiaodianformula gongshifraction fenshuproper fraction, zhenfenshu£¬improper fraction jiafenshufunction hanshufunction determined implicitly by equation youfangchengquedingdeyinhanshufunction determined by parametric equation youcanshufangchengquedingdehanshuFoundation Theorem of Calculus weijifenjibendinglifundamental solution jichujieGGauss-Jordan Elimination gaosi-ruoerdangxiaoyuanfageneral equation of a plane pingmiandeyibanshifangchenggeneral solution tongjiegenerator fenmugeometry jihegeometric meaning (interpretation, significance) of derivative daoshudejiheyiyigiven geiding£¬shegradient tidugradient vector tiduxianglianggraph of a function hanshutuxianggravitational force yinliHhemisphere banqiumianhomogeneous equation qicifangchenghorizontal shuipinghorizontal asymptote shuipingjianjinxianhydrostatic force shuiyalihyperbola shuangquxianhyperbolic cylinder shuangquzhumianhyperboloid shuangqumianhyperboloid of one sheet danyeshuangqumianhypothesis jiashe¡¢tishehypothesis testing jiashejianyanIidentity hengdengshiimaginary part xubuimproper integral fanchangjifenincrement zengliangindefinite integral budingjifenindependent variable zibianliangindeterminate form weidingshiindex zhibiaoinequality budengshiinfinitesimal wuqiongxiaolianginfinitesimal of higher order gaojiewuqiongxiaoequivalent of infinitesimals dengjiawuqiongxiaoinflection point guaidianinitial-value problem chuzhiwentiinteger zhengshupositive (negative) integer zheng£¨fu£©zhengshuintegral jifenintegral calculus jifenxueintegrating factor jifenyinziLebesgue integral lebeigejifenRiemann integral limanjifenintegrable kejideintegrable with variable upper limit jifenshangxianhanshuintegrand beijihanshuintegration by parts fenbujifenfaintegration by substitution huanyuanjifenfaintegration curve jifenquxianintercept jieju£¬x-intercept x zhoushangdejiejuinterior point neidianIntermediate value Theorem jiezhidingliintersect xiangjiaointersection jiaojiinterval qujianclosed (open) interval bi£¨kai£©qujianinterval of convergence shoulianqujianinverse fan¡¢niinverse function fanhanshuinverse matrix nijuzheninverse trigonometric function fansanjiaohanshuinversely proportional to fanbiyuirrational number wulishuiterated integral leicijifeniteration zhidaiJJacobian matrix yagebijuzhenLlaminar pingmianbaopianLaw of Parallelogram pingxingsibianxingfazelemma yinlilength of an arc huchanglet she¡¢linglimit jixianright-hand (left-hand) limit you£¨zuo£©jixianthe limit of a sequence shuliejixianthe limit of f(x) as x approaches x dangx qujinyux shif(x) dejixianthe limit of f(x) as x approaches infinity dangqujinyuwuqiongdashif(x) dejixianline integral quxianjifenline segment xianduanlinear algebra xianxingdaishulinear approximation xianxingbijinlinear combination xianxingzuhelinear function xianxinghanshulinear operations xianxingyunsuanlinearly dependent (independent) xianxingxiangguan/wuguanlogarithmic differentiation duishuqiudaofalogarithmic function duishuhanshulower limit jifenxiaxianMmapping yingshemathematics induction shuxueguinafamatrix, matrics juzhenblock matrix fenkuaizhendiagonal matrix duijiaozhenelementary matrix chudengjuzhenidentity matrix danweijuzhenunit matrix danweijuzheninvertible matrix kenijuzhensingular matrix qiyizhen£¬jiangzhizhennon-degenerate matrix feituihuazhenscalar matrix shuliangzhensquare matrix fangzhenorthogonal matrix zhengjiaozhensymmetric matrix duichengzhenskew-symmetric matrix fanduichengzhenfull rank matrix manzhizhenmaximum zuidazhimaximal linearly independent subset zuidaxianxingwuguanzumean value theorem zhongzhidinglimedian zhongweishuminimum zuixiaozhimixed product, box product hunhejimode zhongshumoment juliangmoment matrix juliangjuzhenmoment generating function juliangmuhanshumoment of a force lijumoment of inertia about x-axis guanyux zhoudezhuandongguanliangmonotonely decrease dandiaojianshaomonotonely increase dandiaozengjiamonotonicity dandiaoxingmultiplication, multiple, product ji£¬chengfa£¬xiangchengmultivariable function duoyuanhanshuNnatural number ziranshunatural domain zirandingyiyunecessary condition biyaotiaojianneighborhood linyudeleted neighborhood quxinlinyunontrivial solution feipingfanjienorm fanshunormal line faxiannormal plane fapingmiannormal vector faxiangliangnotation jihaonumerator fenziOodd function qihanshuorder cixu/ jie/daoshudejie/juzhendejie/xinglieshidejieoperation yunsuanoptimization zuiyouhuaorder-reducible differential equation kejiangjieweifenfangchengordinary differential equation (ODE) changweifenfangchengordinate, y-coordinate zongzuobiaoorthogonal zhengjiaodeorthogonal basis zhengjiaojiorthonormal basis guifanzhengjiaojioscillatory zhendongdePparabola paowuxianparabolic cylinder paowuzhumianparaboloid paowumianparallel to pingxingyuparallelogram pingxingsibianxingparameter canshuparametric equations of a line zhixiandecanshufangchengparity of a function hanshudeqiouxingpartial derivative piandaoshufirst partial derivative yijiepiandaoshumixed higher partial derivative gaojiehunhepiandaoshupart bufenintegration by parts fenbujifenfapartial differential equation (PDE) pianweifenfangchengpartial fraction decomposition bufenfenshifenjiepartial sum sequence bufenheshulieparticular solution tejiepencil of planes pingmianshuperiod of a function hanshudezhouqiperiodic function zhouqihanshupermutation pailieperpendicular to chuizhiyuplane pingmianplane region pingmiantuxingplane rectangular coordinate system pingmianzhijiaozuobiaoxiplane analytic geometry pingmianjiexijihepoint diancommon point gonggongdian£¬jiaodianpoint-normal equation of a plane pingmiandedianfashifangchengpolar coordinate system jizuobiaoxipolygon duobianxingpolynomial function duoxiangshihanshuposition function weizhihanshupower chengmipower function mihanshupower series mijishuprobability gailvprobability density function gailvmiduhanshuprobability generating function gailvmuhanshuprobability mass function gailvzhilianghanshuproblem, question wentiproduct chengjiprojection touyingproof, prove zhengmingproperties xingzhiproportional to zhengbiyuinversely proportional to fanbiyuproposition mingtipyramid lengzhuiQquadratic ercide£¬erciquadrature jifenguocheng£¬zhengjiaodequadric surfaces erciqumianquality zhiliangquantity shuliangquotient shangRradian huduradius banjingrandom variable suijibianliangrank of a matrix juzhendezhirange zhiyuthe rate of change of y with respect to x y guanyux debianhualvrational function youlihanshurational number youlishuratio test bizhipanbiefareal number shishurectangle juxingregression huiguilinear regression xianxinghuiguirelated rate of change xiangguanbianhualvright circular cylinder yuanzhumianright-hand coordinate system youshouzuobiaoxiroot-extract kaigenroot of an equation fangchengdegenroot test genzhipanbiefarose of three loops sanyemeiguixianrow xingelementary row transformation (operation) chudengxingbianhuanSsaddle maanmiansample yangbenscalar shuliang£¬biaoliangsecant zhenggesecant line gexiansecond-order homogeneous linear equation with constant coefficienterjiechangxishuqiciweifenfangchengsecond-order nonhomogeneous linear equation with constant coefficient erjiechangxishufeiqiciweifenfangchengsequence shulieseries jishuinfinite series wuqiongjishuTaylor series (expansion) tailegongshiset jiheshow zhengmingsingle variable function yiyuanhanshuslope xielvspace kongjianvector space xiangliangkongjianlinear space xianxingkongjianspace analytic geometry kongjianjiexijihe2D(Dimension) space erweikongjianspace rectangular coordinate system kongjianzhijiaozuobiaoxisqueeze rule jiabizhunzesolid litisolid of revolution xuanzhuantisolution, solve jiegeneral solution tongjieparticular solution tejiespeed sulvspan shengcheng£¬zhangchengsphere qiumianstandard deviation (std) biaozhunchastate xushustationary point zhudianstochastic suijidestochastic differential equation (SDE) suijiweifenfangchengstraight line zhixiansubset zijisubspace zikongjiansubstitute, substitution dairu£¬zhihuanintegration by substitute huanyuanjifenfasufficient condition chongfentiaojiansum, summation he£¬qiuhesum of a series jishudehesuppose, supposition jiashesurface integral qumianjifensymbol fuhaosymmetry, symmetric duichengsymmetric equations of a line zhixiandeduichengshifangchengsystem of equations fangchengzusystem of linear equations xianxingfangchengzuTtangent zhengqietangent line qiexiantangent plane qiemiantheorem dinglitransformation bianhuantranslation pingyitrajectory guijitrapezoid tixingtriangle sanjiaoxingtrigonometric function sanjiaohanshuhyperbolic trigonometric function shuangqusanjiaohanshutriple integral sanzhongjifentotal differential quanweifentotal increment quanzengliangUunbiased wupiandeunion quanjiunit vector danweixiangliangunknown weizhishuupper limit jifenshangxianVvalue zhivariable bianliang£¬kebiandevariance fangchavector xiangliangn-dimensional vector N weixiangliangvelocity suduverify zhengmingvertex dingdian (fushuvertices)vertical yanzhengvertical asymptote qianzhijianjinxianvolume of a solid lititijithe volume of a solid of revolution xuanzhuantidetijiWthe work done by a force moulisuozuodegongZzero lingzeros of a polynomial duoxiangshidelingdianMathematical Sentence Patterns1. If ¡­¡­ , (then) ¡­¡­ (ruoshe¡­¡­£¬zeyou¡­¡­)2. Let ¡­¡­ , then ¡­¡­ . Therefore ¡­¡­ , so ¡­¡­ (ling¡­¡­£¬ze¡­¡­ £»yushi¡­¡­£¬yinci¡­¡­)3. By ¡­¡­ , we have ¡­¡­ (genju¡­¡­£¬kede¡­¡­)4. Prove (that) ¡­¡­ (zhengming¡­¡­)5. Compute that ¡­¡­ (jisuan¡­¡­)6. Given ¡­¡­ , find ¡­¡­ (she¡­¡­£¬zhengming¡­¡­)7. Solve the equation for y in terms of x (jiangfangchengzhongdey guanyux jiechulai)8. Since ¡­¡­ , (we have, it follows that) ¡­¡­ (yinwei¡­¡­£¬suoyiketuide¡­¡­)9. Assume (suppose) that ¡­¡­ , then ¡­¡­. Hence, ¡­¡­ (jiashe¡­¡­£¬zeyou¡­¡­£»yinci¡­¡­ )10. By hypothesis ¡­¡­ , hence ¡­¡­, and therefore ¡­¡­ (genjutishe¡­¡­£¬kede¡­¡­£¬yinci¡­¡­)11. The above results imply that ¡­¡­ (genjushangshujieguokede¡­¡­)12. When ¡­¡­ , ¡­¡­ becomes ¡­¡­ (dang¡­¡­shi£¬¡­¡­bianwei¡­¡­)13. Similarly ¡­¡­(xiangside/ tonglikede¡­¡­)14. In general ¡­¡­ (yibande¡­¡­)15. Specially ¡­¡­ (tebiede¡­¡­)16. Without loss of generality, we assume that ¡­¡­ (bushiyibanxing£¬keshe¡­¡­)17. 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