2024年9月trapezoidalsum(用龙贝格法求积分)

 更新时间:2024-09-21 06:57:36

  ⑴trapezoidalsum(用龙贝格法求积分

  ⑵先用另外种方法。formatlong%【】精确值。符号积分it=int(’(/sqrt(pi))*exp(-x)’,,)Aurate=eval(it)y=inline(’(/sqrt(pi))*exp(-x)’)%【】Simpson方法Simpson=quad(y,,)delta=Simpson-Aurate结果:Aurate=.y=Inlinefunction:y(x)=(/sqrt(pi))*exp(-x)Simpson=.delta=.e-【】从网上找到一个,存为romberg.m%=================functionR=romberg(f,a,b,n)formatlong%ROMBERG--puteRombergtableintegralapproximation.%%SYNOPSIS:%R=romberg(f,a,b,n)%%DESCRIPTION:%putesthepleteRombergtableapproximationtotheintegral%%/b%I=|f(x)dx%/a%%PARAMETERS:%f-Theintegrand.Assumedtobeafunctioncallableas%y=f(x)%with`x’in.%a-Leftintegrationintervalendpoint.%b-Rightintegrationintervalendpoint.%n-MaximumlevelinRombergtable.%%RETURNS:%R-Rombergtable.Representedasan(n+)-by-(n+)lower%triangularmatrixofintegralapproximations.%%SEEALSO:%TRAPZ,QUAD,QUADL.%NOTE:allindicesadjustedforMATLAB’sone-basedindexingscheme.%Pre-allocatetheRombergtable.Avoidssubsequentre-allocationwhich%isoftenverycostly.R=zeros();%Initialapproximation.Singleintervaltrapezoidalrule.R(+,+)=(b-a)/*(feval(f,a)+feval(f,b));%FirstcolumnofRombergtable.Increasinglyauratetrapezoidal%approximations.fori=:n,h=(b-a)/^i;s=;fork=:^(i-),s=s+feval(f,a+(*k-)*h);endR(i+,+)=R(i-+,+)/+h*s;end%RichardsonextrapolationgivesremainderofRombergtable.%%Note:Thetableisputedbycolumnsratherthanthemore%traditionalrowversion.Thereasonisthatthispreventsfrequent%(andneedless)re-putationofthe`fac’quantity.%%Moreover,MATLABmatricesinternallyuse``columnmajor’’orderingso%thisversionislessharmfultoputermemorycachesystems.This%reasonisanimplementationaldetail,though,andlessimportantin%introductorycoursessuchasMA.forj=:n,fac=/(^j-);form=j:n,R(m+,j+)=R(m+,j-+)+fac*(R(m+,j-+)-R(m-+,j-+));endendfunctionff=f(x)ff=/sqrt(pi)*exp(-x);%=================运行:》》R=romberg(’f’,,,)R=.....................

  ⑶高等数学arcsin(x分之的定义域是什么

  ⑷点“考研竞赛数学”↑可每天“涨姿势”哦!图片来源:pexels.内容来源:上海外教网V、X、ZValueoffunction:函数值Variable:变数Vector:向量Velocity:速度Verticalasymptote:垂直渐近线Volume:体积X-axis:x轴x-coordinate:x坐标x-intercept:x截距Zerovector:函数的零点Zerosofapolynomial:多项式的零点TTangentfunction:正切函数Tangentline:切线Tangentplane:切平面Tangentvector:切向量Totaldifferential:全微分Trigonometricfunction:三角函数Trigonometricintegrals:三角积分Trigonometricsubstitutions:三角代换法Tripeintegrals:三重积分SSaddlepoint:鞍点Scalar:纯量Secantline:割线Secondderivative:二阶导数SecondDerivativeTest:二阶导数试验法Secondpartialderivative:二阶偏导数Sector:扇形Sequence:数列Series:级数Set:集合Shellmethod:剥壳法Sinefunction:正弦函数Singularity:奇点Slantasymptote:斜渐近线Slope:斜率Slope-interceptequationofaline:直线的斜截式Smoothcurve:平滑曲线Smoothsurface:平滑曲面Solidofrevolution:旋转体Space:空间Speed:速率Sphericalcoordinates:球面坐标SqueezeTheorem:夹挤定理Stepfunction:阶梯函数Strictlydecreasing:严格递减Strictlyincreasing:严格递增Sum:和Surface:曲面Surfaceintegral:面积分Surfaceofrevolution:旋转曲面Symmetry:对称RRadiusofconvergence:收敛半径Rangeofafunction:函数的值域Rateofchange:变化率Rationalfunction:有理函数Rationalizingsubstitution:有理代换法Rationalnumber:有理数Realnumber:实数Rectangularcoordinates:直角坐标Rectangularcoordinatesystem:直角坐标系Relativemaximumandminimum:相对极大值与极小值Revenuefunction:收入函数Revolution,solidof:旋转体Revolution,surfaceof:旋转曲面RiemannSum:黎曼和Riemanniangeometry:黎曼几何Right-handderivative:右导数Right-handlimit:右极限Root:根P、QParabola:抛物线Paraboliylinder:抛物柱面Paraboloid:抛物面Parallelepiped:平行六面体Parallellines:并行线Parameter:参数Partialderivative:偏导数Partialdifferentialequation:偏微分方程Partialfractions:部分分式Partialintegration:部分积分Partiton:分割Period:周期Periodicfunction:周期函数Perpendicularlines:垂直线Piecewisedefinedfunction:分段定义函数Plane:平面Pointofinflection:反曲点Polaraxis:极轴Polarcoordinate:极坐标Polarequation:极方程式Pole:极点Polynomial:多项式Positiveangle:正角Point-slopeform:点斜式Powerfunction:幂函数Product:积Quadrant:象限QuotientLawoflimit:极限的商定律QuotientRule:商定律M、N、OMaximumandminimumvalues:极大与极小值MeanValueTheorem:均值定理Multipleintegrals:重积分Multiplier:乘子Naturalexponentialfunction:自然指数函数Naturallogarithmfunction:自然对数函数Naturalnumber:自然数Normalline:法线Normalvector:法向量Number:数Octant:卦限Oddfunction:奇函数One-sidedlimit:单边极限Openinterval:开区间Optimizationproblems:最佳化问题Order:阶Ordinarydifferentialequation:常微分方程Origin:原点Orthogonal:正交的LLaplacetransform:Leplace变换LawofCosines:余弦定理Leastupperbound:最小上界Left-handderivative:左导数Left-handlimit:左极限Lemniscate:双钮线Length:长度Levelcurve:等高线L’Hospital’srule:洛必达法则Limacon:蚶线Limit:极限Linearapproximation:线性近似Linearequation:线性方程式Linearfunction:线性函数Linearity:线性Linearization:线性化Lineintheplane:平面上之直线Lineinspace:空间之直线Lobachevskigeometry:罗巴切夫斯基几何Localextremum:局部极值Localmaximumandminimum:局部极大值与极小值Logarithm:对数Logarithmicfunction:对数函数IImplicitdifferentiation:隐求导法Implicitfunction:隐函数Improperintegral:瑕积分Increasing/DecreasingTest:递增或递减试验法Increment:增量IncreasingFunction:增函数Indefiniteintegral:不定积分Independentvariable:自变数Indeterminatefrom:不定型Inequality:不等式Infinitepoint:无穷极限Infiniteseries:无穷级数Inflectionpoint:反曲点Instantaneousvelocity:瞬时速度Integer:整数Integral:积分Integrand:被积分式Integration:积分Integrationbypart:分部积分法Intercepts:截距IntermediatevalueofTheorem:中间值定理Interval:区间Inversefunction:反函数Inversetrigonometricfunction:反三角函数Iteratedintegral:逐次积分HHighermathematics高等数学/高数E、F、G、HEllipse:椭圆Ellipsoid:椭圆体Epicycloid:外摆线Equation:方程式Evenfunction:偶函数ExpectedValued:期望值ExponentialFunction:指数函数Exponents,lawsof:指数率Extremevalue:极值ExtremeValueTheorem:极值定理Factorial:阶乘FirstDerivativeTest:一阶导数试验法Firstoctant:第一卦限Focus:焦点Fractions:分式Function:函数FundamentalTheoremofCalculus:微积分基本定理Geometricseries:几何级数Gradient:梯度Graph:图形GreenFormula:格林公式Half-angleformulas:半角公式Harmonicseries:调和级数Helix:螺旋线HigherDerivative:高阶导数Horizontalasymptote:水平渐近线Horizontalline:水平线Hyperbola:双曲线Hyperboloid:双曲面DDecreasingfunction:递减函数Decreasingsequence:递减数列Definiteintegral:定积分Degreeofapolynomial:多项式之次数Density:密度Derivative:导数ofapositefunction:复合函数之导数ofaconstantfunction:常数函数之导数directional:方向导数domainof:导数之定义域ofexponentialfunction:指数函数之导数higher:高阶导数partial:偏导数ofapowerfunction:幂函数之导数ofapowerseries:羃级数之导数ofaproduct:积之导数ofaquotient:商之导数asarateofchange:导数当作变率right-hand:右导数second:二阶导数astheslopeofatangent:导数看成切线之斜率Determinant:行列式Differentiablefunction:可导函数Differential:微分Differentialequation:微分方程partial:偏微分方程Differentiation:求导法implicit:隐求导法partial:偏微分法termbyterm:逐项求导法Directionalderivatives:方向导数Discontinuity:不连续性Diskmethod:圆盘法Distance:距离Divergence:发散Domain:定义域Dotproduct:点积Doubleintegral:二重积分changeofvariablein:二重积分之变数变换inpolarcoordinates:极坐标二重积分alculus:微积分differential:微分学integral:积分学Cartesiancoordinates:笛卡儿坐标一般指直角坐标Cartesiancoordinatessystem:笛卡儿坐标系Cauch’sMeanValueTheorem:柯西均值定理ChainRule:连锁律Changeofvariables:变数变换Circle:圆Circularcylinder:圆柱Closedinterval:封闭区间Coefficient:系数positionoffunction:函数之合成poundinterest:复利Concavity:凹性Conchoid:蚌线Cone:圆锥Constantfunction:常数函数Constantofintegration:积分常数Continuity:连续性atapoint:在一点处之连续性ofafunction:函数之连续性onaninterval:在区间之连续性fromtheleft:左连续fromtheright:右连续Continuousfunction:连续函数Convergence:收敛intervalof:收敛区间radiusof:收敛半径Convergentsequence:收敛数列series:收敛级数Coordinate:s:坐标Cartesian:笛卡儿坐标cylindrical:柱面坐标polar:极坐标rectangular:直角坐标spherical:球面坐标Coordinateaxes:坐标轴Coordinateplanes:坐标平面Cosinefunction:余弦函数Criticalpoint:临界点Cubicfunction:三次函数Curve:曲线Cylinder:圆柱CylindricalCoordinates:圆柱坐标A、BAbsoluteconvergence:绝对收敛Absoluteextremevalues:绝对极值Absolutemaximumandminimum:绝对极大与极小Absolutevalue:绝对值Absolutevaluefunction:绝对值函数Aeleration:加速度Antiderivative:反导数Approximateintegration:近似积分Approximation:逼近法bydifferentials:用微分逼近linear:线性逼近法bySimpson’sRule:Simpson法则逼近法bytheTrapezoidalRule:梯形法则逼近法Arbitraryconstant:任意常数Arclength:弧长Area:面积underacurve:曲线下方之面积betweencurves:曲线间之面积inpolarcoordinates:极坐标表示之面积ofasectorofacircle:扇形之面积ofasurfaceofarevolution:旋转曲面之面积Asymptote:渐近线horizontal:水平渐近线slant:斜渐近线vertical:垂直渐近线Averagespeed:平均速率Averagevelocity:平均速度Axes,coordinate:坐标轴Axesofellipse:椭圆之轴Binomialseries:二项级数

  ⑸翻译,不要用翻译机,翻译好再加分

  ⑹heassociatedthesefactswithcalculus:dyisthedifferentialofthefirstorder,andthesumofthemisy,forinstance,+++=.Leibenizthoughtthattheinvertibilityofdifferenceandsumequalstotheinvertiblityofthesolutionoftangentlineandintegration.theonlydistinctionisthatthedifferenceoftwoelements,belongingtothepascalalgebraicaltriangleandharmonicaltrianglerespectively,isfinite,whilethedifferentialofco-ordinateisinfinitelysmall.thisshowsthathehasalreadyassociatedhisearilerstudyonfinitequantityandtheinvertiblityofdifferentialwiththethoughtonthecalculationofinfinitelysmallquantities.italsocanbeobservedthattheviewofleibenizoncalculusisalgebraical,notgeometrical.tosolvetheproblemofintegration,leibeniznotedyastheareaofcurved-trapezoidalundertheplane-curve.thus,thelongitudinalcoordinateisrelatedtothevariableofarea.fewyearslater,henotedSydxasthearea,inwhich“∫”isthestretchedinitialletterofwordsum.onsolvingtheproblemofdifferential,thatis,differentiation,leibenizintroducednotationx/dtomotethedifferentiationofx,whichmeansreductionofthesameorder.healsothoughtthatiftherearedifferentialofdistinctorder,onlythelowestoneshouldbetaken,andabandonallthehigherorder.astothereason,heprovidedseveralexplanation,however,noneofthemissufficient.actually,heregardedthemethodasanpostulate.lateron,healteredx/dintodx,whichhasbeenadoptedandisusetillnow.绝对亲自翻译,好久不干这个,差点蒙了

  ⑺谁能帮我把下列短文翻译成英文

  ⑻----TheOlympicGamesandthesmallsailingshipworldseriesalladoptstheroutematchthepetitionform.Attendstheidenticalprojectpetitiontheshipunificationtosetsail.Apetitiongenerallycarrieson-turn,eachwheelpetesthefirstminute,thesecondminute,analogizesinturn.Removesoneaftertwoturnsofworstresult,arrangesthefinalpositionaordingtotheeachturnofresultsumofintegral,scorespointsfewfortobesuperior.Eachturnofpetitiongenerallymustcarryonminutestohours.petitionperiod,theemulationboardbasisdailywindpowercondition,arrangestwotothreeturnsofpetitions.UsesthepetitionroutearemanyfortheOlympicstrapezoidalroute,thisroutehascontainedagainstthewind,thecrosswindand尾风therange.Inadditionalsohasthetrianglerouteandthesausageshaperoute.Stemmingfromtothemeteorologyandthesafeconsideration,theemulationboardmayreduceapetitionturnoforderaordingtothewindpowersize.----Thesailingshippetitioninaquaticmeetsafavorableopportunitytohavetocarryoutasetonlandtrafficregulationstobemoreplexthanmanytrafficrules.Theathletewantstowanttoobtaintheresult,mustripelypasspageofthickcontestrules(EnglishtobecalledRRS),pageofthickregularcasesanalysesandapageofaboverankrule.Infrontofthematchalsomuststudyothertworegulartexts--contestrule(NoR)andthenavigationregulation(SIs).Howusestherulesuppressionmatch,causesoneselftomakeaprofitistheimportanttopicwhichtheathleteandthetrainerneedstoconcentrateonstudy.Thesailingshipcontestrulemainlyincludesthetrafficrules,thepetitionimplementationruleandtheprotesttriestostipulatethreemajorparts.ThisruleeveryyearsreviseaftertheOlympicGamesyeartime.Theinternationalsailassociationalsodistributestheruletoexplain,casewhichdistributesincludingeveryyear.Allcasesallareobeythenewestrulerevisiontopileandprint.----Inthetrafficrulesmonlyusedarrivesis--theportesthewindthesailingshiptohavetogivewaytotrafficthestarboardtoethewindtheship;Isintheweathergagetheshiptohavetogivewaytotraffictheleewardship;Whenmeetstheroutebuoyortheobstacle,latterapproachedthisobjecttheshiptohavetogivewaytotrafficalreadyapproachesthisobjecttheship,wasintheflanktheshiptohavetogivewaytotraffictheinsideship.Thepetitionimplementationrulehadmainlystipulatedthepetitionanizationandthemanagementstandard,likesetsailthemethodandthesignalnoticemethodandsoon.Theprotesttriesthestipulationissolvestheathleteinaquatictomeetoneanotherwithbumpshasthedisputeorviolatesaregulationanafterentiresetofrulingmethod.

  ⑼复化梯形求积公式和复化矩形求积公式在求权系数时有啥不同

  ⑽main.mg=(t)exp(-t.^);x=linspace(,,);y=zeros(,);y=zeros(,);fori=:y(i)=/sqrt(pi)*Simpson(g,,x(i),);%幸普森公式y(i)=/sqrt(pi)*trapezoidal(g,,x(i),);%复合梯形公式endplot(x,y,’r-’,x,y,’b.’);legend(’辛普森公式’,’复合梯形公式’);Simpson.mfunctiony=Simpson(f,a,b,M)%f被积函数;a积分下限;b积分上限;M子区间个数(将x分为多少个区间h=(b-a)/(*M);s=;s=;fori=:Mx=a+(*i-)*h;s=s+f(x);endforj=:(M-)x=a+*j*h;s=s+f(x);endy=h/*(f(a)+*s+*s+f(b));endtrapezoidal.mfunctiony=trapezoidal(f,a,b,n)h=(b-a)/n;x=zeros(,n+);F=zeros(,n+);fork=:nx(k+)=a+k*h;ifx(k+)==x(k+)=^(-);endendT_=h/*(f(x())+f(x(n+)));fori=:nF(i)=h*f(x(i));endT_=sum(F);y=T_+T_;end

  ⑾V、X、Z:Valueoffunction:函数值Variable:变数Vector:向量Velocity:速度Verticalasymptote:垂直渐近线Volume:体积X-axis:x轴x-coordinate:x坐标x-intercept:x截距Zerovector:函数的零点Zerosofapolynomial:多项式的零点T:Tangentfunction:正切函数Tangentline:切线Tangentplane:切平面Tangentvector:切向量Totaldifferential:全微分Trigonometricfunction:三角函数Trigonometricintegrals:三角积分Trigonometricsubstitutions:三角代换法Tripeintegrals:三重积分S:Saddlepoint:鞍点Scalar:纯量Secantline:割线Secondderivative:二阶导数SecondDerivativeTest:二阶导数试验法Secondpartialderivative:二阶偏导数Sector:扇形Sequence:数列Series:级数Set:集合Shellmethod:剥壳法Sinefunction:正弦函数Singularity:奇点Slantasymptote:斜渐近线Slope:斜率Slope-interceptequationofaline:直线的斜截式Smoothcurve:平滑曲线Smoothsurface:平滑曲面Solidofrevolution:旋转体Space:空间Speed:速率Sphericalcoordinates:球面坐标SqueezeTheorem:夹挤定理Stepfunction:阶梯函数Strictlydecreasing:严格递减Strictlyincreasing:严格递增Sum:和Surface:曲面Surfaceintegral:面积分Surfaceofrevolution:旋转曲面Symmetry:对称R:Radiusofconvergence:收敛半径Rangeofafunction:函数的值域Rateofchange:变化率Rationalfunction:有理函数Rationalizingsubstitution:有理代换法Rationalnumber:有理数Realnumber:实数Rectangularcoordinates:直角坐标Rectangularcoordinatesystem:直角坐标系Relativemaximumandminimum:相对极大值与极小值Revenuefunction:收入函数Revolution,solidof:旋转体Revolution,surfaceof:旋转曲面RiemannSum:黎曼和Riemanniangeometry:黎曼几何Right-handderivative:右导数Right-handlimit:右极限Root:根P、Q:Parabola:抛物线Paraboliylinder:抛物柱面Paraboloid:抛物面Parallelepiped:平行六面体Parallellines:并行线Parameter:参数Partialderivative:偏导数Partialdifferentialequation:偏微分方程Partialfractions:部分分式Partialintegration:部分积分Partiton:分割Period:周期Periodicfunction:周期函数Perpendicularlines:垂直线Piecewisedefinedfunction:分段定义函数Plane:平面Pointofinflection:反曲点Polaraxis:极轴Polarcoordinate:极坐标Polarequation:极方程式Pole:极点Polynomial:多项式Positiveangle:正角Point-slopeform:点斜式Powerfunction:幂函数Product:积Quadrant:象限QuotientLawoflimit:极限的商定律QuotientRule:商定律M、N、O:Maximumandminimumvalues:极大与极小值MeanValueTheorem:均值定理Multipleintegrals:重积分Multiplier:乘子Naturalexponentialfunction:自然指数函数Naturallogarithmfunction:自然对数函数Naturalnumber:自然数Normalline:法线Normalvector:法向量Number:数Octant:卦限Oddfunction:奇函数One-sidedlimit:单边极限Openinterval:开区间Optimizationproblems:最佳化问题Order:阶Ordinarydifferentialequation:常微分方程Origin:原点Orthogonal:正交的L:Laplacetransform:Leplace变换LawofCosines:余弦定理Leastupperbound:最小上界Left-handderivative:左导数Left-handlimit:左极限Lemniscate:双钮线Length:长度Levelcurve:等高线L’Hospital’srule:洛必达法则Limacon:蚶线Limit:极限Linearapproximation:线性近似Linearequation:线性方程式Linearfunction:线性函数Linearity:线性Linearization:线性化Lineintheplane:平面上之直线Lineinspace:空间之直线Lobachevskigeometry:罗巴切夫斯基几何Localextremum:局部极值Localmaximumandminimum:局部极大值与极小值Logarithm:对数Logarithmicfunction:对数函数I:Implicitdifferentiation:隐求导法Implicitfunction:隐函数Improperintegral:瑕积分Increasing/DecreasingTest:递增或递减试验法Increment:增量IncreasingFunction:增函数Indefiniteintegral:不定积分Independentvariable:自变数Indeterminatefrom:不定型Inequality:不等式Infinitepoint:无穷极限Infiniteseries:无穷级数Inflectionpoint:反曲点Instantaneousvelocity:瞬时速度Integer:整数Integral:积分Integrand:被积分式Integration:积分Integrationbypart:分部积分法Intercepts:截距IntermediatevalueofTheorem:中间值定理Interval:区间Inversefunction:反函数Inversetrigonometricfunction:反三角函数Iteratedintegral:逐次积分H:Highermathematics高等数学/高数E、F、G、H:Ellipse:椭圆Ellipsoid:椭圆体Epicycloid:外摆线Equation:方程式Evenfunction:偶函数ExpectedValued:期望值ExponentialFunction:指数函数Exponents,lawsof:指数率Extremevalue:极值ExtremeValueTheorem:极值定理Factorial:阶乘FirstDerivativeTest:一阶导数试验法Firstoctant:第一卦限Focus:焦点Fractions:分式Function:函数FundamentalTheoremofCalculus:微积分基本定理Geometricseries:几何级数Gradient:梯度Graph:图形GreenFormula:格林公式Half-angleformulas:半角公式Harmonicseries:调和级数Helix:螺旋线HigherDerivative:高阶导数Horizontalasymptote:水平渐近线Horizontalline:水平线Hyperbola:双曲线Hyperboloid:双曲面D:Decreasingfunction:递减函数Decreasingsequence:递减数列Definiteintegral:定积分Degreeofapolynomial:多项式之次数Density:密度Derivative:导数ofapositefunction:复合函数之导数ofaconstantfunction:常数函数之导数directional:方向导数domainof:导数之定义域ofexponentialfunction:指数函数之导数higher:高阶导数partial:偏导数ofapowerfunction:幂函数之导数ofapowerseries:羃级数之导数ofaproduct:积之导数ofaquotient:商之导数asarateofchange:导数当作变率right-hand:右导数second:二阶导数astheslopeofatangent:导数看成切线之斜率Determinant:行列式Differentiablefunction:可导函数Differential:微分Differentialequation:微分方程partial:偏微分方程Differentiation:求导法implicit:隐求导法partial:偏微分法termbyterm:逐项求导法Directionalderivatives:方向导数Discontinuity:不连续性Diskmethod:圆盘法Distance:距离Divergence:发散Domain:定义域Dotproduct:点积Doubleintegral:二重积分changeofvariablein:二重积分之变数变换inpolarcoordinates:极坐标二重积分C:Calculus:微积分differential:微分学integral:积分学Cartesiancoordinates:笛卡儿坐标,一般指直角坐标Cartesiancoordinatessystem:笛卡儿坐标系Cauch’sMeanValueTheorem:柯西均值定理ChainRule:连锁律Changeofvariables:变数变换Circle:圆Circularcylinder:圆柱Closedinterval:封闭区间Coefficient:系数positionoffunction:函数之合成poundinterest:复利Concavity:凹性Conchoid:蚌线Cone:圆锥Constantfunction:常数函数Constantofintegration:积分常数Continuity:连续性atapoint:在一点处之连续性ofafunction:函数之连续性onaninterval:在区间之连续性fromtheleft:左连续fromtheright:右连续Continuousfunction:连续函数Convergence:收敛intervalof:收敛区间radiusof:收敛半径Convergentsequence:收敛数列series:收敛级数Coordinate:s:坐标Cartesian:笛卡儿坐标cylindrical:柱面坐标polar:极坐标rectangular:直角坐标spherical:球面坐标Coordinateaxes:坐标轴Coordinateplanes:坐标平面Cosinefunction:余弦函数Criticalpoint:临界点Cubicfunction:三次函数Curve:曲线Cylinder:圆柱CylindricalCoordinates:圆柱坐标A、B:Absoluteconvergence:绝对收敛Absoluteextremevalues:绝对极值Absolutemaximumandminimum:绝对极大与极小Absolutevalue:绝对值Absolutevaluefunction:绝对值函数Aeleration:加速度Antiderivative:反导数Approximateintegration:近似积分Approximation:逼近法bydifferentials:用微分逼近linear:线性逼近法bySimpson’sRule:Simpson法则逼近法bytheTrapezoidalRule:梯形法则逼近法Arbitraryconstant:任意常数Arclength:弧长Area:面积underacurve:曲线下方之面积betweencurves:曲线间之面积inpolarcoordinates:极坐标表示之面积ofasectorofacircle:扇形之面积ofasurfaceofarevolution:旋转曲面之面积Asymptote:渐近线horizontal:水平渐近线slant:斜渐近线vertical:垂直渐近线Averagespeed:平均速率Averagevelocity:平均速度Axes,coordinate:坐标轴Axesofellipse:椭圆之轴Binomialseries:二项级

  ⑿求两个matlab的程序,分别利用复化梯形公式和辛普森公式求解误差函数erf(x)

  ⒀g=(t)exp(-t.^);

  ⒁x=linspace(,,);

  ⒂y=zeros(,);

  ⒃y=zeros(,);

  ⒄y(i)=/sqrt(pi)*Simpson(g,,x(i),);?%幸普森公式

  ⒅y(i)=/sqrt(pi)*trapezoidal(g,,x(i),);%复合梯形公式

  ⒆plot(x,y,’r-’,x,y,’b.’);

  ⒇legend(’辛普森公式’,’复合梯形公式’);

  ⒈functiony=Simpson(f,a,b,M)

  ⒉%f被积函数;a积分下限;b积分上限;M子区间个数(将x分为多少个区间

  ⒊h=(b-a)/(*M);

  ⒋x=a+(*i-)*h;

  ⒌forj=:(M-)

  ⒍y=h/*(f(a)+*s+*s+f(b));

  ⒎trapezoidal.m

  ⒏functiony=trapezoidal(f,a,b,n)

  ⒐h=(b-a)/n;

  ⒑x=zeros(,n+);

  ⒒F=zeros(,n+);

  ⒓x(k+)=a+k*h;

  ⒔x(k+)=^(-);

  ⒕T_=h/*(f(x())+f(x(n+)));

  ⒖F(i)=h*f(x(i));

  ⒗T_=sum(F);

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