Matlab與科學(xué)計(jì)算樣題 (加主觀題答案)

Matlab與科學(xué)計(jì)算考試樣題（客觀題）1下面的MATLAB語(yǔ)句中正確的有:2a=pi;recordl=3+4ia=2.0,c=l+6j2.已知水的黏度隨溫度的變化公式如下，其中a=0.03368,b=0.000221,計(jì)算溫度t為20,30,40度時(shí)的粘度分別是：\+at+bt2(a)0.0018(b)0.0010Ao為0C水的黏度，值為1.785x10-3；a、b為常數(shù)，分別為0.03368\+at+bt2(a)0.0018(b)0.00100.0010 0.00070.0007 0.0005 (0.0010 0.0008 0.0007)1.7850e-0031.0131e-0036.6092e-0041.0131e-0036.6092e-0044.6772e-004(1.0131e-0038.0795e-0046.6092e-004)a=0.03368;b=0.000221;uO=l.785e-3;t=[203040];u=u0./(l+a*t+b?t.A2)?formatshort%fbrmatshorte?u3.請(qǐng)補(bǔ)充語(yǔ)句以畫(huà)出如圖所示的圖形:[x,y]=meshgrid(-2:0.1:2,-2:().1:2);Z=x*exp(-x.A2-y.A2);Plot3(x,y,Z)plot3(x,y,Z)mesh(x,y,Z)plot3(x,y,z)4.設(shè)y=span{l,x,x2},用最小一乘法擬合如下表數(shù)據(jù)。X0.51.01.52.02.53.()y1.752.453.814.808.008.60計(jì)算的結(jié)果為：a)0.49001.25010.85600.85601.25010.4900-0.63413.8189-3.7749

3.8189-3.77492.8533解釋說(shuō)明：?x=0.5:0.5:3.0;?y=[1.75,2.45,3.81,4.80,8.00,8.60];?a=polyfit(x,y,2)a=0.4900 1.2501 0.8560?xl=[O.5:O.25:3.O];?yl=a(l)*xl.A2+a(2)*x1+a(3)?plot(x,y；*')?holdon?plot(xl,yl；-r')5.求方程在x二0.5附近的根.a)0.6180a)-1.1719e-25fzero('x.A2+x-l',0.5)-1fzero('x.A2+x-l',0.5)-1.61806.用Newton-Cotes方法計(jì)算如下積分J(2x+3)dr1(a)133.6625))bedz(x/(X/(\23.860087.9027-1.6180functionf=fun(x)f=x.*x.*sqrt(2*x+3)quadl('fun',l,5,le-10)或quadl('x.*x.*sqrt(2*x+3)',l,5,le-10)或fun=@(x)(x.*x.*sqrt(2*x+3));quadl(fun,l,5,le-IO)a)\7\J/

cdy=ln(1+x),求x=1時(shí)y"的近似值。-0.250.5-0.6137-1.6137symsxy=log(l+x)f=diff(y,2)subs(f,l)8.某公司用3臺(tái)軋機(jī)來(lái)生產(chǎn)規(guī)格相同的鋁合金薄板。取樣測(cè)量薄板的厚度，精確至％。厘米。得結(jié)果如下：軋機(jī)1:0.2360.2380.2480.2450.243軋機(jī)2:0.2570.2530.2550.2540.261

軋機(jī)3:0.2580.2640.2590.2670.262計(jì)算方差分析結(jié)果，并判定各臺(tái)軋機(jī)所生產(chǎn)的薄板的厚度有無(wú)顯著的差異？a）p=1.3431e-005,沒(méi)有顯著差異。b)c)d)P=0.9688，沒(méi)有顯著差異。p=0.4956,有顯著差異。p=0.9688,有顯著差異。?X=[0.2360.2380.2480.2450.243;0.2570.2530.2550.2540.261:0.2580.2640.2590.2670.262];?P=anoval(X，)9.求解如下非線性方程組在（x=-1,y=-1）附近的解2x-y=e~xa)0.56710.5671-x+2y=e~yb)無(wú)解c)無(wú)窮解functionF=myfun(x)d)00F=(2*x(l)-x(2)-exp(-x(l));-x(l)+2*x(2)-exp(-x(2))J;x=fsolve(,myfun,,[-l.l])或者fsolveC[2*x(l)-x(2)-exp(-x(l));-x(l)+2*x(2)-exp(-x(2))]',[-lH)10.采用0DE45求解如下多階常微分方程，并求出當(dāng)x=1.8505時(shí)的函數(shù)值。31.644174.690731.644174.6907118.786263.2564建立求解函數(shù)文件myfun03functiondy=myfun03(x,y)dy=zeros(3,l)%初始化變量dy,改行可以沒(méi)有dy(l)=y(2);%dy⑴表示y的一階導(dǎo)數(shù),其等于y的第二列值dy(2)=y(3);%dy(2)表示y的二階導(dǎo)數(shù)dy(3)=2*y(3)/xA3+3*y(2)/xA3+3*exp(2*x)/xA3%dy(3)表示y的三階導(dǎo)數(shù)求解過(guò)程：(x45,y45]=ode45(,myfun03,,[l,10],[l1030]);査workspace中的矩陣框0.4096%,+0.1234毛+0.3678七+0.2943x4=0.404311.求解I、.列方程組。0.2246石+0.3872沔+0.4015^+0.1129x4=11.求解I、.列方程組。0.3645x,+0.1920巧+0.3781易+00643易=0.42400.1784a-,+0.4002易+0.2786x3+0.3927xd=-0.2557a)-0.1819-1.66302.2172-0.4467-o.7841-o.00372.1994-0.4226-0.44672.2172-1.6630-0.1819-0.42262.1994-0.0037-0.7841a=[0.40960.12340.36780.2943;022460.38720.4015 0.1129;0.3645 0.1920 0.37810.0643;0.!7840.40020.27860.3927];b=(0.40430.15500.4240-0.2557]'x=a\b或x=inv(a)*bsymsxsymsxf=(xA3+xA2+x+1)A(1/3)-sqrt(xA2+x+1)*log(exp(x)+x)/xlimii(f,x,inf)12.求極限limy/j^+x2+x+\+y/jT+x+l a)-1/6Inf-Inf-1有關(guān)上機(jī)考試說(shuō)明：樣題中每一題對(duì)應(yīng)一組相似的題，每個(gè)人考試的時(shí)候每一組題目只會(huì)出現(xiàn)一道題，同組題可能會(huì)有一些細(xì)節(jié)的變化，比如說(shuō)某個(gè)參數(shù)變化了或者某個(gè)積分函數(shù)發(fā)生了變化，但是所用到的基本命令是一樣的?？荚嚨臅r(shí)候可以啟動(dòng)Matlab運(yùn)行以得到所需要的結(jié)果。考試采用閉卷考試，但是可以使用聯(lián)機(jī)幫助。Matlab與科學(xué)計(jì)算考試樣題(主觀題)考試要求：1、 要求獨(dú)立完成不得與他人共享，答卷雷同將做不及格處理。2、 答卷用Word文件遞交，文件名為學(xué)號(hào)+姓名.doc,試卷寫(xiě)上姓名及學(xué)號(hào)。3、 答卷內(nèi)容包括：程序；運(yùn)行結(jié)果及其分析；圖也要粘貼在文檔中。1.求vanderPol方程y”—"(1~J2)/+y=0的數(shù)值解(/1=1),并作出y(X)和y(x)的圖形。(15，)functiondy=vdpl(t,y);dy=[y(2);(1-y(1)A2)*y(2)-y(1)];調(diào)用Matlab函數(shù)。對(duì)于初值_y(0)=2,火0)=0,解為[T,Y]=ode45(,vdpl\[020],[2;0]);觀察結(jié)果。利用圖形輸出解的結(jié)果：plot(T,Y(:,l),’-’，T,Y(:,2),‘一')；title('SolutionofvanderPolEquation,mu=l');xlabel('timet');ylabel('solutiony');legend('yl','y2f)或者plot(T,Y(:,l),'-*);holdon;plot(T,Y(:,2),'--');title('SolutionofvanderPolEquation,mu=l');xlabel(*timet');ylabel('solutiony')10 12t次tSolutionat3derPoiEquation.fnu=1Auo弓10 12t次tSolutionat3derPoiEquation.fnu=1Auo弓32.在金屬材料塑性變形時(shí)的流變應(yīng)力。與應(yīng)變￡的近似表達(dá)式為b=k礦，對(duì)于某金屬材料測(cè)得實(shí)驗(yàn)數(shù)據(jù)如下:應(yīng)力a925112516252125262531253625應(yīng)變￡0.110.160.350.480.610.710.85計(jì)算參數(shù)k和n,并分別畫(huà)出實(shí)驗(yàn)測(cè)試數(shù)據(jù)點(diǎn)和擬合曲線.（15'）0近似表達(dá)式可以寫(xiě)成lnb=lnA+〃lnsy=[925,1125,1625,2125,2625,3125,3625];x=[0.11,0.16,0.35,0.48,0.61,0.71,0.85];xl=log(x);yl=log(y);p二polyfit(xl,yl,1);n=p(l),k=exp(p(2))xi=linspace(0.1,0.9,800);xi=0.1:0.001:0.9;yi=exp(polyval(p,log(xi)));yi二k*xi.n;plot(x,y,'o',xi,yi)xlabel('\cpsilon')ylabel('\sigma')legendCexperimental','Fitting')3.在4個(gè)子圖中繪制不同的三角函數(shù)圖(10')o函數(shù)范圍：x=0:0.1*pi:2*pi;函數(shù)為：sin(x);cos(x)：sin(x)+cos(x)；sin(x).*cos(x)?x=0:0.1*pi:2