精讲多练matlab习题

1第一章2.设A=1.2,B=-4.6,C=8.0,D=3.5,E=-4.0计算：22arctanEABCTDA=1.2;B=-4.6;C=8.0;D=3.5;E=-4.0;T=atan(2*pi*A+E/(2*pi*B*C))/DT=0.4112x=pi/180*45;(sin(x)+sqrt(35))/72^(1/5)ans=2.81583.设45x，计算5sin()3572xx=pi/180*45;(sin(x)+sqrt(35))/72^(1/5)ans=2.81584.设5.67,7.811,ab计算：()()10logababe2a=5.67;b=7.811;exp(a+b)/log10(a+b)ans=6.3351e+0055.计算2316()(3.2)/(7.7)yxxxxx在3x时的值。x=3;y=sqrt(x)-6*(x+1/x)+(x-3.2)^2/(x+7.7)^3y=-18.26796.已知圆的半径为15，求其直径，周长及面积。r=15;d=2*r;c=pi*2*rc=94.2478s=pi*r*rs=706.85837已知某三角形的三个边的边长为8.5,14.6和18.4，求该三角形的面积。提示：()()()areassasbsc其中：()/2,sabca、b、c分别为三角形三边边长。3a=8.5;b=14.6;c=18.4;s=(a+b+c)/2;area=sqrt(s*(s-a)*(s-b)*(s-c))area=60.6106第二章1.设矩阵311212123A111210111B求：22(1)2(2)43(3)(4)(5)ABABABBAABBAA=[311;212;123];B=[11-1;2-10;1-11];（1）2*A+Bans=731614337（2）4*A*A-3*B*Bans=4422138401946403356（3）A*Bans=61-26-108-42（4）B*Aans=400410222（5）A*B-B*Aans=21-22-206-602.设三阶矩阵AB、，满足16,ABAABA其中5100310041007A求矩阵B。A=[1/300;01/40;001/7];B=6*inv(inv(A)-eye(3))B=3000200013.设11(2)TECBAC，其中E是4阶单位矩阵，TA是4阶矩阵A的转置。其中1232012300120001B1201012000120001C求矩阵A。B=[12-3-2;012-3;0012;0001];C=[1201;0120;0012;0001];A=(inv(2*eye(4)-inv(C)*B)*inv(C))'A=1000-210061-21001-214.设二阶矩阵A、B、X，满足2XABX，其中2112A0220B求矩阵X。A=[2-1;-12];B=[02;-20];X=(2*A+B)/2X=20-225.求解线性方程组12412341234123423285223742212xxxxxxxxxxxxxxxA=[2-302;1521;3-11-1;4122];B=[8;2;7;12];x=A\Bx=3.00000.0000-1.000071.00006.求解一元六次方程654331247810xxxxx的根。A=[31247081];x=roots(A)x=-3.8230-0.5275+0.8497i-0.5275-0.8497i0.5007+0.6749i0.5007-0.6749i-0.12347.求多项式65433124781xxxxx被3(3)(5)xxx除后的结果。a=[31247081];A=[3];b=poly(A);c=[1050];d=conv(b,c);[div,rest]=deconv(a,d)div=32152rest=000103557881第三章81.求极限0limcosxxxx=sym('x');limit((cos(sqrt(x)))^(pi/x),x,0,'right')ans=exp(-1/2*pi)2.求极限213sinxxcoslim1cosln1xxxxx=sym('x');f=sym('(3*sin(x)+x^2*cos(1/x))/((1+cos(x))*log(1+x))');limit(f,x,0)ans=3/23.求极限22411limsinxxxxxxx=sym('x');f=sym('(sqrt(4*x^2+x-1)+x+1)/sqrt(x^2+sin(x))');limit(f,x,-inf)ans=914.求极限222200lim(xy)xyxysymsxy;f=sym('(x^2+y^2)^(x^2*y^2)');limit(limit(f,x,0),y,0)ans=15.已知求y’x=sym('x');y=sym('(tan(sqrt(x+sqrt(x+sqrt(2*x)))))^2');diff(y,x)ans=tan((x+(x+2^(1/2)*x^(1/2))^(1/2))^(1/2))*(1+tan((x+(x+2^(1/2)*x^(1/2))^(1/2))^(1/2))^2)/(x+(x+2^(1/2)*x^(1/2))^(1/2))^(1/2)*(1+1/2/(x+2^(1/2)*x^(1/2))^(1/2)*(1+1/2*2^(1/2)/x^(1/2)))6.已知求y’x=sym('x');22ytgxxx221cos(x)sinyx10y=sym('cos(x^2)*sin(1/x)^2');diff(y,x)ans=-2*sin(x^2)*x*sin(1/x)^2-2*cos(x^2)*sin(1/x)*cos(1/x)/x^27.求积分x=sym('x');y=sym('sqrt(sin(x)-sin(x)^3)');int(y,x,0,pi)ans=4/38.求积分x=sym('x');y=sym('sqrt((x+1)/(x-1))/x');int(y,x)ans=-((1+x)/(x-1))^(1/2)*(x-1)*(atan(1/(-1+x^2)^(1/2))-log(x+(-1+x^2)^(1/2)))/((1+x)*(x-1))^(1/2)9.求下列微分方程的通解dsolve('D2y+4*Dy+4*y=exp(-2*x)','x')ans=30sinsinxxdx11x1xdxx2''4'4yexyy111/2*exp(-2*x)*(2*C2+2*x*C1+x^2)10.求微分方程dsolve('x^2*Dy+x*y=y^2','y(1)=1')ans=x*exp(1/x)/(exp(1/x)+exp(1/x*t)*x-exp(1/x*t))第四章1.已知向量1240510112131,请绘图表示。A=[1240510112131];plot(A)2.绘制单位圆。提示：使用axis(‘square’)命令保证图形的纵横坐标刻度比例相同。123456789100510152025221',|1xxyxyyy12ezplot('x^2+y^2=1')axissquare3.绘制伏安特性曲线：URI，假设R分别为1,5,10和20。R=[151020];I=0:0.1:10;U=I'*R;plot(I,U)legendR=1R=5R=10R=20gridonxyx2+y2=1-1.5-1-0.500.511.5-1.5-1-0.500.511.5134.某地区一年中每月的平均气温和平均降雨量如下表4-5所示，请画出其图形，要求标注出坐标轴、数据点位置、数据点大小等。表4–5温度-降雨量数据月份湿度降雨量10.24.622.33.638.72.1418.52.9524.63.0632.12.7736.82.2837.12.5928.34.31017.83.4012345678910020406080100120140160180200伏安特性曲线电流/A电压/VR=1R=5R=10R=2014116.42.112-3.23.7month=1;12;degree=[0.22.38.718.524.632.136.837.128.317.86.4-3.2];rain=[4.63.62.12.93.02.72.22.54.33.42.13.7];plot(month,degree,'+',month,rain,'p')month=1:12;degree=[0.22.38.718.524.632.136.837.128.317.86.4-3.2];rain=[4.63.62.12.93.02.72.22.54.33.42.13.7];plot(month,degree,'+',month,rain,'p')gridonxlabel('month')ylabel('degree&rainfall')text(5,24.6,'\leftarrowdegree');text(3,2.1,'\leftarrowrainfall');title('Temperature&rainfall');155.已知矩阵11111111222221122222112222211111111请绘图表示。A=ones(5,7);A(2:4,2:6)=2;plot(A)024681012-50510152025303540monthdegree&rainfalldegreerainfallTemperature&rainfall166.绘制22zxy的三维立体图。x=-5:0.1:5;y=x;[X,Y]=meshgrid(x,y);Z=X.^2+Y.^2;surf(X,Y,Z)11.522.533.544.5511.11.21.31.41.51.61.71.81.92-505-50501020304050177.绘制由函数222/4/9/161xyz形成的立体图，并通过改变观察点来获得该图形在各个坐标平面上的平面投影。theta=(0:0.01:2)*pi;phi=theta;x=zeros(length(theta),length(phi));y=x;z=x;fori=1:length(theta)forj=1:length(phi)x(i,j)=2*sin(theta(i))*cos(phi(j));y(i,j)=3*sin(theta(i))*sin(phi(j));z(i,j)=4*cos(theta(i));endendaxissquaresubplot(2,2,1)mesh(x,y,z)title('三维')subplot(2,2,2)mesh(x,y,z)view(90,0)title('x轴视图')18subplot(2,2,3)mesh(x,y,z)view(0,0)title('y轴视图')subplot(2,2,4)