北京科技大学-MATLAB数学实验期末考试题目及答案.docx

第1张1.figure(1)x=-pi:pi/50:pi;y=cos(2*(x.^2));plot(x,y,r-.)figure(2)x=-pi:pi;y=cos(2*(x.^2));xi=-pi:pi/8:pi;yi1=interp1(x,y,xi,*nearest);yi2=interp1(x,y,xi,*linear);yi3=interp1(x,y,xi,*spline);yi4=interp1(x,y,xi,*cubic);plot(x,y,ro,xi,yi1,--,xi,yi2,-,xi,yi3,k.-,xi,yi4,m:)2.functionxdot=exf(t,x)u=t^3;xdot=[0 1;-5 0]*x+[0 3]*u;clf,t0=0;tf=10;x0t=[1;2];[t,x]=ode23(exf,[t0,tf],x0t)y1=x(:,1),y2=x(:,2);plot(t,y1,-,t,y2,o)第2张1.第一张dsolve(D2y+4*y=t*cos(t),y(0)=1,Dy(0)=1,t)第二张 functionxdot=exf(t,x)u=t*cos(t);xdot=[0 1;-4 0]*x+[0 1]*u;第三张t0=0;tf=10;x0t=[1;1];[t,x]=ode23(exf,[t0,tf],x0t)y1=x(:,1)y2=cos(2*t) + (2*sin(2*t))./9 - cos(2*t).*(sin(3*t)/36 + sin(t)./4 - (t.*cos(3*t))./12 - (t.*cos(t))./4) + sin(2*t).*(cos(3*t)./36 + cos(t)./4 + (t.*sin(3*t))./12 + (t.*sin(t))./4)plot(x,y1,b-,x,y2,r-.)legend(y的图像,y的一阶导图像)2.x=0:2*pi/9:2*pi;y=(sin(2*x)).^2p3=polyfit(x,y,3);p5=polyfit(x,y,5);p7=polyfit(x,y,7);disp(三阶拟合函数),f3=poly2str(p3,x)disp(五阶拟合函数),f5=poly2str(p5,x)disp(七阶拟合函数),f7=poly2str(p7,x)x1=0:pi/50:2*pi;y3=polyval(p3,x1);y5=polyval(p5,x1);y7=polyval(p7,x1);plot(x,y,rp,x1,y3,--,x1,y5,k-,x1,y7,-);legend(拟合点,三阶拟合,五阶拟合,七阶拟合)第3张1.t1=-pi:pi/4:pi;x1=cos(t1);y1=sin(t1);z1=t1;subplot(1,2,1),plot3(x1,y1,z1)t2=-4:0.25:4[x2,y2]=meshgrid(t2);z2=sin(x2+y2);subplot(1,2,2),surf(x2,y2,z2),title(sin(x+y))2.functionxdot=exf(t,x)u=0;xdot=[0 1;-17/4 -1]*x+[0 0]*u;clf,t0=0;tf=8;x0t=[-1;2];[t,x]=ode23(exf,[t0,tf],x0t)y1=x(:,1)y2=x(:,2)plot(t,y1,b-,t,y2,r-.)legend(y的图像,y的一阶导图像)第4张1、figure(1)[x,y]=meshgrid(-2:.5:2); z=x.^2+y.^2+3; [x1,y1]=meshgrid(-2:.1:2); z1=x1.^2+y1.^2+3; subplot(1,2,1),mesh(x,y,z),title(数据点) subplot(1,2,2),mesh(x1,y1,z1),title(函数图象) [xi,yi]=meshgrid(-2:.125:2); zi1=interp2(x,y,z,xi,yi,*nearest); zi2=interp2(x,y,z,xi,yi,*linear); zi3=interp2(x,y,z,xi,yi,*spline); zi4=interp2(x,y,z,xi,yi,*cubic);figure(2) subplot(221),mesh(xi,yi,zi1),title(最近点插值) subplot(222),mesh(xi,yi,zi2),title(线性插值) subplot(223),mesh(xi,yi,zi3),title(样条插值) subplot(224),mesh(xi,yi,zi4),title(立方插值) 2、functionxdot=