matlab 第三章作业

第三章作业第一题：formatlongsymsxc1=int((x^4*(1-x)^4)/(1+x^2),0,1);%符号工具箱int计算c1=eval(c1);%指令eval一般应用于int后结果较复杂时，进一步求数值解。f=@(x)(x.^4.*(1-x).^4)./(1+x.^2);c2=quad(f,0,1);%数值积分指令quad要求积分限为常数第二题：formatlongf=@(x)((2/sqrt(pi))*exp(-x.^2));%定义误差函数fork=0.1:0.1:1.0c1=quad(f,0,k);c2=erf(k);c=abs(c1-c2);bar(k,c)holdonend第三题：vp=1578;f=@(v)((4/sqrt(pi))*((v.^2)/vp^3).*exp((-v.^2)/vp^2));c1=quad(f,0,vp)c2=quad(f,0,3.3*vp)c3=quad(f,3e4,3e8)结果：c1=0.427593285448571c2=0.999927444001040在0~3.3间的分子数接近为全部c3=3.520658577050803e-151速度很大的分子数很少第四题：clear;R=1;y=-4:0.11:4;z=-4:0.11:4;the=-0.5*pi:pi/400:0.5*pi;[Y,Z,T]=meshgrid(y,z,the);r=sqrt(cos(T).^2+Z.^2+(Y-sin(T)).^2);dv=1./r;v=trapz(dv,3);[ey,ez]=gradient(-v,0.5);figure(1)subplot(2,2,1)contour(Y(:,:,1),Z(:,:,1),v,10)subplot(2,2,2)[SY,SZ]=meshgrid(-4:0.2:4,[0.1,-0.1]);streamline(Y(:,:,1),Z(:,:,1),ey,ez,SY,SZ);[SY,SZ]=meshgrid([-4:0.2:4],[-0.005,0.005]);streamline(Y(:,:,1),Z(:,:,1),ey,ez,SY,SZ);R=1;the=0:pi/20:2*pi;x=-0.2:0.11:3;y=-0.2:0.11:3;z=-0.2:0.11:3;[X,Y,Z,T]=ndgrid(y,x,z,the);r=sqrt((X-cos(T)).^2+(Y-sin(T)).^2+Z.^2);dv=1./r;v=trapz(dv,4);[ex,ey,ez]=gradient(-v,0.5);[XX,YY,ZZ]=meshgrid(-0.2:0.11:3);[SX,SY,SZ]=meshgrid(0:0.5:3,0:0.5:3,[0.05]);subplot(2,2,3)Zmin=min(Z(:));Zmax=max(Z(:));streamslice(XX,YY,ZZ,ex,ey,ez,[],[],0.01)subplot(2,2,4)x=cos(the);y=sin(the);z=zeros(1,length(the));plot3(x,y,z,'LineWidth',3,'Color','r');holdonh1=streamline(XX,YY,ZZ,ex,ey,ez,SX,SY,SZ);h2=copyobj(h1,gca);rotate(h2,[1,0,0],180,[000]);h3=copyobj(allchild(gca),gca);rotate(h3,[0,1,0],180,[000]);view(-28,8)第五题：%亥姆霍兹线圈组成clearallM0=4*pi*1e-7;%初始化,给定环半径、电流、图形I0=5.0;Rh=1;C0=M0/(4*pi)*I0;Nx=21;Ny=21;%设定观测点网格数x=linspace(-Rh,Rh,Nx);%设定观测点范围及数组y=linspace(-Rh,Rh,Ny);Nh=20;%电流环分段T0=linspace(0,2*pi,Nh+1);%环的圆周角分段T1=T0(1:Nh);yb=Rh*cos(T1);zb=Rh*sin(T1);%设置环各段向量的起点坐标yb,zbT2=T0(2:Nh+1);ye=Rh*cos(T2);ze=Rh*sin(T2);%设置环各段向量的终点坐标ye,zedlx=0;dly=ye-yb;dlz=ze-zb;%计算环各段向量dl的三个长度分量xc=0;yc=(yb+ye)/2;zc=(zb+ze)/2;%计算环各段向量中点的三个坐标分量fori=1:Ny%循环计算各网格点上的B(x,y)值forj=1:Nxrx=x(j)-xc;ry=y(i)-yc;rz=0-zc;%观测点在z=0平面上r3=sqrt(rx.^2+ry.^2+rz.^2).^3;dlXr_x=dly.*rz-dlz.*ry;%计算叉乘积dlXr的x和y的分量dlXr_y=dlz.*rx-dlx.*rz;Bx(i,j)=sum(C0*dlXr_x./r3);%把环各段产生的磁场分量累加By(i,j)=sum(C0*dlXr_y./r3);endendBax=Bx(:,11:21)+Bx(:,1:11);Bay=By(:,11:21)+By(:,1:11);subplot(1,2,1);mesh(x(11:21),y,Bax);xlabel(x);ylabel(y);%画出其B分布三维图subplot(1,2,2);plot(y,Bax),grid,xlabel(y);ylabel(Bx);