matlab教程张志涌课后习题答案.doc

第二章 %分段函数的写法syms y xz=int(x*y,x,0,1);g = evalin(symengine,[' piecewise([y > 1/2,' char(z) '], [y <= 1/2, 1])'])G=int(g,y)g = piecewise([1/2 < y, y/2], [y <= 1/2, 1]) G = piecewise([1/2 < y, y^2/4], [y <= 1/2, y])%习题2-1class(vpa(sym(3/7+0.1),4))%习题2-2findsym(sym('sin(w*t)'),1)findsym(sym('a*exp(-X)'),1)findsym(sym('z*exp(j*th)'),1)%习题2-3syms x a positivex_1=solve('x^3-44.5')syms x unrealx_2=solve('x^2-a*x+a^2')syms a unrealx_2=solve('x^2-a*x+a^2')x_3=solve('x^2-a*x-a^2')syms x realevalin(symengine,'anames(Properties)')evalin(symengine,'getprop(x)')%习题2-47/3, pi/3 , pi*3^(1/3)a = pi*3^(1/3) ,b = sym( pi*3^(1/3) ),c = sym( pi*3^(1/3),'d'),d = sym( 'pi*3^(1/3) ' )vpa(abs(a-d)) , vpa(abs(b-d)) , vpa(abs(c-d))%习题2-5syms a11 a12 a13 a21 a22 a23 a31 a32 a33A = [a11 a12 a13;a21 a22 a23;a31 a32 a33]a=det(A)B=inv(A)C=subexpr(B)[RS,w]=subexpr(B,'w')%习题2-6syms ksyms a positive% fk =a^k * heaviside(k)fk =a^k s=symsum(fk,k,0,inf) %习题2-7clear allsyms ksyms x positivefk =2/(2*k+1)*(((x-1)/(x+1))^(2*k+1))s=symsum(fk,k,0,inf) s1=simple(s)%习题2-8clear all, syms ty=abs(sin(t))df=diff(y),class(df)df1=limit(df,t,0,'left')df2=subs(df,'t',sym(pi/2))%习题2-9clear all, syms x;f=exp(-abs(x)).*abs(sin(x)); fint=int(f,x,-5*pi,1.7*pi), digits(64), vpa(fint)class(fint)%习题2-10clear all,syms x y,f=x.^2+y.^2, fint=(int(int(f,y,1,x.^2),x,1,2)), double(fint)%习题2-11clear all, syms t x; f=sin(t)/t, yx=int(f,t,0,x), ezplot(yx,[0 2*pi])fint=subs(yx,x,4.5),%或yxd=int(f,t,0,4.5),fint=double(yxd)hold on, plot(4.5,fint,'*r')%习题2-12% clear all, syms x n; f=(sin(x))^n; yn=int(f,'x',0,pi/2), class(yn)clear all, syms x n; syms n positive ; f=(sin(x))^n; yn=int(f,'x',0,pi/2), class(yn)% y(1/3)=?yn1=subs(yn,'n',sym(1/3)),vpa(yn1) %或yn=limit(yn,n,1/3),vpa(yn)%或yy=int(sin(x).^(1/3),x,0,pi/2) ,vpa(yy)%习题2-23clear, syms x y SS = dsolve('Dy*y/5+x/4=0','x')ezplot(subs(S(1),'C3',1),[-2,2 -2,2],1), hold onezplot(subs(S(2),'C3',1),[-2,2 -2,2],1)%解为 S = % 2^(1/2)*(C3 - (5*x^2)/8)^(1/2)% -2^(1/2)*(C3 - (5*x^2)/8)^(1/2)ezplot(subs(S(1),'C3',1),[-2,2 -2,2],1), hold onezplot(subs(S(2),'C3',1),[-2,2 -2,2],1) % 用此两条指令绘圆，在 y=0处有间隙ezplot(subs(y^2-(S(1))^2, 'C3', 1),[-2,2 -2,2],2) %用椭圆方程绘图不产生间隙colormap([0 0 1]) %用ezplot(fun)绘图时，如果fun中只有一个参数，绘图的颜色是蓝色；如果fun中有两个参数，绘图的颜色是绿色，此指令设置图形颜色为蓝。

grid on S1=subs(S(1),'C3',1)subs(S1,{x},{1.6^(1/2)})y=double(solve(S1))t=linspace(y(2),y(1),100)S2=subs(S(2),'C3',1)figureplot(t,subs(S1,x,t)), hold onplot(t,subs(S2,x,t))axis([-2,2 -2,2]) %习题2-24x=dsolve('Dx=a*t^2+b*t','x(0)=2','t')%习题2-25[f,g]=dsolve('Df=3*f+4*g','Dg=-4*f+3*g','f(0)=0','g(0)=1','x')第三章%习题3-1 a=0:2*pi/9:2*pi b=linspace(0,2*pi,10) %习题3-2rand( 'twister',0),A=rand(3,5)[I1,J1]=find(A>0.5)subindex_A=sub2ind(size(A),I1,J1)subindex_A=find(A>0.5)[I,J]=ind2sub(size(A),subindex_A)index_A=[I J]%122_2rand('twister',0),A=rand(3,5),B=A>0.5,C=find(B)[ci,cj]=ind2sub(size(A),C) %此法太繁[Ci,Cj]=find(B)%122_5t=linspace(1,10,100) (1) y=1-exp(-0.5.*t).*cos(2.*t),plot(t,y)(2) L=length(t)for k=1:L, yy(k)=1-exp(-0.5*t(k))*cos(2*t(k)), end, plot(t,yy)%122_6clear,format long, rand('twister',1),A=rand(3,3),B=diag(diag(A)),C=A.*(~B)%或C=A-B%或C=triu(A,1)+tril(A,-1)%习题3-3% s=sign(randint(1,1000,[],123)-.5);% n=sum(s==-1)rand('state',123),s=sign(rand(1,1000)-.5),n=sum(s==-1)%习题3-4clear allA=[1 2;3 4]B1=A.^(0.5), B2=A^(0.5),A1=B1.^2A2=B2^2A1-Anorm(A1-A)A1-A2norm(A1-A2)clear allA=sym('[1 2;3 4]')B1=A.^(0.5), B2=A^(0.5),A1=simple(B1.^2)A2=simple(B2^2)A1-Avpa(A1-A)A1-A2vpa(A1-A2)%习题3-5t=linspace(1,10,100) %(1)L=length(t)for k=1:L yy(k)=1-exp(-0.5*t(k))*cos(2*t(k)) endfigure(1),plot(t,yy)%(2)y=1-exp(-0.5.*t).*cos(2.*t),figure(2),plot(t,y) figure(3),subplot(1,2,1),plot(t,y)subplot(1,2,2),plot(t,yy)%习题3-6clear,format long, rand('twister',1),A=rand(3,3),B=diag(diag(A)),C=A.*(~B)%或C=A-B%或C=triu(A,1)+tril(A,-1)%习题3-7clear,x=-3*pi:pi/15:3*pi; y=x; [X,Y]=meshgrid(x,y); % X=ones(size(y))*x;Y=y*ones(size(x));warning off; Z=sin(X).*sin(Y)./X./Y;% (1)“非数”数目m=sum(sum(isnan(Z))); %k=Z(isnan(Z));m=length(k)% (2)绘图surf(X,Y,Z); shading interp% (3)“无裂缝”图形的全部指令：x=-3*pi:pi/15:3*pi;y=x';[X,Y]=meshgrid(x,y); % X=ones(size(y))*x;Y=y*ones(size(x));X=X+(X==0)*eps;Y=Y+(Y==0)*eps;Z=sin(X).*sin(Y)./X./Y;surf(X,Y,Z);shading interp%习题3-8clearfor k=10:-1:1; A=reshape(1:10*k,k,10); Sa(k,:)=sum(A,1);endSa clearfor k=10:-1:1; A=reshape(1:10*k,k,10); if k==1 Sa(k,:)=A; else Sa(k,:)=sum(A); endendSa 第四章%习题4-1clear allload prob_data401;diff_y=diff(y)./diff(t);gradient_y=gradient(y)./gradient(t);% plot(t(1:end-1),diff_y,t,gradient_y)figure(1)subplot(1,2,1),plot(t,y,t(1:end。