《MATLAB基礎教程（第六版）（微課版）》習題答案 薛山 - 第7-12章

?PAGE29?附錄各章習題參考答案附錄各章習題參考答案第7章習題參考答案1.答：>>f=sym('sin(x)+x');2.答：>>digits(2);vpa(subs(f,x,pi/6))ans=1.0>>digits(3);vpa(subs(f,x,pi/6))ans=1.02>>digits(5);vpa(subs(f,x,pi/6))ans=1.0236>>digits(10);vpa(subs(f,x,pi/6))ans=1.02359877563．答：>>f=sym('x^4+x^2+1');>>g=sym('x^3+4*x^2+5*x+8');(1)>>f+gans=x^4+x^3+5*x^2+5*x+9(2)>>f*gans=(x^4+x^2+1)*(x^3+4*x^2+5*x+8)(3)>>finverse(g)ans=1/(9*(x/2+((x/2-82/27)^2-1/729)^(1/2)-82/27)^(1/3))+(x/2+((x/2-82/27)^2-1/729)^(1/2)-82/27)^(1/3)-4/3(4)>>symsx>>compose(g,f,x)ans=4*(x^4+x^2+1)^2+(x^4+x^2+1)^3+5*x^2+5*x^4+134．答：(1)>>f=sym('3*x-2*x^2+5+3*x^2-2*x-5');>>collect(f)ans=x^2+x(2)>>f=sym('2*x^2-3*x*y+y^2-2*x*y-2*x^2+5*x*y-2*y+1');>>collect(f)ans=y^2-2*y+15．答：(1)>>factor(sym('779866'))ans=2*149*2617(2)>>factor(sym('-2*m^8+512'))ans=-2*(m-2)*(m+2)*(m^2+4)*(m^4+16)(3)>>factor(sym('3*a^2*(x-y)^3-4*b^2*(y-x)^2'))ans=(x-y)^2*(3*a^2*x-3*a^2*y-4*b^2)6．答：(1)>>f=str2sym('sin(x)+x^2');>>ezplot(f,[0,2*pi]);(2)>>f=str2sym('x^3+2*x^2+1');>>ezplot(f,[-22]);7．答：(1)>>limit(str2sym('(tan(x)-sin(x))/(1-cos(2*x))'))ans=0(2)>>y=str2sym('x^3-2*x^2+sin(x)');>>diff(y)ans=cos(x)-4*x+3*x^2(3)>>symsxy>>f=x*y*log(x+y);>>fx=diff(f,x)fx=y*log(x+y)+(x*y)/(x+y)(4)>>symst>>y=log(1+t);>>int(y)ans=(log(t+1)-1)*(t+1)>>int(y,0,27)ans=28*log(28)-278．答：>>taylor(str2sym('sin(x)'))ans=x^5/120-x^3/6+x9．答：>>[x,y]=solve(str2sym('2*x+3*y=1'),str2sym('3*x+2*y=-1'))x=-1y=110．答：(1)>>symsxy>>z=x*exp(-(x^2+y^2));>>symsuv>>fourier(z,x,u)ans=-(u*pi^(1/2)*exp(-u^2/4-y^2)*1i)/2(2)>>laplace(z,y,v)ans=(x*pi^(1/2)*erfc(v/2)*exp(v^2/4)*exp(-x^2))/2(3)>>ztrans(z,x,u)ans=-u*diff(ztrans(exp(-x^2-y^2),x,u),u)>>ztrans(z,y,v)ans=x*ztrans(exp(-x^2-y^2),y,v)11．答：>>symsxy>>z=1/(2*pi)*exp(-(x^2+y^2));>>ezsurf(x,y,z,[-3,3,-3,3]);第8章習題參考答案1.答：>>x=0:pi/10:2*pi;>>sinx=sin(x);>>cosx=cos(x);>>figure,plot(x,sinx,'LineWidth',4)>>holdon,plot(x,cosx,'r:','LineWidth',4)>>holdon,plot(x(find(cosx==sinx)),cosx(find(cosx==sinx)),'r*','LineWidth',4)2．答：(1)>>x=0:pi/10:10*pi;>>plot(x,sin(x))(2)>>[X,Y]=meshgrid(-10:0.5:10);>>Z=X.^2+6*X*Y+Y.^2+6*X+2*Y-1;>>plot3(X,Y,Z)(3)>>[X,Y]=meshgrid(-16:0.4:16,-4:0.1:4);>>Z=X.^2/16-Y.^2/4;>>plot3(X,Y,Z)3.答：(1)利用pie函數(略)。(2)>>hist(round(rand(100,1)*10))(3)>>X=round(rand(10,1)*10);>>stairs(X)4.答：界面交互方式略。函數方式的參考答案如下(繪制圖形略)。>>title('正弦曲線和余弦曲線');>>gtext('sin(x)')>>gtext('cos(x)')>>legend('sin(x)','cos(x)')答：使用view函數和colormap函數。第9章習題參考答案1.答：>>figure,plot(0:0.2:10,log(0:0.2:10)),title('對數函數的圖像')2.答：figure('Color','y');set(gca,'DefaultLineLineWidth',4);a=4;b=3;x=linspace(-a,a,100);y1=sqrt((1-x.^2/(a^2))*b^2);y2=-sqrt((1-x.^2/(a^2))*b^2);plot(x,y1);holdon;plot(x,y2);3.答：t=-2:0.1:2;x=cos(t/pi);y=2*sin(t/(2*pi));figure,plot(t,x);holdon;plot(t,y);%ifwaitforbuttonpresswhile(1)ifwaitforbuttonpress==0get(gcf,'CurrentObject');c=ceil((rand)*5);switchccase1set(get(gcf,'CurrentObject'),'Color','r');case2set(get(gcf,'CurrentObject'),'Color','g');case3set(get(gcf,'CurrentObject'),'Color','b');case4set(get(gcf,'CurrentObject'),'Color','k');case5set(get(gcf,'CurrentObject'),'Color','y');endendend第10章習題參考答案答：略答：略答：略答：略答：略第11章習題參考答案1.答：略。2.答：Simulink中的連線圖如下求解出的，，的解如下從上到下的三條曲線分別對應的是，，的解。3.答：S函數的代碼如下function[sys,x0,str,ts]=sfuntmpl(t,x,u,flag)switchflag,case0,[sys,x0,str,ts]=mdlInitializeSizes;case3,sys=mdlOutputs(t,x,u);case{1,2,4,9},sys=[];otherwiseerror(['Unhandledflag=',num2str(flag)]);endfunction[sys,x0,str,ts]=mdlInitializeSizessizes=simsizes;sizes.NumContStates=0;sizes.NumDiscStates=0;sizes.NumOutputs=-1;siz