基礎(chǔ)與應(yīng)用教程習(xí)題答案 作者 蔡旭暉 劉衛(wèi)國(guó) 蔡立燕 答案

1、第1章一、思考題4. （1） B=A(2:5,1:2:5)（2）A(7)=（3） A=A+30（4）size(A)（5） t(find(t=0)=eps（6）t=reshape(x,3,4)（7）abs('matlab')（8）char(93)5. A=97,67,34,10;-78,75,65,5;32,5,-23,-59;0,-12,54,7 (1) B=A(1:3,:) C=A(:,1:2) D=A(2:4,3:4) E=B*C(2)A(find(A>=50 & A<=100)二、實(shí)驗(yàn)題1.x=-74/180*pi;y=-27/180*pi;sin(x

2、*x+y*y)/sqrt(tan(abs(x+y)+pi2.a=-3.0:0.1:3.0; exp(-0.3*a).*sin(a+0.3)3.x=2,4;-0.45,5;log(x+sqrt(1+x.*x)/24. A=3,54,2;34,-45,7;87,90,15;B=1,-2,67;2,8,74;9,3,0;（1）A*Bans = 129 432 4197 7 -407 -1052 402 591 12489A.*Bans = 3 -108 134 68 -360 518 783 270 0（2） A3ans = -28917 240246 -4368 137883 -259101 27

3、669 171333 252504 38673A.3ans = 27 157464 8 39304 -91125 343 658503 729000 3375（3）A/Bans = -5.8845 5.3549 -0.2028 6.3554 -5.6596 4.3293 -6.6325 6.2078 9.0241B/Aans = 30.2855 19.2643 -8.5614 33.4394 21.1547 -9.3974 -0.7443 -0.3938 0.2830（4）A,Bans = 3 54 2 1 -2 67 34 -45 7 2 8 74 87 90 15 9 3 0 A(1,3,

4、:);B2ans = 3 54 2 87 90 15 600 183 -81 684 282 726 15 6 8255.a=1+2i;b=3+4i;c=exp(pi*i/6)c = 0.8660 + 0.5000ic+a*b/(a+b)ans = 1.6353 + 1.8462i第2章一、思考題3.s=0;for n=0:63 s=s+2n;enddisp(s)n=0:63;s=sum(2.n)二、實(shí)驗(yàn)題1.x=input('輸入一個(gè)四位整數(shù)：');y=fix(x/1000),mod(fix(x/100),10),mod(fix(x/10),10),mod(x,10)z=mo

5、d(y+7),10)x=z(3)*1000+z(4)*100+z(1)*10+z(2)2. gh=input('輸入工號(hào)');h=input('輸入工時(shí)');dj=84;if h>120 gz=dj*120+1.15*dj*(h-120);elseif h<60 gz=dj*h-700;else gz=dj*h;endformat bank;display(gh,gz)3. 循環(huán)結(jié)構(gòu)n=input('input n:');s=0;for k=1:n s=s+1/k2;enddisplay(sqrt(s*6)向量運(yùn)算n=input(&#

6、39;input n:');k=1:n;display(sqrt(sum(1./k.2)*6)4.y=0;k=0;while y<3 k=k+1; y=y+1/(2*k-1);enddisplay(k-1,y-1/(2*k-1) 5. x0=0;x=1;k=0;a=input('a=');b=input('b=');while abs(x-x0)>=1e-5 && k<500 x0=x; x=a/(b+x0); k=k+1;enddisplay(k,x);display(-b+sqrt(b2+4*a)/2,(-b-sqr

7、t(b2+4*a)/2);6.y=fun(40)/(fun(30)+fun(20)（1）函數(shù)文件fun.mfunction f=fun(n)f=n+log(n2+5);（2）函數(shù)文件fun.mfunction f=fun(n)a=1:n;f=sum(a.*(a+1);第3章一、思考題4. t=0:0.01:1.5;y=sqrt(3)/2*exp(-4*t).*sin(4*sqrt(3)*t+pi/3);5. x=-10:0.01:10;y=linspace(-6,6,size(x,2)z=x.3+3*x.*y.2;plot3(x,y,z)6. x=100:100:400;y=100:100:4

8、00;z=636,697,624,478;698,712,630,478;680,674,598,412;662,626,552,334;X,Y=meshgrid(x,y);mesh(X,Y,z)二、實(shí)驗(yàn)題1. （1）x=-10:0.01:10;plot(x,x-x.3/3/2)（2）plot(x,exp(-x.*x/2)/2/pi)（3）x=-8:0.01:8;plot(x,sqrt(64-x.*x)/2)（4）t=0:pi/100:6*pi;plot(t.*sin(t),t.*cos(t)2. （1）x1=linspace(0,1,100);y1=2*x1-0.5;t=linspace(0

9、,pi,100);x=sin(3*t).*cos(t);y=sin(3*t).*sin(t);plot(x1,y1,'r-',x,y,'b:');text(0.4,1,'y=2x-0.5');text(-0.4,0.5,'x=sin(3t)cos(t)');text(-0.4,0.3,'y=sin(3t)sin(t)');（2） subplot(1,2,1);scatter(x1,y1,10) title('y=2x-0.5');subplot(1,2,2);scatter(x,y,10)3. su

10、bplot(1,21); x=1:1:100; y=sin(1./x);plot(x,y)subplot(1,2,2);fplot('sin(1/x)',1,100)4. subplot(2,2,1);bar(t,y);subplot(2,2,2);stairs(t,y);subplot(2,2,3);stem(t,y)subplot(2,2,4);semilogy(t,y);5. theta=linspace(-pi,pi,100);ro=5.*cos(theta)+4;polar(theta,ro);fi=linspace(0,2*pi,100);a=1r=a.*(1+co

11、s(fi);polar(fi,r);6. t=0:pi/20:2*pi;x=exp(-t./20).*cos(t);y=exp(-t./20).*sin(t);z=t;plot3(x,y,z);t=0:0.01:1;x=t;y=t.2;z=t.3;plot3(x,y,z);7. x=-30:0.1:0;y=0:0.1:30;x,y=meshgrid(x,y);z=10.*sin(sqrt(x.2+y.2)./sqrt(1+x.2+y.2);meshc(x,y,z);8. x=linspace(-3,3,100);y=linspace(-3,3,100);x y=meshgrid(x,y);fx

12、y=-5./(1+x.2+y.2);i=find(abs(x)<=0.8 & abs(y)<=0.5);fxy(i)=NaN;surf(x,y,fxy)9. u=linspace(1,10,100);v=linspace(-pi,pi,100);u,v=meshgrid(u,v);x=3.*u.*sin(v);y=2.*u.*cos(v);z=4*u.2;x=3*u.*sin(v);y=2*u.*cos(v);z=4*u.2;surf(x,y,z);shading interp;light('position',1,0,1);10. t=0:pi/100:2

13、*pi;y=sin(t);comet(t,y)第4章一、思考題5.（1）A=eye(3);（2）C=100+(200-100)*rand(5,6);（3）D=1+sqrt(0.2)*randn(1,500);（4）E=ones(size(A);（5）A=A+30*eye(size(A);（6）B=diag(diag(A)二、實(shí)驗(yàn)題1. P=pascal(5);H=hilb(5);Dp=det(P);Dh=det(H);Kp=cond(P);Kh=cond(H);P矩陣的性能更好，因?yàn)镵p較小2.A=1,-1,2,3;0,9,3,3;7,-5,0,2;23,6,8,3B=3,pi/2,45;32

14、,-76,sqrt(37);5,72,4.5e-4;exp(2),0,97A1=diag(A);B1=diag(B);A2=triu(A);B2=triu(B);A3=tril(A);B3=tril(B);rA=rank(A);rB=rank(B);nA=norm(A);nb=norm(B);cA=cond(A);cB=cond(B);3. A=31,1,0;-4,-1,0;4,-8,-2；V,D=eig(A);4. A=diag(-1,-1,-1,-1,-1)+diag(-1,-1,-1,-1,1)+diag(2,2,2,2,2)b=1,0,0,0,0'x1=inv(A)*b;x2=

15、Ab;L,U=lu(A);x3=U(Lb);Q,R=qr(a);Q,R=qr(A);x4=R(Qb)R=chol(A);x5=R(R'b)5. B=sparse(A);x1=inv(B)*b;x2=Bb;L,U=lu(B);x3=U(Lb);第5章一、思考題3.A=randn(10,5);mean(A)std(A)max(max(A)min(min(A)sum(A,2)sum(sum(A)sort(A,1)sort(A,2,'descend')二、實(shí)驗(yàn)題1. A=rand(1,30000);mean(A)std(A)max(A)min(A)size(find(A>

16、0.5)/size(A)2. h=466,715,950,1422,1635;w=7.04,4.28,3.40,2.52,2.13;hh=500,900,1500;ww=interp1(h,w,hh,'spline')3. x=linspace(1,10,50);y=log(x);f=polyfit(x,y,5);yy=polyval(f,x);plot(x,y,'r-',x,yy,'g.')4. N=64; % 采樣點(diǎn)數(shù)T=5; % 采樣時(shí)間終點(diǎn)t=linspace(0,T,N); % 給出N個(gè)采樣時(shí)間ti(I=1:N)x=3*exp(-t);

17、 % 求各采樣點(diǎn)樣本值xdt=t(2)-t(1); % 采樣周期f=1/dt; % 采樣頻率(Hz)X=fft(x); % 計(jì)算x的快速傅立葉變換XF=X(1:N/2+1); % F(k)=X(k)(k=1:N/2+1)f=f*(0:N/2)/N; % 使頻率軸f從零開始plot(f,abs(F),'-*') % 繪制振幅-頻率圖xlabel('Frequency');ylabel('|F(k)|')5. （1）p1=1 2 0 0 7;p2=1 -2;p3=1 0 0 5 1;p12=conv(p1,p2);p=p12+zeros(1,size

18、(p12,2)-size(p3,2),p3;roots(p)（2）A=-1,4,3;2,1,5;0,5,6;Px=polyval(p,A)Pxm=polyvalm(p,A)6.（1） z=fzero('3*x-sin(x)+1',0)（2） 建立函數(shù)文件myfun.mfunction F=myfun(X)x=X(1);y=X(2);F(1)=x*x+y*y-9;F(2)=x+y-1;在命令窗口中輸入以下命令：x=fsolve(myfun,3,0',optimset('Display','off')第6章一、思考題2.fx=inline(&

19、#39;1./(1+x.2)');I,n=quad(fx,-100000,100000,1e-3);I,n=quadl(fx,-100000,100000,1e-3);x=-100000:0.01:100000;y=1./(1+x.*x);trapz(x,y);3.(1) fx=inline('-2*y+2*x*x+2*x');t,y=ode23(fx,0,0.5,1)(2) fx=inline('y-exp(x)*cos(x)');t,y=ode23(fx,0,3,1)二、實(shí)驗(yàn)題1. for x=1:3 fx=x,x2,x3;1,2*x,3*x;0,2

20、,6*x; diff(fx)end2.（1）x=0:0.01:1;y=x.10+10.x+1./log10(x);dy=diff(y)/0.01;（2）x=0:0.01:1;y=log(1+x);dy=diff(y,2)/0.01;plot(x(1:99),dy)3.（1）fx=inline('x.2.*sqrt(2*x.*x+3)'); quad(fx,1,5)（2）fx=inline('x./sin(x).2'); quad(fx,pi/4,pi/3)（3）fx=inline('abs(cos(x+y)'); dblquad(fx,0,pi,

21、0,pi)（4）syms x y;fx=x*y; int(int(fx,y2,y+2),-1,2)x的積分區(qū)間為【0，2】時(shí)fx=inline('x.*y'); dblquad(fx,0,2,-1,2)4.x=0.3:0.2:1.5;y=0.3895,0.6598,0.9147,1.1611,1.3971,1.6212,1.8325;trapz(x,y)5.（1）yp=inline('-(1.2+sin(10*x)*y'); t,y=ode23(yp,0,5,1); （2）令，則可寫出原方程的狀態(tài)方程形式： -> 建立函數(shù)文件ztfun.mfunction

22、 y=ztfun(t,x)b=0;0;cos(t);y=0,1,0;0,0,1;-1/(3+sin(t),-1,5*cos(2*t)/(t+1)2*x+b;解微分方程組t,y=ode23(ztfun,0,5,1;0;2);6.建立函數(shù)文件ztfun.mfunction yy=ztfun(t,y)yy=y(2)*y(3);-y(1)*y(3);-0.51*y(1)*y(2);解微分方程組t,y=ode23(ztfun,0,5,0;1;1)第7章一、思考題3.（1）數(shù)值積分fx=inline('exp(x).*(1+exp(x).2');quad(fx,0,log(2)符號(hào)積分f=sym('exp(x)*(1+exp(x)2');v=int(f,0,log(2);eval(v)（2）略二、實(shí)驗(yàn)題1.A=sym('1,2,3;x,y,z;3,2,1')rank(A)inv(A)det(A)2.(1) y=sym('sqrt(