MATLAB程序设计教程课后答案.docx
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MATLAB程序设计教程课后答案.docx
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MATLAB程序设计教程课后答案
unit3
实验指导
1、n=input('请输入一个三位数:
');
a=fix(n/100);
b=fix((n-a*100)/10);
c=n-a*100-b*10;
d=c*100+b*10+a
2
(1)
n=input('请输入成绩');
switchn
casenum2cell(90:
100)
p='A';
casenum2cell(80:
89)
p='B';
casenum2cell(70:
79)
p='C';
casenum2cell(60:
69)
p='D';
otherwise
p='E';
end
price=p
(2)n=input('请输入成绩');
ifn>=90&n<=100
p='A';
elseifn>=80&n<=89
p='B';
elseifn>=70&n<=79
p='C';
elseifn>=60&n<=69
p='D';
else
p='E';
end
price=p
(3)try
n;
catch
price='erroe'
end
3
n=[1,5,56,4,3,476,45,6,3,76,45,6,4,3,6,4,23,76,908,6];
a=n
(1);
b=n
(1);
form=2:
20
ifn(m)>a
a=n(m);
elseifn(m)
b=n(m);
end
end
max=a
min=b
法2
n=[1,5,56,4,3,476,45,6,3,76,45,6,4,3,6,4,23,76,908,6];
min=min(n)
max=max(n)
4
b=[:
:
];
forn=1:
61
a=b(n);
y(n)=(exp*a)-exp*a))/2*sin(a++log(+a)/2);
end
y
5
y1=0;
y2=1;
n=input('请输入n的值:
');
fori=1:
n
y1=y1+1/i^2;
y2=y2*((4*i*i)/((2*i-1)*(2*i+1)));
end
y1
y2
6
A=[1,1,1,1,1,1;2,2,2,2,2,2;3,3,3,3,3,3;4,4,4,4,4,4;5,5,5,5,5,5;6,6,6,6,6,6];
n=input('请输入n的值:
');
ifn<=5&n>=0
disp(A([n],:
));
elseifn<0
disp(lasterr);
elsedisp(A([6],:
));
disp(lasterr);
end
7
(1)
f=[];
forn=1:
40
f(n)=n+10*log(n^2+5);
end
y=f(40)/(f(30)+f(20))
(2)
f=[];a=0;
forn=1:
40
f(n)=a+n*(n+1);
a=f(n);
end
y=f(40)/(f(30)+f(20))
8
y=0;
m=input('输入m的值:
');
n=input('输入n值:
');
fori=1:
n
y=y+i^m;
end
y
************************************************************
functions=shi8_1(n,m)
s=0;
fori=1:
n
s=s+i^m;
end
************************************************************
shi8_1(100,1)+shi8_1(50,2)+shi8_1(10,1/2)
思考练习
2
N=[1,2,3,4,5];
2.*N
N./2
1./N
1./N.^2
3
s=fix(100*rand(1,20)*9/10+10)
y=sum(s)/20
j=0;
fori=1:
20
ifs(i) j=j+1; A(j)=s(i); elsecontinue; end end A 4 y1=0;y2=0; n=input('请输入n的值: '); fori=1: n y1=y1+-(-1)^i/(2*i-1); y2=y2+1/4^i; end y1 y2 unit4 实验指导 1 (1) x=-10: : 10; y=x-x.^3./6; plot(x,y) (2) x=-10: : 10; ezplot('x^2+2*y^2-64',[-8,8]); gridon; 2 t=-pi: pi/10: pi; y=1./(1+exp(-t)); subplot(2,2,1);bar(t,y); title('条形图(t,y)'); axis([-pi,pi,0,1]); subplot(2,2,2); stairs(t,y,'b'); title('阶梯图(t,y)'); axis([-pi,pi,0,1]); subplot(2,2,3); stem(t,y,'k'); title('杆图(t,y)'); axis([-pi,pi,0,1]); subplot(2,2,4); loglog(t,y,'y'); title('对数坐标图(t,y)'); 3 (1) t=0: pi/50: 2*pi; r=5.*cos(t)+4; polar(t,r); title('\rho=5*cos\theta+4'); (2) t=-pi/3: pi/50: pi/3; r=5.*((sin(t)).^2)./cos(t); polar(t,r); 4 (1) t=0: pi/50: 2*pi; x=exp(-t./20).*cos(t); y=exp(-t./20).*sin(t); z=t; plot3(x,y,z); gridon; (2) [x,y]=meshgrid(-5: 5); z=zeros(11)+5; mesh(x,y,z); shadinginterp; 5 [x,y,z]=sphere(20); surf(x,y,z); axisoff; shadinginterp; m=moviein(20); fori=1: 20 axis([-i,i,-i,i,-i,i]) m(: i)=getframe; end movie(m,4); 思考练习 2 (1) x=-5: : 5; y=(1./(2*pi)).*exp((-(x.^2))/2); plot(x,y); (2) t=-2*pi: : 2*pi; x=t.*sin(t); y=t.*cos(t); plot(x,y); gridon; 3 t=0: pi/1000: pi; x=sin(3.*t).*cos(t); y1=sin(3.*t).*sin(t); y2=2.*; plot(x,y1,'k',x,y2); holdon; k=find(abs(y1-y2)<1e-2); x1=x(k); y3=2.*; plot(x1,y3,'rp'); 4 x=-2: : 2; y=sin(1./x); subplot(2,1,1); plot(x,y); subplot(2,1,2); fplot('sin(1./x)',[-2,2],1e-4); 5 (1) i=-4*pi: : 10; j=12./sqrt(i); polar(i,j); title('{\rho}=12/sqrt(\theta)') (2) a=-pi/6: : pi/6; b=3.*asin(a).*cos(a)./((sin(a)).^3+(cos(a)).^3); polar(a,b); 6 (1) [u,v]=meshgrid(-4: : 4); x=3.*u.*sin(v); y=2.*u.*cos(v); z=4.*u.^2; subplot(2,1,1); mesh(x,y,z); subplot(2,1,2); surf(x,y,z); (2) [x,y]=meshgrid(-3: : 3); z=-5./(1+x.^2+y.^2); subplot(1,2,1); mesh(x,y,z); subplot(1,2,2); surf(x,y,z); unit5 实验指导 1 A=randn(10,5) x=mean(A) y=std(A) Max=max(max(A)) Min=min(min(A)) Sumhang=sum(A,2) SumA=sum(Sumhang) B=sort(A); C=sort(B,2,'descend'); C 2 (1) a=0: 15: 90; b=a./180.*pi; s=sin(b) c=0: 15: 75; d=c./180.*pi; t=tan(d) e=input('请输入想计算的值: '); S=sin(e/180*pi) T=tan(e/180*pi) S1=interp1(a,s,e,'spline') T1=interp1(c,t,e,'spline') P1=polyfit(a,s,5); P2=polyfit(c,t,5); S2=polyval(P1,e) T2=polyval(P2,e) (2) n=[1,9,16,25,36,49,64,81,100]; N=sqrt(n); x=input('jisuanzhi: '); interp1(n,N,x,'cubic') 3 N=64; T=5; t=linspace(0,T,N); h=exp(-t); dt=t (2)-t (1); f=1/dt; X=fft(t); F=X(1: N/2+1); f=f*(0: N/2)/N; plot(f,abs(F),'-*') 4 P=[2,-3,0,5,13]; Q=[1,5,8]; p=polyder(P) q=polyder(P,Q) [a,b]=polyder(P,Q) 5 P1=[1,2,4,0,5]; P2=[0,1,2]; P3=[1,2,3]; P=P1+conv(P2,P3) X=roots(P) A=[-1,,;,2,;0,5,]; p=polyval(P,A) 思考练习 4 A=rand(1,30000); a=mean(A) b=std(A) Max=max(A) Min=min(A) n=0; fori=1: 30000 if(A(i)> n=n+1; end end n y=n/30000 5 p=[45,74,54,55,14;78,98,45,74,12;87,98,85,52,65] [M,S]=max(p) [N,H]=min(p) junzhi=mean(p,1) fangcha=std(p,1,1) zong=sum(p,2); [Max,wei]=max(zong) [Min,wei]=min(zong) [zcj,xsxh]=sort(zong,'descend') 6 x=[1: 10: 101]; y=[0,,,,,,,,,,]; [p,s]=polyfit(x,y,5) a=1: 5: 101; y1=polyval(p,a); plot(x,y,': o',a,y1,'-*') unit6 实验指导 1 A=[1/2,1/3,1/4;1/3,1/4,1/5;1/4,1/5,1/6]; p=[,,]'; x=A\p A=[1/2,1/3,1/4;1/3,1/4,1/5;1/4,1/5,1/6]; p=[,,]'; x=A\p cond(A) 2 (1) x1=fzero(@funx1,-1) functionfx=funx1(x) fx=x^41+x^3+1; (2) x2=fzero(@funx2, functionfx=funx2(x) fx=x-sin(x)/x; (3) options=optimset('Display','off'); x=fsolve(@fun3,[1,1,1]',options) q=fun3(x) functionq=fun3(p) x=p (1); y=p (2); z=p(3); q (1)=sin(x)+y^2+log(z)-7; q (2)=3*x+2^y-z^3+1; q(3)=x+y+z-5; 3 (1) t0=0; tf=5; y0=1; [t,y]=ode23(@fun4,[t0,tf],y0); t' y' functionyp=fun4(t,y) yp=-+sin(10*t))*y; (2) t0=0; tf=5; y0=1; [t,y]=ode23(@fun5,[t0,tf],y0); t' y' functionyp=fun5(t,y) yp=cos(t)-y/(1+t^2); 4 x=fminbnd(@mymin,0,2); -mymin(x) functionfx=mymin(x) fx=-(1+x.^2)/(1+x.^4); 5 options=optimset('Display','off'); [x,fval]=fmincon(@fun6,[0,0,0],[],[],a,b,lb,ub) -fval functionf=fun6(x) f=-(sqrt(x (1))+(400-x (1))*+(sqrt(x (2))+(400-x (1))* (2))*+sqrt(3)+(((400-x (1))* (2))*(3))*+sqrt(x(x4))); 思考练习 1 (1) A=[2,3,5;3,7,4;1,-7,1]; B=[10,3,5]'; C1=inv(A)*B C2=A\B [L,U]=lu(A); x=U\(L\B) (2) A=[6,5,-2,5;9,-1,4,-1;3,4,2,-2;3,-9,0,2]; B=[-4,13,1,11]'; C1=inv(A)*B C2=A\B [L,U]=lu(A); x=U\(L\B) 2 (1) x1=fzero(@funx1, functionfx=funx1(x) fx=3*x+sin(x)-exp(x); (2) x1=fzero(@funx2,1) functionfx=funx2(x) fx=x-1/x+5; (3) options=optimset('Display','off'); x=fsolve(@fun3,[3,0]',options) q=fun3(x) functionq=fun3(p) x=p (1); y=p (2); q (1)=x^2+y^2-9; q (2)=x+y-1; 3 (1) t0=0; tf=5; y0=[0,1]; [t,y]=ode45(@vdpol,[t0,tf],y0); [t,y] functionydot=vdpol(t,y); ydot (1)=(2-3*y (2)-2*t*y (1))./(1+t^2); ydot (2)=y (1); ydot=ydot'; (2) t0=0; tf=5; y0=[1;0;2]; [t,y]=ode45(@vdpoll,[t0,tf],y0); [t,y] functionydot=vdpoll(t,y); ydot (1)=cos(t)-y(3)./(3+sin(t))+5*y (1).*cos(2*t)/((t+1).^2)-y (2); ydot (2)=y (1); ydot(3)=y (2); ydot=ydot'; 4 x=fminbnd(@mymin,0,pi); -mymin(x) functionfx=mymin(x) fx=-sin(x)-cos(x.^2); 5 [x,y1]=fminbnd(@mymax,0,; -y1 functionfx=mymax(x); fx=-(9*x+4*x.^3-12*x.^2); unit7 实验指导 1 (1) formatlong fx=inline('sin(x)./x'); [I,n]=quadl(fx,0,2,1e-10) (2) formatlong fx=inline('1./(.^2+-1./(.^2+-6'); [I,n]=quad(fx,0,1,1e-10) 2 (1) globalki; ki=0; I=dblquad(@fxy,0,1,0,1) ki (2) f=inline('abs(cos(x+y))','x','y'); I=dblquad(f,0,pi,0,pi) 3 X=: : ; F=[,,,,,,]; trapz(X,F) 4 p=0: pi/5: 2*pi; forn=1: 3 n DX=diff(sin(p),n) end 5 f=inline('sin(x)./(x+cos(2.*x))'); g=inline('(cos(x).*(x+cos(2*x))-sin(x).*(1-2.*sin(2*x)))/(x+cos(2.*x)).^2'); x=-pi: : pi; p=polyfit(x,f(x),5); dp=polyder(p); dpx=polyval(dp,x);%求dp在假设点的函数值 dx=diff(f([x,]))/;%直接对f(x)求数值导数 gx=g(x);%求函数f的导函数g在假设点的导数 plot(x,dpx,x,dx,'.',x,gx,'-');%作图 思考练习 2 formatlong fx=inline('1./(1+x.^2)'); [I,n]=quad(fx,-Inf,Inf,1e-10) [I,n]=quadl(fx,-Inf,Inf,1e-10) x=-100000: 100000; y=1./(1+x.^2); trapz(x,y) formatshort 3 (1) formatlong fx=inline('log(1+x)./(1+x.^2)'); [I,n]=quad(fx,0,1,1e-10) (2) formatlong fx=inline('sqrt(cos(t.^2)+4*sin((2*t).^2)+1)'); [I,n]=quad(fx,0,2*pi,1e-10) 4 f=inline('4.*x.*z.*exp(-z.^2.*y-x.^2)'); I=triplequad(f,0,pi,0,pi,0,1) 5 f=inline('sin(x)'); g=inline('cos(x)'); x=0: : 2*pi; p=polyfit(x,f(x),5); dp=polyder(p); dpx=polyval(dp,x); dx=diff(f([x,2*pi+]))/; gx=g(x); plot(x,dpx,x,dx,'.',x,gx,'-') unit8 实验指导 1 symsxy; s=x^4-y^4; factor(s) factor(5135) 2 symsx; f=(x-2)/(x^2-4); limit(f,x,2) symx; f=(sqrt(pi)-sqrt(acos(x)))/sqrt(x+1); limit(f,x,-1,'right') 3 symx; f=sin(1/x); diff(f,'x') diff(f,'x',2) symx; f=(1-cos(2*x))/x; diff(f,'x') diff(f,'x',2) 4 symx; f=sqrt(exp(x)+1); int(f,'x') symsxy; f=x/(x+y); int(f,'y') symx; f=exp(x)*(1+exp(x))^2; int(f,'x',0,log (2)) symx; f=x*log(x); int(f,'x',1,exp (1)) 5 symx; s=symsum((-1)^(x+1)/x,1,Inf) symy; z=symsum(y^(2*y-1)/(2*y-1),1,Inf) 6 symx; f1=(exp(x)+exp(-x))/2; f2=sqrt(x^3-2*x+1); taylor(f1,x,5,0) taylor(f2,x,6,0) 7 symsxya; x=solve('x^3+a*x+1=0','x') x=solve('sin(x)+2*cos(x)-sqrt(x)=0','x') [xy]=solve('log(x/y)=9','exp(x+y)=3','x','y') 8 symsn; [x,y]=dsolve('x*(D2y)+(1-n)*(Dy)+y=0','y(0)=0','Dy(0)=0','x') 思考练习 2 symsxB1B2ab s1=2*((cos(x))^2)-(sin(x))^2; s2=sin(B1)*cos(B2)-cos(B1)*sin(B2); s3=sqrt((a+sqrt(a^2-b))/2)+sqrt((a-sqrt(a^2-b))/2); s4=(4*x^2+8*x+3)/(2*x+1); h1=simplify(s1) h2=simplify(s2) h3=simplify(s3) h4=simplify(s4) 3 symsxa; f=abs(x)/x; limit(f,x,0,'left') f=(x+a/x)^x; limit(f,x,inf) 4 symsxym f=sqrt(x+sqrt(x+sqrt(x))); m=diff(f,'x') diff(m,'x') symsxy; f=x+y-sqrt(x^2+y^2); z1=diff(f,x) z2=diff(f,y) 5 symsxy; f=x+y-sqrt(x^2+y^2); z1=diff(f,x) z2=diff(f,y) symx; f=1/(asin(x)^2*(1-x^2)^(1/2)); int(f) 6 symsx f=1/(1+x); int(f,0,4) symx; f=x^3*sin(x)^2/(x^6+2*x^4+1); int(f,-1,1) symx; f=x^3*sin(x)^2/(x^6+2*x^4+1); int(f,-1,1) 7 symsn s=symsum(1/4^n,1,inf) symn; s=symsum(((n+1)/n)^(1/2),1,inf) eval(y) 8 symsx f=tan(x); taylor(f,x,3,0) s
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