matlab总练习题(完整版)

vpa('pi',20)ans=3.1415926535897932385vpa('exp(1)',20)ans=2.7182818284590452354x=linspace(-pi,pi,21);y=sin(x)y=Columns1through6-0.0000-0.3090-0.5878-0.8090-0.9511-1.0000Columns7through12-0.9511-0.8090-0.5878-0.309000.3090Columns13through180.58780.80900.95111.00000.95110.8090Columns19through210.58780.30900.0000k=1:1000;kk=1./k;kkk=kk./k;res=sum(kkk)-(pi^2)/6res=-9.9950e-04%承接上题sum(kk)-log(1000)ans=0.5777power(1+eps,1/eps)ans=2.7183a=rand(2,3)a=0.81470.12700.63240.90580.91340.0975x=a(1,:)x=0.81470.12700.6324y=a(2,:)y=0.90580.91340.0975norm(x)ans=1.0391norm(y)ans=1.2900acos(dot(x,y)/norm(x)/norm(y))ans=0.8189rand(3,3)ans=0.27850.96490.95720.54690.15760.48540.95750.97060.8003det(ans)ans=0.2937线性无关a=0.39220.70600.65550.03180.17120.2769x=a(1,:)x=0.39220.7060y=a(2,:)y=0.65550.0318z=a(3,:)z=0.17120.2769alpha=x-zalpha=0.22100.4291beta=y-zbeta=0.4843-0.2451alpha=[alpha0]alpha=0.22100.42910beta=[beta0]beta=0.4843-0.24510cross(alpha,beta)ans=00-0.2620面积0.2620a=11:19;b=a;fork=1:8b=[b;a+10*k];endrank(b)ans=2a=vander(1:9);b=fliplr(a)b=Columns1through5111111248161392781141664256152512562516362161296174934324011864512409619817296561Columns6through911113264128256243729218765611024409616384655363125156257812539062577764665627993616796161680711764982354357648013276826214420971521677721659049531441478296943046721det(b)ans=5.0566e+15方式一f=@(x,y)exp(x+y)+sin((x^2)+(y^2))f=@(x,y)exp(x+y)+sin((x^2)+(y^2))f(1,2)ans=19.1266方式二functionf=myfunfun(x,y)f=exp(x+y)+sin((x^2)+(y^2));myfunfun(1,2)ans=19.1266Char1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727a=ans；sqrt2char(3-2)=a(3)sqrt2char=4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727forx=1:100b(x)=str2num(sqrt2char(x))endsum(b)/100ans=4.8100f=@(x)(x^3)*sin(x)+(x^2)/3+x*cos(x)f=@(x)(x^3)*sin(x)+(x^2)/3+x*cos(x)ezplot(f,-2,1)x0=fzero(f,-1)x0=-0.7889另一根为0，是显然的functiony=difun(x)ifx-piy=-x-pi;elseifx-pi&xpiy=sin(x);elsey=(x-pi)/2;endendy=[]y=[]forx=-6:0.05:6y=[ydifun(x)];endplot(x,y)plot([-6:0.05:6],y)pi/4ans=0.7854%pi/4的理想值矩形公式：functiony=rectangle(n)x=0:1/n:1;a=1./(1+x.*x);y=sum(a)*(1/n);endrectangle(1000)ans=0.7861rectangle(10000)ans=0.7855rectangle(100000)ans=0.7854梯形公式：functiony=trapezoid(n)x=0:1/n:1;a=1./(1+x.*x);begin=a(1);endd=a(n+1);a(1)=0;a(n)=0;y=sum(a)*(1/n)+begin*(1/n)*0.5+endd*(1/n)*0.5;endtrapezoid(1000)ans=0.7854trapezoid(100)ans=0.7853Simpson公式functiony=simpson(n)x=0:1/n:1;a=thefun(x);begin=a(1);endd=a(n+1);medium=[];forx=1:nmedium=[medium(a(x)+a(x+1))*0.5];enda(1)=0;a(n)=0;y=begin*(1/n)*(1/6)+endd*(1/n)*(1/6)+sum(a)*(1/n)*(1/3)+sum(medium)*(1/n)*(1/6)*4;endfunctione=thefun(r)e=1./(1+r.*r);endsimpson(100)ans=0.7854simpson(10)ans=0.7832A=[621-1;2410;114-1;-10-13];b=[615-5]';x=A\bx=0.7906-0.36130.8639-1.1152[diag(1:4)eye(4)]ans=10001000020001000030001000040001functionyh=yhsj(n)yh=1;disp(1);fork=2:nyh=[yh,0]+[0,yh];disp(yh)endend%n=11运行x=sym('x');f=sqrt(1+((4/9)*x^(1/2))^2)f=((16*x)/81+1)^(1/2)a=sym('a');b=sym('b');int(f,a,b)ans=(16*b+81)^(3/2)/216-(16*a+81)^(3/2)/216t=sym('t');a=sym('a');x=a*(t-sin(t))x=a*(t-sin(t))y=a*(1-cos(t))y=-a*(cos(t)-1)dx=diff(x)dx=-a*(cos(t)-1)dy=diff(y)dy=a*sin(t)int(sqrt(dx^2+dy^2),0,2*pi)ans=8*(a^2)^(1/2)p=polyfit([-pi-pi/20pi/2pi],[0-1010],5)p=Columns1through5-0.03490.00000.3440-0.00000Column6-0.0000plot([-pi:pi/100:pi],polyval(p,-pi:pi/100:pi));holdonplot([-pi:pi/100:pi],sin(-pi:pi/100:pi));functiona=num2p(n)strr=num2str(n);index=size(strr);indexx=index(2);a=[];fork=indexx-1:-1:0a=[arem(fix(n/(10^k)),10)];endendnum2p(95489298494)ans=Columns1through895489298Columns9through11494functionppi=ttry(n)pointx=-1+2*rand(1,n);pointy=-1+2*rand(1,n);index=pointx.*pointx+pointy.*pointy;indexx=index=1;ppi=4*sum(indexx)/n;endttry(100)ans=3.1200ttry(10000)ans=3.1376functiony=collatz(n)ifn==1y=1return;elseifrem(n,2)==0n=n/2;elsen=3*n+1;endny=collatz(n);endcollatz(12)n=6n=3n=10n=5n=16n=8n=4n=2n=1y=1f=@(x)1./(1+x.^2)f=@(x)1./(1+x.^2)y=f(x);x=0:0.1:1;y=f(x);p=polyfit(x,y,5)p=Columns1through5-0.23720.35290.5071-1.13430.0115Column60.9999intp=polyint(p)intp=Columns1through5-0.03950.07060.1268-0.37810.0058Columns6through70.99990res1=polyval(intp,1)-polyval(intp,0)res1=0.7854%这是插值拟合解atan(1)ans=0.7854%actan(1)公式解fid=fopen('C:\陈民权的文档2\matlab作业\pi_1m.txt','r')fid=3b=fscanf(fid,'%s');fclose(fid)ans=0b(1:55)=[];编辑“givemerun.m”文件：y=1;n=zeros(1,10)flag=0;forx=1:1500000ify==1000001breakelseifb(x)~='['&flag==0&isempty(str2num(b(x)))~=1c=b(x);d=str2double(c);n(d+1)=n(d+1)+1;y=y+1;elseifb(x)=='['flag=1;elseifb(x)==']'flag=0;endendendngivemerun%运行“givemerun”n=0000000000n=n=Columns1through39995999758100026Columns4through6100229100230100359Columns7through9995489980099985Column10100106%分别为0，1，2，…，8，9在前一百万位出现的次sum(n)ans=1000000cc=num2str(n)cc=9995999758100026100229100230100359995489980099985100106