1、>> vpa('pi',20)ans =3.1415926535897932385>> vpa('exp(1)',20)ans =2.7182818284590452354>> x=linspace(-pi,pi,21);>> y=sin(x)y = Columns 1 through 6 -0.0000 -0.3090 -0.5878 -0.8090 -0.9511 -1.0000 Columns 7 through 12 -0.9511 -0.8090 -0.5878 -0.3090 0 0.3090 Colu

2、mns 13 through 18 0.5878 0.8090 0.9511 1.0000 0.9511 0.8090 Columns 19 through 210.5878 0.3090 0.0000å ->> k=1:1000;>> kk=1./k;>> kkk=kk./k;>> res=sum(kkk)-(pi2)/6res =-9.9950e-04%承接上題>> sum(kk)-log(1000)ans =0.5777>> power(1+eps,1/eps)ans =2.7183>> a=r

3、and(2,3)a = 0.8147 0.1270 0.63240.9058 0.9134 0.0975>> x=a(1,:)x =0.8147 0.1270 0.6324>> y=a(2,:)y =0.9058 0.9134 0.0975>> norm(x)ans = 1.0391>> norm(y)ans =1.2900>> acos(dot(x,y)/norm(x)/norm(y)ans = 0.8189>> rand(3,3)ans = 0.2785 0.9649 0.9572 0.5469 0.1576 0.48

4、54 0.9575 0.9706 0.8003>> det(ans)ans =0.2937線性無關(guān)a = 0.3922 0.7060 0.6555 0.0318 0.1712 0.2769>> x=a(1,:)x = 0.3922 0.7060>> y=a(2,:)y = 0.6555 0.0318>> z=a(3,:)z = 0.1712 0.2769>> alpha=x-zalpha = 0.2210 0.4291>> beta=y-zbeta =0.4843 -0.2451>> alpha=alpha 0

5、alpha = 0.2210 0.4291 0>> beta=beta 0beta = 0.4843 -0.2451 0>> cross(alpha,beta)ans = 0 0 -0.2620面積0.2620>> a=11:19;>> b=a;>> for k=1:8b=b;a+10*k;end>> rank(b)ans = 2>> a=vander(1:9);>> b=fliplr(a)b = Columns 1 through 5 1 1 1 1 1 1 2 4 8 16 1 3 9 27 8

6、1 1 4 16 64 256 1 5 25 125 625 1 6 36 216 1296 1 7 49 343 2401 1 8 64 512 4096 1 9 81 729 6561 Columns 6 through 9 1 1 1 1 32 64 128 256 243 729 2187 6561 1024 4096 16384 65536 3125 15625 78125 390625 7776 46656 279936 1679616 16807 117649 823543 5764801 32768 262144 2097152 16777216 59049 531441 47

7、82969 43046721>> det(b)ans = 5.0566e+15方式一>> f=(x,y) exp(x+y)+sin(x2)+(y2)f = (x,y)exp(x+y)+sin(x2)+(y2)>> f(1,2)ans = 19.1266方式二function f=myfunfun(x,y)f=exp(x+y)+sin(x2)+(y2);>> myfunfun(1,2)ans = 19.1266>> Char1.4142135623730950488016887242096980785696718753769480731

8、766797379907324784621070388503875343276415727>> a=ans；>> sqrt2char(3-2)=a(3)sqrt2char =4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727>> for x=1:100b(x)=str2num(sqrt2char(x)end>> sum(b)/100ans = 4.8100f=(x) (x3)*sin(x)+(x2)

9、/3+x*cos(x)f = (x)(x3)*sin(x)+(x2)/3+x*cos(x)>> ezplot(f,-2,1)>> x0=fzero(f,-1)x0 = -0.7889另一根為0，是顯然的function y=difun(x)if x<-pi y=-x-pi;elseif x>-pi & x<pi y=sin(x);else y=(x-pi)/2;endend>> y=y = >> for x=-6:0.05:6y=y difun(x);end>> plot(x,y)>> plot(

10、-6:0.05:6,y)>> pi/4ans = 0.7854%pi/4的理想值矩形公式：function y=rectangle(n)x=0:1/n:1;a=1./(1+x.*x);y=sum(a)*(1/n);end>> rectangle(1000)ans = 0.7861>> rectangle(10000)ans = 0.7855>> rectangle(100000)ans =0.7854梯形公式：function y=trapezoid(n)x=0:1/n:1;a=1./(1+x.*x);begin=a(1);endd=a(n+1)

11、;a(1)=0;a(n)=0;y=sum(a)*(1/n)+begin*(1/n)*0.5+endd*(1/n)*0.5;endtrapezoid(1000)ans = 0.7854>> trapezoid(100)ans = 0.7853Simpson 公式function y=simpson(n)x=0:1/n:1;a=thefun(x);begin=a(1);endd=a(n+1);medium=;for x=1:n medium=medium (a(x)+a(x+1)*0.5;enda(1)=0;a(n)=0;y=begin*(1/n)*(1/6)+endd*(1/n)*(

12、1/6)+sum(a)*(1/n)*(1/3)+sum(medium)*(1/n)*(1/6)*4;endfunction e=thefun(r)e=1./(1+r.*r);end>> simpson(100)ans = 0.7854>> simpson(10)ans =0.7832>> A=6 2 1 -1;2 4 1 0;1 1 4 -1;-1 0 -1 3;>> b=6 1 5 -5'>> x=Abx = 0.7906 -0.3613 0.8639 -1.1152>> diag(1:4) eye(4)ans

13、= 1 0 0 0 1 0 0 0 0 2 0 0 0 1 0 0 0 0 3 0 0 0 1 0 0 0 0 4 0 0 0 1function yh=yhsj(n)yh=1; disp(1);for k=2:n yh=yh,0+0,yh; disp(yh)endend% n=11運(yùn)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

14、)ans =(16*b + 81)(3/2)/216 - (16*a + 81)(3/2)/216>> t=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(dx2+dy2),0,2*pi)ans =8*(a2)(1/

15、2)>> p=polyfit(-pi -pi/2 0 pi/2 pi,0 -1 0 1 0,5)p = Columns 1 through 5 -0.0349 0.0000 0.3440 -0.0000 0 Column 6 -0.0000>> plot(-pi:pi/100:pi,polyval(p,-pi:pi/100:pi);>> hold on>> plot(-pi:pi/100:pi,sin(-pi:pi/100:pi);>>function a=num2p(n)strr=num2str(n);index=size(strr

16、);indexx=index(2);a=;for k=indexx-1:-1:0 a=a rem(fix(n/(10k),10);endend>> num2p(95489298494)ans = Columns 1 through 8 9 5 4 8 9 2 9 8 Columns 9 through 11 4 9 4function ppi=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(index

17、x)/n;end>> ttry(100)ans = 3.1200>> ttry(10000)ans = 3.1376function y=collatz(n)if n=1 y=1return;elseif rem(n,2)=0 n=n/2;else n=3*n+1;end n y=collatz(n);end>> collatz(12)n = 6n = 3n = 10n = 5n = 16n = 8n = 4n = 2n = 1y = 1>> f=(x) 1./(1+x.2)f = (x)1./(1+x.2)>> y=f(x);>

18、;> x=0:0.1:1;>> y=f(x);>> p=polyfit(x,y,5)p = Columns 1 through 5 -0.2372 0.3529 0.5071 -1.1343 0.0115 Column 6 0.9999>> intp=polyint(p)intp = Columns 1 through 5 -0.0395 0.0706 0.1268 -0.3781 0.0058 Columns 6 through 7 0.9999 0>> res1=polyval(intp,1)-polyval(intp,0)res1 =

19、 0.7854%這是插值擬合解>> atan(1)ans =0.7854%actan(1)公式解fid=fopen('C:陳民權(quán)的文檔2matlab作業(yè)pi_1m.txt','r')fid = 3>> b=fscanf(fid,'%s');>> fclose(fid)ans = 0>> b(1:55)=;編輯“givemerun.m”文件：y=1;n=zeros(1,10)flag=0;for x=1:1500000if y=1000001breakelseif b(x)='' &a

20、mp; flag=0 & isempty(str2num(b(x)=1 c=b(x); d=str2double(c); n(d+1)=n(d+1)+1; y=y+1;elseif b(x)='' flag=1;elseif b(x)='' flag=0;endendendn>> givemerun%運(yùn)行“givemerun”n = 0 0 0 0 0 0 0 0 0 0n =n = Columns 1 through 3 99959 99758 100026 Columns 4 through 6 100229 100230 100359

21、Columns 7 through 9 99548 99800 99985 Column 10 100106 %分別為0，1，2，8，9在前一百萬位出現(xiàn)的次>> sum(n)ans = 1000000>> cc=num2str(n)cc =99959 99758 100026 100229 100230 100359 99548 99800 99985 100106>> fopen('res.txt','w')ans = 6>> fprintf(6,cc)ans =78function f=veryfun(n)if

22、 n=6174returnelseindex(1)=(n-rem(n,1000)/1000;index(2)=fix(n/100)-index(1)*10;index(3)=rem(fix(n/10),10);index(4)=rem(n,10);index2=sort(index,'ascend');index3=sort(index,'descend');a=1000 100 10 1;max=index3*(a');min=index2*(a');max-minveryfun(max-min);endend>> veryfun(9864)ans = 5175ans = 5994ans = 5355ans = 1998ans = 8082ans = 8532ans = 6174function m=tem(ind