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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 Columns 13 through 18 0.5878 0.8090 0.9511 1.0000 0.
2、9511 0.8090 Columns 19 through 210.5878 0.3090 0.0000 - k=1:1000; kk=1./k; kkk=kk./k; res=sum(kkk)-(pi2)/6res =-9.9950e-04%承接上题 sum(kk)-log(1000)ans =0.5777 power(1+eps,1/eps)ans =2.7183 a=rand(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
3、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 0.4854 0.9575 0.9706 0.8003 det(ans)ans =0.2937线性无关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
4、.1712 0.2769 alpha=x-zalpha = 0.2210 0.4291 beta=y-zbeta =0.4843 -0.2451 alpha=alpha 0alpha = 0.2210 0.4291 0 beta=beta 0beta = 0.4843 -0.2451 0 cross(alpha,beta)ans = 0 0 -0.2620面积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
5、 1 2 4 8 16 1 3 9 27 81 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 16
6、777216 59049 531441 4782969 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 Char 1.414213562373095048801688724209698078569671875376948073176679737990732478
7、4621070388503875343276415727 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)/3+x*cos(x)f = (x)(x3)*sin(x)+(x2)/3+x*cos(x) ezp
8、lot(f,-2,1) x0=fzero(f,-1)x0 = -0.7889另一根为0，是显然的function y=difun(x)if x-pi & x y=y = for x=-6:0.05:6y=y difun(x);end plot(x,y) plot(-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 r
9、ectangle(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);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);mediu
10、m=;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)*(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
11、.3613 0.8639 -1.1152 diag(1:4) eye(4)ans = 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)end end% 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)/2
12、16 - (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)(1/2) p=polyfit(-pi -pi/2 0 pi/2 pi,0 -1 0 1 0,5)p = Columns 1 through 5 -0.0349 0.0000 0.344
13、0 -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);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
14、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 ttry(100)ans = 3.1200 ttry(10000)ans = 3.1376function y=collatz(n)if n=1 y=1 return;else if rem(n,2)=0 n=n/2; else n=3*n+1; end n y=collatz(n);end collatz(12)n
15、 = 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); 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 throu
16、gh 7 0.9999 0 res1=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2matlab作业pi_1m.txt,r)fid = 3 b=fscanf(fid,%s); fclose(fid)ans = 0 b(1:55)=;编辑“givemerun.m”文件：y=1;n=zeros(1,10)flag=0;for x=1:1500000 if y=1000001 breakelseif b(x)= & flag=0 & ise
17、mpty(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 %运行“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 Columns 7 through 9 99548 99800 99985 Column 1
18、0 100106 %分别为0，1，2，8，9在前一百万位出现的次 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 n=6174 returnelseindex(1)=(n-rem(n,1000)/1000;index(2)=fix(n/100)-index(1)*10;index(3)=rem(fix(n/
19、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(index,t)m=index(1).*exp(index(2).*t)end index
20、,r,j,c,m,e=nlinfit(t,m,tem,0 0)index = 78.7137 -0.1047%在这里省略中间的迭代过程和表格变量输入过程 m=tem(index,0:0.1:25); plot(0:0.1:25,m)function son=sonfind(A)index=sum(A)/2;for k=1:5 b=nchoosek(1:10,k); sizee=size(b); kk=sizee(1); for x=1:kk c=b(x,:); A_son=; for y=c A_son=A_son A(y); end if sum(A_son)=index son=A_son
21、; break return end end end end%集合元素有互异性，但不影响验证！ sonfind(11:20) sonfind(10 5 5 10 60 10 10 10 10 10)ans = 5 5 60 sonfind(10 10 10 10 90 10 10 10 10 10)ans =90%进一步验证（这里元素互异） sonfind(21 22 23 24 25 11 12 13 14 65)ans = 21 22 23 24 25 sort(21 22 23 24 25 11 12 13 14 65)ans = 11 12 13 14 21 22 23 24 25 65 sonfind(ans)ans =11 12 13 14 652016 12