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数学建模练习题答案(程序代码)

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练习一答案

1, x=eye(3,3)

x=ones(3,3) :x=zeros(3,3)

(3)取整数 x=unifrnd(-1,1,3,3); >> x=randint(1,9,[-1,1]); >> x=reshape(x,3,3)

取小数>> x=unifrnd(-1,1,3,3); x=-1+(0+2).*rand(3,3) (4)x=normrnd(1,2,3,3); x(find(x>1))=1; x(find(x<1))=0 2,x=0; y=10;

a=fix(x+(y-x)*rand(10,10));寻找 b=a>5;

c=sum(sum(b))

3,a=[0 0 0 0;1 1 0 1;1 1 0 1;1 1 0 1];

a(find(sum(abs(a'))==0),:)=[];a’表示转至的意思a是一个列向量 a(:,find(sum(abs(a))==0))=[]矩阵是提前给定的 4奇数,x=randint(10,10,[0,1000]);rand cntodd=length(find(mod(x,2)==1)) 素数(质数)

x=randint(10,10,[0,1000]);

cntprime=length(find(isprime(x))) 偶数

x=randint(10,10,[0,1000]);

>> cnteren=length(find(mod(x,2)==0)) 5,

>> x=0:0.25:10; y1=2*x+5;

y2=x.^2-3*x+1;

plot(x,y1,'y*',x,y2,'r+') plot是画图的命令 xlabel('x'); ylabel('y');

text(2,11,'curve y1'); text是标注 text(2.5,-1,'curve y2'); >> legend('y1','y2')图例

6,[x,y]=meshgrid(0:0.25:4*pi); 曲面 z=sin(x)*cos(y)*exp(-sqrt(x.^2+y.^2)); mesh(x,y,z) 画等高线 7,x=[1 5 8 10 12 5 3]; subplot(1,3,1) pie3(x);

title('1');

subplot(1,3,2) bar3(x); title('2');

subplot(1,3,3) bar(x); title('3')

8,x=-8:0.5:8; y=[]; for x0=x;

if x0>=-3&x0<=-1;

y=[y,(-x0.^2-4*x0-3)/2]; elseif x0>=-1&x0<1 y=[y,(-x0.^2+1)]; elseif x0>=1&x0<3

y=[y,(-x0.^2+4*x0-3)/2]; else y=[y,0]; end end y

9,a=zeros(1,15); b=a; c=a; a(1)=2; a(2)=3;

b(1)=1;b(2)=2; for i=3:15

a(i)=a(i-1)+a(i-2); b(i)=b(i-1)+b(i-2); end

>> format rat有理数形式输出 >> c=a./b 法二;:x=[2/1 3/2 5/3 8/5 13/8 21/13 34/21 55/34 /55 144/ 233/144 377/233 610/377 987/610 1597/987]; r=sum(x)

10,a=unifrnd(10,100,1,20); >> b=floor(a); >> p=mean(b); >> m=find(b> c=b(m);

>> n=find(mod(c,2)==0); >> d=c(n)

11,a=primes(100) 12,b=0;

for i=1:40; b=b+i*(i+1); f(i)=b end f(i)

f(40)/(f(30)+f(20)) 13,a=randi([10,99],1,10); >> b=reshape(a,1,10); >> b=sort(b);

>> [b,i]=sort(b,'descend'); >> a=b(randperm(length(b))) 14,,t=1:10;

y=[4.842,4.362,3.7,3.368, 3.169,3.038,3.034,3.016,3.012,3.005]; x1=exp(-t) x2=t.*exp(-t)

y1=polyfit(x1,y,1)

y1=5.2165*exp(-t)+3.15 y2=polyfit(x2,y,1) y2=5.0273*t.*exp(-t)

plot(t,y,t,y1,'r--',t,y2,'gx')

15,第一个:建立

m文件:

function f=jifen1(x) f=exp(-2*x); 在命令窗口输入: [z1,n]=quad(@jifen1,0,2) 得到结果: z1= 0.4908 n = 25

第二个:

x=0:0.01:2; z2=exp(2*x); trapz(x,z2) 得到结果: ans = 26.8000 第三个: t=-1:0.01:1; z3=x.^2-3*x+0.5; trapz(x,z3) 得到结果: ans = 1.6667

第四个syms x y

F2=int(int(exp(-x^2/2)*sin(x^2+y),x,-2,2),y,-1,1) >> VF2=vpa(F2)

161(1),t=0:0.01:25;

[x,y]=dsolve('Dx=0.5-x','Dy=x-4*y','x(0)=1','y(0)=-0.5','t')求方程 再求图像t=0:0.01:25; x=1/2+1/2*exp(-t);

y =1/8+1/6*exp(-t)-19/24*exp(-4*t); plot(t,x,t,y)

(2)y=dsolve('D2y*x+(1-5)*Dy+y=0','y(0)=0,Dy(0)=0','x') 17,t=[0 0.3 0.8 1.1 1.6 2.3];

y=[0.5 0.82 1.14 1.25 1.35 1.41]; tt=0:0.01:2.3;

a=polyfit(t,y,2) 拟合曲线命令

yy1=polyval(a,tt); 多项式模拟 z1=polyval(a,t);

wucha1=sqrt(sum((z1-y).^2)) 均方误差

B=[ones(size(t')) exp(-t)' ( t.*exp(-t))']; 指数函数模拟 b=B\\y'

yy2=b(1)+b(2)*exp(-tt)+b(3)*tt.*exp(-tt); z2=b(1)+b(2)*exp(-t)+b(3)*t.*exp(-t); wucha2=sqrt(sum((z2-y).^2)) figure(1); 再一个图中画出 plot(t,y,'+',tt,yy1,t,z1,'o') 18,(1),x=-1:0.01:1;

y=exp(x)-1.5*cos(2*pi*x); plot(x,y,'g') hold on >> y0=0;

>> plot(x,y0,'k') z=fzero('f',-0.8) z = -0.7985 (2)f.m

function y=f(x);

y=exp(x)-1.5*cos(2*pi*x);

x=fminsearch('f',-0.2,0.2) 寻找极小值在-0.2到0.2之间

x =-0.0166

>> x=fminsearch('f',-1,1) x =-1.0062 f1.m

function y=f(x);

y=-exp(x)+1.5*cos(2*pi*x);

x=fminsearch('f1',0.4,0.6)

x =

0.5288

>> x=fminsearch('f1',-0.6,-0.4) x =

-0.47

x1=-1.0062 ;

y1=exp(x1)-1.5*cos(2*pi*x1) y1 =

-1.1333 plot(x1,y1,'*')

19, (1)

[x1,x2,x3]=solve('10*x1-x2=9','-x1+10*x2-2*x3=7','-3*x1+10*x3=6') (2)法一:function q=myxyz(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;

命令窗口:x=fsolve('myxyz',[1 1 1])或xyz0=[1 1 1]; >> x=fsolve('myxyz',xyz0) 0.5991 2.3959 2.0050

法二

[x,y,z]=solve('sin(x)+y^2+ln(z)-7=0','3*x+2^y-z^3+1=0','x+y+z-5=0','x','y','z') 20, syms x y=sin(x^2); taylor(y,10) 22,

22,max=x+2*y; 2*x+y-12<=0; 3*x-2*y+10>=0; x-4*y+10<=0;

End Global optimal solution found.

结果分析Objective value: 18.00000 最优值 Infeasibilities: 0.000000 Total solver iterations: 2

Variable Value Reduced Cost

X 2.000000 0.000000 最优的x,y,解

Y 8.000000 0.000000

Row Slack or Surplus Dual Price 1 18.00000 1.000000 2 0.000000 1.142857 3 0.000000 -0.4285714 4 20.00000 0.000000 23, model:

sets: %定义 day/1..7/:a,x; endsets

data: %赋值 a=28 15 24 25 19 31 28; enddata

min=@sum(day:x); %对于day中的每个x的值进行求和的最小值 @for(day:@gin(x)); %gin(x)x为整数 表示对每个x取整都有 @for(day(i):@sum(day(j):x(j))-x(@mod(i,7)+1)-x(@mod(i+1,7)+1)>=a(i)); End

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