西南交通大学数学实验参考答案.docx

1、西南交通大学数学实验参考答案%sy1ljy20111514%第一大题%1x=3,2*pi;y1=sin(x)+exp(x)%y1 = 20.2267 535.4917%2x=2:2:10y2=x.2+sqrt(2*x)% x =2 4 6 8 10%y2 = 6.0000 18.8284 39.4641 68.0000 104.4721%3a=2*pi;b=35*pi/180;c=exp(2)y31=sin(a/5)+cos(b)*c%c = 7.3891%y2 = 6.0000 18.8284 39.4641 68.0000 104.4721%4Formal rational%6a=-6.2

2、8;a2=7.46;a3=5.37;a11=fix(a1),a21=fix(a2),a31=fix(a3)%7y71=abs(a1*a2+a3)y72=a12*sqrt(a2*a3/2)Formal short%8save sy2clear%9load sy1%10A=2 -5 6;8 3 1;-4 6 9A1=A,A2=det(A),A3=5*Asave sy1 A1 A2 A3%第二大题%1X=0:pi/10:2*pi;Y=cos(X);S=X,Y%2a22=input(a22=);b22=input(b22=);c22=input(c22=);s=(a22+b22+c22)/2;A2=s

3、qrt(s*(s-a22)*(s-b22)*(s-c22)%3sumjs=0;sumos=0;for i=1:2:99sumjs=sumjs+i;sumos=sumos+i+1;endsumjssumos%4n=1000;i=1;k=1;while k=0 y1=2*x-sin(4*x)else y1=exp(x)+x.3end%y1=12.5664 y1=-1.7280e+003%2.2x=input(x=)if x0 y2=5*x+3elseif x0 y3=log(2*x)else y3=2*x.3-x+5end%f3(4)=2.0794 f3(0)=5 f3(-2)=-9%第四大题%4

4、.1for i=1:6 for j=1:6 if i=j A4(i,j)=5; elseif abs(i-j)=1 A4(i,j)=2; else A4(i,j)=1; end endend%4.2A4A(1,1)=3A(1,2)=2A(1,3)=5A(1,4)=4A(1,5)=-2A(1,6)=-3for i=2:6 for j=1:6 A(i,j)=A(i-1),j)*A(1,j) endendA%4.3n=input(n=)sum=0;k=1;while k=n sum=sum+1/k k=k+1endsum%sum =3.3182 sum =3.5977%4.4a=1,1; for i

5、=3:40; a=a,a(i-2)+a(i-1); endF=reshape(a,10,4)%4.5a=input(a=)n=input(n=)for i=2:n a=a,a(i-1)+a(1)*(10(i-1)endSn=sum(a)%5score=input(成绩);n=score/10switch fix(n)case 10,9disp(优秀);case 8,7disp(良);case 6disp(及格);otherwisedisp（不及格）;end%6n=0;for m=1:200; flag=1;j=m-1; i=2;while i=j&flagif rem(m,i)=0flag=0

6、;endi=i+1;endif flagn=n+1;prime(n)=m;endendprime%7s=input(距离km)p=input(每吨基本运费)w=input(货物重)switch scase (s250)d=0;case (s=250)d=0.02;case (s=500)d=0.05;case (s=1000)d=0.08;case (s=2000)d=0.1;case (s=3000)d=0.15;endf=(1-d)*s*p*w%sy3ljy20111514%一大题x11=2 -5 8 -1 7 1 -8 3 2 5 9%1.2x12=(2:2:22)%1.3x13=lin

7、space(0,2*pi,20)%1.4x14=rand(1,8)%1.5x15=rand(6,1)%1.6x16=x11(abs(x11)3)%1.7m1=5 4 9;m2=8 6 3;m=m1-m2;a=norm(m)%1.8x18=4+x11+7*x12%1.9x19=x11*x12%1.10x10=cross(x11(1,2,3),x12(1,2,3)%2大题%2.1figureaxis(0 8 0 8);x=2 4 4 2 2 4 6 6 4 2 2 4 4 6 6 4;y=5 5 3 3 5 5 5 3 3 3 1 1 3 3 1 1;line(x,y)%2.2figurey=4

8、5 5 3 2 3 5 6 7 8;plot(y)%2.3figurex23=(0.1:0.01:10);y23=30./x23;plot(y23)%2.4figurex24=linspace(-5,5,30);y24=5*x24.*cos(x24);plot(y24)%2.5figurex25=linspace(-2*pi,2*pi,50);y25=sin(x25);plot(y25)hold onz25=cos(x25);4;plot(z25,r-);hold off%2.6subplot(2,3,1);fplot(3*x2,-8,8);title(f1=3x2);subplot(2,3,

9、2);fplot(exp(x+1),-8,8);title(f2=e(x+1)%3.1t=linspace(-2,2,50)*pi;a=input(a=);b=input(b=);x=a*cos(t);y=b*sin(t);plot(x,y,r);axis equaltext(-0.5,0,x2/a2+y2/b2=1);%3.2t=linspace(0,4*pi,50)r=cos(t/3);subplot(1,3,1)plot(t,r);hold ont=linspace(0,5*pi,50)r=exp(0.3*t);subplot(1,3,2)plot(t,r);hold ont=linsp

10、ace(0.6*pi,6*pi,50)r=4./t;subplot(1,3,3)plot(t,r);hold off%3.3t=0:pi/12.5:8*pi;plot3(sin(t),cos(t),t);label(x),ylabel(y)%sy4wangchao20121652%1.1t=1:0.5:10;r=2+cos(t)+sin(t);cylinder(r,30)title(旋转抛物面图);%1.2x,y=meshgrid(-3:0.5:3);z2=x.*y;mesh(x,y,z2);title(双曲抛物面);%1.3x,y=meshgrid(-5:0.5:5);z3=sqrt(abs

11、(x.2-2.*y);surf(x,y,z3);title(曲面表面图);%1.4function xx,yy,zz=sphere(n);if nargin=0,n=20;end;theta=(-n:2:n)/n*pi;phi=(-n:2:n)/n*pi/2;cosphi=cos(phi);cosphi(1)=0;cosphi(n+1)=0;sintheta=sin(theta);sintheta(1)=0;sintheta(n+1)=0;x=cosphi*cos(theta);y=cosphi*sintheta;z4=cos(phi).2*ones(1,n+1).2;surf(x,y,z4)

12、shading interp%1.5ezsurf(x,y)(x2+y2+6*sin(2*x),-2*pi 2*pi -2*pi 2*pi)shading interp%2.1x21=1:1:10;y21=fix(rand(1,10)*30);bar(x21,y21)%2.2y221=2.5 3 4.5 5 2.8;y222=2 2.2 3 2.5 1.8;x=1:5;area(x,y221,facecolor,0.75 0.6 0.9,edgecolor,b);hold on;area(x,y222,facecolor,0.5 0.9 0.7,edgecolor,r);hold off;gte

13、xt(五年某地区住房修建统计)gtext(入住率)%2.3y22=fix(rand(1,50)*30);hist(y22,5)%2.4y23=46 75 148 214 98 35;pie3(y23,0 0 0 1 0 0)%2.5x,y,z=peaks(30);subplot(2,2,1)surf(x,y,z)subplot(2,2,2)contour(x,y,z,15)%3(1)sc1=56 21 31 27 21 26 56 24 32sc2=36 19 31 40 51 29 10 13 10sc3=4 51 23 14 24 9 5 31 14sc4=4 9 15 19 4 26 2

14、9 32 44subplot(2,2,1)pie3(sc1)subplot(2,2,2)pie3(sc2)subplot(2,2,3)pie3(sc3)subplot(2,2,4)pie3(sc4)%(2)x=1:9;sc1=56 21 31 27 21 26 56 24 32sc2=36 19 31 40 51 29 10 13 10sc3=4 51 23 14 24 9 5 31 14sc4=4 9 15 19 4 26 29 32 44subplot(2,2,1)bar(x,sc1)subplot(2,2,2)bar(x,sc2)subplot(2,2,3)bar(x,sc3)subpl

15、ot(2,2,4)bar(x,sc4)%4.1t=-5*pi:pi/200:5*pi;comet(sin(t),t.*cos(t)%4.2t=0:0.01:100;x=2*t.2;y=2*sin(t);z=5*cos(3*t);comet3(x,y,z)%sy5wmy20111510%1.1a1=1 3 5 7; 2 4 6 8;9 8 6 3;-6 0 4 3%1.2a2=3 5 -2 3;4 8 3 0;6 7 4 -1;2 5 6 9%1.3a3=sym(x*1 x*2 x*3 x*4 x*5;y*1 y*2 y*3 y*4 y*5)a4=sym(sin(x) x2;1+x cos(x)

16、b=fix(rand(4,4)*20)%1.4t=2 3 4 2 5 3f1=vander(t)f=rot90(f1)%1.5c=magic(4)%1.6q=zeros(4,4)e=eye(4)n=ones(4,4)%1.7a6=b e q;n c a1%2.1.1a1=1 3 5 7; 2 4 6 8;9 8 6 3;-6 0 4 3a21=max(a1) x y=find(a1=max(max(a1) %2.1.2a1=1 3 5 7; 2 4 6 8;9 8 6 3;-6 0 4 3a22=min(a1)x y=find(a1=min(min(a1)%2.1.3a1=1 3 5 7; 2

17、 4 6 8;9 8 6 3;-6 0 4 3a23=mean(a1)a24=median(a1)%2.1.4a1=1 3 5 7; 2 4 6 8;9 8 6 3;-6 0 4 3a25=std(a1)a26=sum(a1)%2.2a1=1 3 5 7; 2 4 6 8;9 8 6 3;-6 0 4 3a2=3 5 -2 3;4 8 3 0;6 7 4 -1;2 5 6 9a27=a1+a2a28=a1*a2%2.3a2=3 5 -2 3;4 8 3 0;6 7 4 -1;2 5 6 9a29=a2(1,3,2,3)%3.1a=fix(rand(6,6)*20)%3.2a31=aa34=de

18、t(a)a33=rank(a)%3.3a=fix(rand(6,6)*20)a34=inv(a)%3.4a=fix(rand(6,6)*20)d,x=eig(a)%4.1a=1 -5 2 -3;5 3 6 -1 ;2 4 2 1b=11;-1 -6a1=a bifrank(a1)=rank(a)rr=rref(a1)%5m=1 1 0;1 1 -1;0 -1 4d,x=eig(m)p=orth(d)y=p(-1)*x%f=-0.1284*y12+1.7984*y22+4.3301*y32%6.1a21,x=max(a21c1=4 2 6 2 7 5 8;p1=poly2sym(c1)%6.2c

19、2=1,4,7c22=poly(c2)p2=poly2sym(c22)%6.3c3=1 -2 4 -6r=root(c3)%6.4c4=1 -9 21 1 -30r=roots(c4)%6.5c51=1 0 4 -3 0 9c52=1 -6 4 8f1=poly2sym(c51)f2=poly2sym(c52)g1=f1+f2gp2=conv(c51,c52)g2=poly2sym(gp2)q,r=deconv(c51,c52)%6.6c66=3 5 -2 4 6 -7 1p66=polyder(c66)f6=poly2sym(p66)%6.7c=1 -7 8 -6 9x=3,2,1y=pol

20、yval(c,x)%6.8x=1:2:15;y=1.9221 -1.8389 -0.3916 2.1648 -1.4101 -0.9911 2.2351 -0.8691c=polyfit(x,y,6)z=polyval(c,x)plot(x,y,ro-,x,z,:)%第一大题%1x=input(x=);if x0 f1=4*x3+5*sqrt(x)-7;else f1=x2+sin(x);endf1%f1(12)= 6.9223e+003%f1(-32)= 1.0234e+003%2function y=f2(x)if x0 y=sin(5*x)+6*x3;else y=x2+sin(x);e

21、nd%f2(-6)=-1.2950e+003%f2(11)=120.0000%3syms x f3=(1+x)/(x-3)g=finverse(f3)%f3 =(1+x)/(x-3)%g =(1+3*x)/(-1+x)%4syms xf4=3*x4+5*x3-6*x2+7;g4=8*x3+2*x2+x-9;u1=f4+g4u2=f4-g4u3=f4*g4u4=f4/g4u5=f4g4u6=compose(f4,g4)%u1 =3*x4+13*x3-4*x2-2+xu2 =3*x4-3*x3-8*x2+16-xu3 =(3*x4+5*x3-6*x2+7)*(8*x3+2*x2+x-9)u4 =

22、(3*x4+5*x3-6*x2+7)/(8*x3+2*x2+x-9)u5 =(3*x4+5*x3-6*x2+7)(8*x3+2*x2+x-9)u6 =3*(8*x3+2*x2+x-9)4+5*(8*x3+2*x2+x-9)3-6*(8*x3+2*x2+x-9)2+7%5syms xf5=-452*x2+224*x3+60*x4-296*x+320;f51=factor(f5)f52=horner(f5)r5=solve(f5)%f51 =4*(5*x-8)*(3*x-2)*(x+5)*(1+x)%f52 =320+(-296+(-452+(224+60*x)*x)*x)*x%r5 = -1 2

23、/3 -5 8/5%6g6=x*exp(x)-2*x2+5;x=fzero(g6,-2.2)%x = -1.5278%第二大题%1syms xy1=(x2)*(3(1/x)+3(-1/x)-2);y11=limit(y1,inf)%y11 =log(3)2%2y21=limit(x*log(sin(x),x,0,right)y22=limit(sin(sqrt(x2+1)-sin(x)/x,inf)%y21=0 y22=0%3f=sin(x);y31=taylor(f,5,1)%y31=sin(1)+cos(1)*(-1+x)-1/2*sin(1)*(-1+x)2-1/6*cos(1)*(-1

24、+x)3+1/24*sin(1)*(%-1+x)4%第三大题syms xf32=limit(exp(x)+x,x,0,right);f33=limit(x2+1,x,0,left);if (f32=f33)&(f32=1) a=函数在分界点连续else a=函数在分界点不连续end %a =函数在分界点连续%第四大题%1f41=sin(x3);f410=diff(f41,x,1)%f410 =3*cos(x3)*x2%2f42=x(1/a)+a(1/x)+x(1/x);f420=diff(f42,x,2)%f420=x(1/a)/a2/x2-x(1/a)/a/x2+a(1/x)/x4*log(

25、a)2+2*a(1/x)/x3*log(a)+x(1/x)*(-1/x2*log(x)+1/x2)2+x(1/x)*(2/x3*log(x)-3/x3)%3f43=atan(log(x);f430=diff(f43,x,2)%f430 =-1/x2/(1+log(x)2)-2/x2/(1+log(x)2)2*log(x)%4f44=x*asin(x)/sqrt(1-x2)+log(1-x2);f440=diff(f44,x,2)%f440 =3*asin(x)/(1-x2)(3/2)*x-x2/(1-x2)2+3*x3*asin(x)/(1-x2)(5/2)% 第五大题%1syms x ;f5

26、1=2*x3-6*x2-18*x+7;x,minf51=fminbnd(f51,1,2)%x = 1.9999 minf51 =-36.9988%2syms x;x,maxf52=fminbnd(-x-sqrt(16-x),-2,2);maxf52=-maxf52x%maxf52 = 5.7416x = 1.9999%第六大题%1syms x ;f=(x5)*cos(x3);y61=int(f)%y61 =cos(x3)/3 + (x3*sin(x3)/3%2syms x ;f=(sin(x)10;y62=int(f)%y62 =(63*x)/256 - (105*sin(2*x)/512 + (15*sin(4*x)/256 -%(15*sin(6*x)/1024 + (5*sin(8*x)/2048 - sin(10*x)/5120%3syms x ;f=1/(x+1)2)*(x+1)4)(1/3);y63=int(f)%y63 =-(x + 1)/(x + 1)6)(1/3)%第七大题