高等数学实验

刘第三次作业

6.(1)clear;x=-2:0.1:2;y=x.^2.*sin(x.^2-x-2);plot(x,y)

clear;x=-2:0.01:2;y=3*sqrt(1-0.25*x.^2);plot(x,y);holdon;y=-3*sqrt(1-0.25*x.^2);plot(x,y);

1

0

-1

-2

-3

-2 -1.5

clear;x=-3:0.1:3;y=x;[x,y]=meshgrid(x,y);z=x.^2+y.^2;surf(x,y,z);

clear;x=-3:0.1:3;y=-3:0.1:13;[x,y]=meshgrid(x,y);z=x.^4+3*x.^2+y.^2-2*x-2*y-2*x.^2.*y+6;surf(x,y,z)

10

5

clear;t=0:0.01:2*pi;x=sin(t);y=cos(t);z=cos(2*t);plot3(x,y,z);

clear;theta=linspace(0,2*pi,50);fai=linspace(0,pi/2,20);[theta,fai]=meshgrid(theta,fai);x

=2*sin(fai).*cos(theta);y=2*sin(fai).*sin(theta);z=2*cos(fai);surf(x,y,z);

2

1.5

1

0.5

0

2

1 2

0 1

0

-1 -1

-2 -2

clear;x=linspace(0,pi,100);y1=sin(x);y2=sin(x).*sin(10*x);...y3=-sin(x);plot(x,y1,y2,y3);

1.clear;a=[1,2,3];b=[2,3,4];a./b,a.\b,a/b,a\bans=

0.5000 0.6667 0.7500

ans=

2.0000 1.5000 1.3333

ans=

0.6897 一元方程近似解

ans=

0

0

0

0

0

0

0.6667

1.0000

1.3333

矩阵的特解

2（1）clear;A=[41-1;32-6;1-53];b=[9;-2;1];rank(A),rank([A,b])

ans=

3

ans=

3 方程唯一解

>>x=A\bx=

2.3830

1.4894

2.0213

（2）clear;A=[4-33;32-6;1-53];b=[-1;-2;1];rank(A),rank([A,b])

ans=

3

ans=

3 可见方程唯一解

>>x=A\bx=

-0.4706

-0.2941

0

（3）clear;A=[41;32;1-5];b=[1;1;1];rank(A),rank([A,b])ans=

2

ans=

3 无解

>>x=A\bx=

0.3311

-0.1219 最小二乘法近似解

（4）clear;a=[2,1,-1,1;1,2,1,-1;1,1,2,1];b=[1;2;3];rank(a),rank([a,b])

ans=

3

ans=

3 无穷多解

>>a\bans=

1

0

1

0 一个特解

3clear;a=[2,1,-1,1;1,2,1,-1;1,1,2,1];b=[1;2;3];x=null(a),x0=a\b

x=

-0.6255

0.6255

-0.2085

0.4170

x0=

1

0

1

0

通解kx+x0

6.(1)a=[41-1;32-6;1-53];det(a),inv(a),[v,d]=eig(a)

ans=

-94

ans=

0.2553

-0.0213

0.0426

0.1596

-0.1383

-0.2234

0.1809

-0.2234

-0.0532

v=

0.0185

-0.9009

-0.3066

-0.7693

-0.1240

-0.7248

-0.6386

-0.4158

0.6170

d=

-3.0527

0

0

0

3.6760

0

0

0

8.3766

clear;a=[11-1;02-1;-120];det(a),inv(a),[v,d]=eig(a)ans=

1

ans=

2.0000

-2.0000

1.0000

1.0000

-1.0000

1.0000

2.0000

-3.0000

2.0000

v=

-0.5774+0.0000i

-0.5773-0.0000i

-0.5773+0.0000i

-0.5774+0.0000i

-0.5773-0.0000i

-0.5773+0.0000i

-0.5773+0.0000i

-0.5774+0.0000i

-0.5774+0.0000i

d=

1.0000+0.0000i

0.0000+0.0000i

0.0000+0.0000i

0.0000+0.0000i

1.0000+0.0000i

0.0000+0.0000i

0.0000+0.0000i

0.0000+0.0000i

1.0000-0.0000i

clear;A=[5765;71087;68109;57910];det(A),inv(A),[v,d]=eig(A)

ans=

1.0000

ans=

68.0000

-41.0000

-17.0000

10.0000

-41.0000

25.0000

10.0000

-6.0000

-17.0000

10.0000

5.0000

-3.0000

10.0000

-6.0000

-3.0000

2.0000

v=

0.8304

0.0933

0.3963

0.3803

-0.5016

-0.3017

0.6149

0.5286

-0.2086

0.7603

-0.2716

0.5520

0.1237

-0.5676

-0.6254

0.5209

d=

0.0102

0

0

0

0

0.8431

0

0

0

0

3.8581

0

0

0

0

30.2887

clear;n=5;

fori=1:n,a(i,i)=5;end

fori=1:(n-1),a(i,i+1)=6;end

fori=1:(n-1),a(i+1,i)=1;enda

a=

5

6

0

0

0

0

1

5

6

0

0

0

1

5

>>det(a)ans=

665

>>inv(a)ans=

0.3173

-0.5865

1.0286

-1.6241

1.9489

-0.0977

0.4887

-0.8571

1.3534

-1.6241

0.0286

-0.1429

0.5429

-0.8571

1.0286

-0.0075

0.0376

-0.1429

0.4887

-0.5865

0.0015

>>[v,d]=eig(a)

-0.0075

0.0286

-0.0977

0.3173

v=

0.7843

-0.7843

-0.9860

-0.9237

-0.9237

0.5546

0.5546

0.0000

0.3771

-0.3771

0.2614

-0.2614

0.1643

-0.0000

0.0000

0.0924