数学实验matlab实验报告

1、

[x,y]=meshgrid(-4:00.125:4);

2-x.^2-y.^2;

meshc(x,y,z)

2、

t=[-2:0.01:2]';

u=0:0.01:2*pi;

x=cosh(t)*cos(u)

y=cosh(t)*sin(u);

z=2*t*(0*u+1);

mesh(x,y,z)

3、

s=[0:0.01:2*pi]';

t=0:0.01:2*pi;

x=(4+sin(s))*cos(t);

y=(4+sin(s))*sin(t);

z=1/4*cos(s)*(0*t+1);

mesh(x,y,z)

4、

t=0:0.01:2*pi;

x=(4+sin(20*t)).*cos(t);

y=(4+sin(20*t)).*sin(t);

z=cos(20*t)/10;

plot3(x,y,z)

5、

TT=0:0.1*pi:2*pi;

c=4;

b=2;

W=-b:0.1:b;

[u,v]=meshgrid(TT,W);

x=(c+0.5*v.*sin(u./2)).*cos(u);

y=(c+0.5*v.*sin(u./2)).*sin(u);

z=0.5*v.*cos(u./2);

mesh(x,y,z)

axis([-55-44-33])

6、

t=0:0.1:6*pi

[x,y,z]=cylinder(6+sin(t));

surf(x,y,z)

7、

symsxy

S=2*x*y/(x^2+y^2);

dfx=diff(S,x)

dfxx=diff(S,x,2)

dfxxy=diff(dfxx,y)

dfx=(2*y)/(x^2+y^2)-(4*x^2*y)/(x^2+y^2)^2

dfxx=(16*x^3*y)/(x^2+y^2)^3-(12*x*y)/(x^2+y^2)^2

dfxxy=(16*x^3)/(x^2+y^2)^3-(12*x)/(x^2+y^2)^2+(48*x*y^2)/(x^2+y^2)^3-(96*x^3*y^2)/(x^2+y^2)^4

8、

symsxyz

F=2*x+y+z-exp(-x*y*z);

Fx=diff(F,x);

Fz=diff(F,z);

zx=-Fx/Fz

zxy=diff(zx,y);

zxy1=simple(zxy)

zx=-((y*z)/exp(x*y*z)+2)/((x*y)/exp(x*y*z)+1)

zxy1=-((2*x-z)*(x*y*z-1))/(exp(x*y*z)*((x*y)/exp(x*y*z)+1)^2)

9、

symsrt

int(int(exp(-r^2)*r,r,0,1),t,0,2*pi)

ans=-pi*(1/exp(1)-1)

10、symsxy

f1=-x-y-1;

f2=-x+y-1

f3=x-y-1;

f4=x+y-1;

ezplot(f1,[-1,1])

holdon

ezplot(f2,[-1,1])

holdon

ezplot(f3,[-1,1])

holdon

ezplot(f4,[-1,1])

11、

[x1,y1]=meshgrid(-1.5:1/4:1.5);

z1=ones(size(x1));

surf(x1,y1,z1)

holdon

symsxyz

z=sqrt(x.^2+y.^2);

ezsurf(z,[-1.5,1.5])

12、

symsrtz

int(int(int((r^2+z)*r,z,r,1),r,0,1),t,0,2*pi)

ans=(7*pi)/20

13、

[x,y]=meshgrid(-4:0.01:4);

z=x*sin(x.^2+y.*2);

meshc(x,y,z)

14、

t=-1:0.01:1;

x=t.*cos(20*pi*t);

y=t.*sin(20*pi*t);

z=t.^3;

plot3(x,y,z)

15、

symsxyz

F=x.^3+y.^3+exp(x.^2*y.^2*z.^2)-10;

Fx=diff(F,x);

Fy=diff(F,y);

Fz=diff(F,z);

zx=-Fx/Fz

zy=-Fy/Fz

zyy=diff(zy,y);

zyy1=simple(zyy)

zx=-(3*x^2+2*x*y^2*z^2*exp(x^2*y^2*z^2))/(2*x^2*y^2*z*exp(x^2*y^2*z^2))

zy=-(3*y^2+2*x^2*y*z^2*exp(x^2*y^2*z^2))/(2*x^2*y^2*z*exp(x^2*y^2*z^2))

zyy1=z/y^2+(3*y*z)/exp(x^2*y^2*z^2)

16、

symsrtz

int(int(int(r,z,1,sqrt(4-r.^2)),r,0,sqrt(3)),t,0,2*pi)

ans=(5*pi)/3

[x1,y1]=meshgrid(-sqrt(3):0.01: