matlab课后习题答案（附图）(3)

2.取适当的参数绘制下列曲面的图形。 （1） clear

>> a=-2:0.1:2; >> b=-3:0.1:3; >> [x,y]=meshgrid(a,b); >> z=(1-(x.^2)/4-(y.^2)/9).^(1/2); >> mesh(x,y,z) >> hold on mesh(x,y,-z)

（2） clear >> a=-1:0.1:1; >> b=-2:0.1:2;

[x,y]=meshgrid(a,b);

>> z=(4/9)*(x.^2)+(y.^2); >> mesh(x,y,z)

(4) clear

>> [x,y]=meshgrid(-1:0.1:1); >> z=(1/3)*(x.^2)-(1/3)*(y.^2); >> mesh(x,y,z)

习题3.2

P49/例3.2.1

命令:syms x y

limit(limit((x^2+y^2)/(sin(x)+cos(y)),0),pi), ans =

-pi^2

limit(limit((1-cos(x^2+y^2))/((x^2+y^2)),0),0), ans = 0

P49/例3.2.2

命令：clear;syms x y z dx dy dz zxz zy zxx zxy z=atan(x^2*y) z =

atan(x^2*y)

zx=diff(z,x),zy=diff(z,y) zx

2*x*y/(1+x^4*y^2) zy =

x^2/(1+x^4*y^2) dz=zx*dx+zy*dy,

dz =

2*x*y/(1+x^4*y^2)*dx+x^2/(1+x^4*y^2)*d zxx=diff(zx,x),zxy=diff(zx,y) zxx =

2*y/(1+x^4*y^2)-8*x^4*y^3/(1+x^4*y^2)^2 zxy =

2*x/(1+x^4*y^2)-4*x^5*y^2/(1+x^4*y^2)^2

3.2.1作图表示函数z=x*exp(-x^2-y^2) (-1

clear

>> a=-1:0.1:1; >> b=0:0.1:2;

>> [x,y]=meshgrid(a,b); >> z=x.*exp(-x.^2-y.^2);

>> [px,py]=gradient(z,0.1,0.1); contour(a,b,z),hold on, >> quiver(a,b,px,py),hold off

习题3.4 1. 解下列微分方程

（1）y=dsolve('Dy=x+y','y(0)=1','x') y =

-x-1+2*exp(x) x=[1 2 3]

x = 1 2 3 -x-1+2*exp(x) ans =

3.4366 11.7781 36.1711

（2）x'=2*x+3*y,y'=2*x+y,x(0)=-2,y(0)=2.8,0

新建M函数

function dy=weifen1(t,y) dy=zeros(2,1); dy(1)=2*y(1)+3*y(2); dy(2)=2*y(1)+y(2); 输入命令 >> t=0:0.1:10;

>> [t,y]=ode15s('weifen1',[0,10],[-2 2.8]); >> plot(t,y)

（3）y''-0.01(y')^2+2*y1=sin(t),y(0)=0,y'(0)=1,0

function dy=weifen2(t,y) dy=zeros(2,1); dy(1)=y(2);

dy(2)=0.01*y(2)^2-2*y(1)+sin(t);

输入命令

>> [t,y]=ode15s('weifen2',[0,5],[0 1]); >> plot(t,y)

1.绘制飞船轨迹图 新建M函数

function dy=weifen3(t,y)

dy=zeros(4,1);

dy(1)=y(3); dy(2)=y(4);

dy(3)=2*y(4)+y(1)-(1-1/82.45)*(y(1)+

1/82.45)/((y(1)+1/82.45)^2+y(2)^2)^(3/2)-(1/82.45)*(y(1)+1/82.45-1)/((y(1)+1-1/82.45)^2+y(2)^2)^(3/2);

dy(4)=-2*y(3)+y(2)-(1-1/82.45)*y(2)^2/((y(1)+1/82.45)^2+y(2)^2)^(3/2)-(1/82.45)*y(2)/((y(1)+1-1/82.45)^2+y(2)^2)^(3/2); 输入命令

>> [t,y]=ode15s('weifen3',[0,10],[1.2 0 0 -1]); >> plot(t,y)

习题4.1

4.1.5（1）>> clear >> p=[1 0 1]; q=[1 0 0 0 1]; [a,b,r]=residue(p,q)

a =

-0.0000 - 0.3536i -0.0000 + 0.3536i 0.0000 - 0.3536i 0.0000 + 0.3536i b =