matlab课后习题答案 附图Word文档格式.docx
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0.1:
2*pi;
x=t-sin(t);
y=2*(1-cos(t));
plot(x,y)
7螺旋线
x=cos(t);
y=sin(t);
z=t;
plot3(x,y,z)
(8)阿基米德螺线
theta=0:
rho1=(theta);
subplot(1,2,1),polar(theta,rho1)
(9)对数螺线
theta=0:
rho1=exp(theta);
subplot(1,2,1),polar(theta,rho1)
(12)心形线
rho1=1+cos(theta);
练习2.2
1.求出下列极限值
(1)
symsn
limit((n^3+3^n)^(1/n))
ans=
3
(2)
symsn
limit((n+2)^(1/2)-2*(n+1)^(1/2)+n^(1/2),n,inf)
0
(3)
symsx;
limit(x*cot(2*x),x,0)
1/2
(4)
symsxm;
limit((cos(m/x))^x,x,inf)
1
(5)
symsx
limit(1/x-1/(exp(x)-1),x,1)
(exp
(1)-2)/(exp
(1)-1)
(6)
limit((x^2+x)^(1/2)-x,x,inf)
练习2.4
1.求下列不定积分,并用diff验证:
Clear
symsxy
y=1/(1+cos(x));
f=int(y,x)
f=
tan(1/2*x)
y=tan(1/2*x);
yx=diff(y,x);
y1=simple(yx)
y1=
1/2+1/2*tan(1/2*x)^2
symsxy
y=1/(1+exp(x));
f=int(y,x)
f=
-log(1+exp(x))+log(exp(x))
y=-log(1+exp(x))+log(exp(x));
yx=diff(y,x);
y1=simple(yx)
y1=
1/(1+exp(x))
y=x*sin(x)^2;
f=int(y,x)
f=
x*(-1/2*cos(x)*sin(x)+1/2*x)-1/4*cos(x)^2-1/4*x^2
symsxyy=x*(-1/2*cos(x)*sin(x)+1/2*x)-1/4*cos(x)^2-1/4*x^2;
y1=simple(yx)
y1=
x*sin(x)^2
(4)
y=sec(x)^3;
1/2/cos(x)^2*sin(x)+1/2*log(sec(x)+tan(x))
y=1/2/cos(x)^2*sin(x)+1/2*log(sec(x)+tan(x));
1/cos(x)^3
2.求下列积分的数值解
1)
y=int(x^(-x),x,0,1)
y=
int(x^(-x),x=0..1)
vpa(y,10)
1.291285997
2)
clear
y=int(exp(2*x)*cos(x)^3,x,clear
y=int((1/(2*pi)^(1/2))*exp(-x^2/2),x,0,1)
y=
7186705221432913/36028797018963968*erf(1/2*2^(1/2))*2^(1/2)*pi^(1/0,2*pi)
22/65*exp(pi)^4-22/65vpa(ans,10)
(3)
symsx
y=int(1/(2*pi)^(1/2)*exp(-x^2/2),0,1);
vpa(y,14)
.34134474606855
2(4)
y=int(x*log(x^4)*asin(1/x^2),1,3);
Warning:
Explicitintegralcouldnotbefound.
Insym.intat58
2.4597721282375
2(5)
y=int(1/(2*pi)^(1/2)*exp(-x^2/2),-inf,inf);
.99999999999999
练习2.5
1判断下列级数的收敛性,若收敛,求出其收敛值。
1)symsn
s1=symsum(1/n^(2^n),n,1,inf)
s1=
sum(1/(n^(2^n)),n=1..Inf)
vpa(s1,10)
ans=
1.062652416
因此不收敛
2)symsn
s1=symsum(sin(1/n),n,1,inf)
s1=
sum(sin(1/n),n=1..Inf)
vpa(s1,10)
不收敛
(3)
symsn
s=symsum(log(n)/n^3,n,1,inf)
s=
-zeta(1,3)
收敛
(4)symsn
s1=symsum(1/(log10(n))^n,n,3,inf)
sum(1/((log(n)/log(10))^n),n=3..inf)
(5)symsn
s1=symsum(1/n*log10(n),n,2,inf)
sum(1/n*log(n)/log(10),n=2..Inf)
(6)
s=symsum((-1)^n*n/n^2+1,n,1,inf)
sum((-1)^n/n+1,n=1..Inf)
习题3.1
1)clear;
[x,y]=meshgrid(-30:
0.3:
30);
z=10*sin(sqrt(x.^2+y.^2))./sqrt(1+x.^2+y.^2);
meshc(x,y,z)
[x,y]=meshgrid(-30:
z=10*sin((x^2+y^2)^(1/2))/(1+x^2+y^2)^(1/2)
mesh(x,y,z)
1.
2.取适当的参数绘制下列曲面的图形。
a=-2:
2;
b=-3:
3;
[x,y]=meshgrid(a,b);
z=(1-(x.^2)/4-(y.^2)/9).^(1/2);
mesh(x,y,z)
holdon
mesh(x,y,-z)
a=-1:
1;
b=-2:
[x,y]=meshgrid(a,b);
z=(4/9)*(x.^2)+(y.^2);
[x,y]=meshgrid(-1:
1);
z=(1/3)*(x.^2)-(1/3)*(y.^2);
习题3.2
P49/例3.2.1
命令:
limit(limit((x^2+y^2)/(sin(x)+cos(y)),0),pi),
-pi^2
limit(limit((1-cos(x^2+y^2))/((x^2+y^2)),0),0),
P49/例3.2.2
clear;
symsxyzdxdydzzxzzyzxxzxy
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<
x<
1,0<
y<
2)沿x轴方向梯度
b=0:
z=x.*exp(-x.^2-y.^2);
[px,py]=gradient(z,0.1,0.1);
contour(a,b,z),holdon,
quiver(a,b,px,py),holdoff
习题3.4
1.解下列微分方程
(1)y=dsolve('
Dy=x+y'
'
y(0)=1'
x'
-x-1+2*exp(x)
x=[123]
x=123
-x-1+2*exp(x)
3.436611.778136.1711
(2)x'
=2*x+3*y,y'
=2*x+y,x(0)=-2,y(0)=2.8,0<
t<
10,做相平面图
新建M函数
functiondy=weifen1(t,y)
dy=zeros(2,1);
dy
(1)=2*y
(1)+