数学实验(第二版)课后习题答案

贵州师范学院2012级数本一班李刚数学实验课后练习答案习题2.11.symsxy;x=-5:0.01:5;y=x.^1/2;plot(x,y)2.fplot('exp(-x.^2)',[-5,5])3.ezplot('x.^3+y.^3-3*x*y',[-5,5])4.ezplot('y.^2-x.^3/(1-x)',[-5,5])5.t=0:0.1:2*pi;x=t-sin(t);y=2*(1-cos(t));plot(x,y)6.t=0:0.1:2*pi;x=cos(t).^3;y=sin(t).^3;plot(t,y)7:t=0:0.1:2*pi;x=cos(t);y=2*sin(t);z=3*t;plot3(x,y,z)8:x=0:0.1:2*pi;r=x;polar(x,r)9:x=0:0.1:2*pi;r=exp(x);polar(x,r)10:x=0:0.1:2*pi;r=sqrt(cos(2*x));polar(x,r)11:x=0:0.1:2*pi;r=sqrt(sin(2*x));polar(x,r)12:x=0:0.1:2*pi;r=1+cos(x);polar(x,r)练习2.21：(1)(2)：symsn;limit('sqrt(n+2)-2*(sqrt(n+1))+sqrt(n)',n,inf)Ans=0(3)::(4):(5):(6):2:3:fplot('x.^2*sin(x.^2-x-2)',[-2,2])练习2.31：（2）：2：练习2.41：（1）（2）：（3）（4）：2：（1）：symsx;int(x^(-x),x,0,1)ans=int(x^(-x),x=0..1)vpa(ans,10)ans=1.291285997（2）：symsx；int(exp(2*x)*cos(x)^3,x,0,2*pi)ans=-22/65+22/65*exp(4*pi)（3）：symsx;int(exp(x^2/2)/sqrt(2*pi),x,0,1)ans=-1125899906842624/5644425081792261*i*erf(1/2*i*2^(1/2))*pi^(1/2)*2^(1/2)vpa(ans,10)ans=.4767191345（4）：symsx;int(x*log(x^4)*asin(1/x^2),x,1,3)ans=int(x*log(x^4)*asin(1/x^2),x=1..3)vpa(ans,10)ans=2.459772128（5）：symsx;int(exp(x^2/2)/sqrt(2*pi),x,-inf,inf)ans=Inf（6）：symsx;int(sin(x)/x,x,0,inf)ans=1/2*pi（7）：symsx;int(tan(x)/sqrt(x),x,0,1)Warning:Explicitintegralcouldnotbefound.Insym.intat58ans=int(tan(x)/x^(1/2),x=0..1)vpa(ans,10)ans=.7968288892（8）：symsx;int(exp(-x^2/2)/(1+x^4),x,-inf,inf)ans=1/4*pi^(3/2)*2^(1/2)*(AngerJ(1/2,1/2)-2/pi^(1/2)*sin(1/2)+2/pi^(1/2)*cos(1/2)-WeberE(1/2,1/2))vpa(ans,10)ans=1.696392536（9）：symsx;int(sin(x)/sqrt(1-x^2),x,0,1)ans=1/2*pi*StruveH(0,1)vpa(ans,10)ans=.8932437410练习2.5（1）：symsn;symsum(1/n^2^n,n,1,inf)ans=sum(1/((n^2)^n),n=1..Inf)（2）：symsn;symsum(sin(1/n),n,1,inf)ans=sum(sin(1/n),n=1..Inf)（3）：symsn;symsum(log(n)/n^3,n,1,inf)ans=-zeta(1,3)（4）：symsn;symsum(1/(log(n))^n,n,3,inf)ans=sum(1/(log(n)^n),n=3..Inf)（5）：symsn;symsum(1/(n*log(n)),n,2,inf)ans=sum(1/n/log(n),n=2..Inf)（6）：ymsn;symsum((-1)^n*n/(n^2+1),n,1,inf)ans=-1/4*Psi(1-1/2*i)+1/4*Psi(1/2-1/2*i)-1/4*Psi(1+1/2*i)+1/4*Psi(1/2+1/2*i)第三章练习3.11：（1）：a=-30:1:30;b=-30:1:30;[x,y]=meshgrid(a,b);z=10*sin(sqrt(x.^2+y.^2))./(sqrt(1+x.^2+y.^2));meshc(x,y,z)（2）：a=-30:1:30;b=-30:1:30;[x,y]=meshgrid(a,b);z=4*x.^2/9+y.^2;meshc(x,y,z)（3）：（4）：a=-30:1:30;b=-30:1:30;[x,y]=meshgrid(a,b);z=x.^2/3-y.^2/3;meshc(x,y,z)（5）：a=-30:1:30;b=-30:1:30;[x,y]=meshgrid(a,b);z=x*y;meshc(x,y,z)（6）：（7）：a=-30:1:30;b=-30:1:30;[x,y]=meshgrid(a,b);z=sqrt(x.^2+y.^2);meshc(x,y,z)（8）：（9）：a=-30:1:30;b=-30:1:30;[x,y]=meshgrid(a,b);z=atan(x./y);meshc(x,y,z)练习3.21;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)holdonquiver(a,b,px,py)2:a=-2:0.1:1;b=-7:0.1:1;[x,y]=meshgrid(a,b);z=y.^3/9+3*x.^2.*y+9*x.^2+y.^2+x.*y+9;plot3(x,y,z)gridon3:[x,y]=meshgrid(-2*pi:0.2:2*pi);z=x.^2+2*y.^2;plot3(x,y,z)holdonezplot('x^2+y^2-1',[-2*pi,2*pi]);gridon4:t=0:0.03:2*pi;s=[0:0.03:2*pi]';x=(0*s+1)*cos(t);y=(0*s+1)*sin(t);z=s*(0*t+1);mesh(x,y,z)holdon[x,y]=meshgrid(-1:0.1:1);z=1-x+y;mesh(x,y,z)5:symsxyzdxdyz=75-x^2-y^2+x*y;zx=diff(z,x),zy=diff(z,y)zx=-2*x+yzy=-2*y+x练习3.31：ezplot('x^2+y^2-2*x',[-2,2]);gridonsymsxy;s=int(int(x+y+1,y,-sqrt(1-(x-1)^2),sqrt(1-(x-1)^2)),x,0,2)s=2*pi2：symsrt;s=int(int(sqrt(1+r^2*sin(t)),r,0,1),t,0,2*pi)s=int(1/2*((1+sin(t))^(1/2)*sin(t)^(1/2)+log(sin(t)^(1/2)+(1+sin(t))^(1/2)))/sin(t)^(1/2),t=0..2*pi)3：symsxyz;s=int(int(int(1/(1+x+y+z)^3,z,0,1-x-y),y,0,1-x),x,0,1)s=-5/16+1/2*log(2)4：s=vpa(int(int(x*exp(-x^2-y^2),y,0,2),x,-1,10))s=0.16224980455070416645061789474030练习3.41：（1）：y=dsolve('Dy=x+y','y(0)=1','x')得：y=-1-x+2*exp(x)（2）：y=dsolve('Dy=2*x+y^2','y(0)=0')y=tan(t*x^(1/2)*2^(1/2))*x^(1/2)*2^(1/2)练习4.11：（1）：p=[5000000000000000-68000-500];x=roots(p)x=000.97680.9388+0.2682i0.9388-0.2682i0.8554+0.5363i0.8554-0.5363i0.6615+0.8064i0.6615-0.8064i0.3516+0.9878i0.3516-0.9878i-0.0345+1.0150i-0.0345-1.0150i-0.4609+0.9458i-0.4609-0.9458i-0.1150+0.8340i-0.1150-0.8340i-0.7821+0.7376i-0.7821-0.7376i-0.9859+0.4106i-0.9859-0.4106i-1.0416-0.7927（2）:p=[8365423];x=roots(p)x=-1.8969+0.6874i-1.8969-0.6874i-0.70632:p1=[10-3-2-1];p2=[1-25];[q2,r2]=deconv(p1,p2)q2=12-4r2=000-20193:symsx;f=x^4+3*x^3-x^2-4*x-3;g=3*x^3+10*x^2+2*x-3;p1=factor(f),p2=factor(g)p1=(x+3)*(x^3-x-1)p2=(x+3)*(3*x^2+x-1)4:symsx;f=x^12-1;p=factor(f)p=(-1+x)*(1+x^2+x)*(1+x)*(1-x+x^2)*(1+x^2)*(x^4-x^2+1)5:(1):p=[101];q=[10001];[a,b,r]=residue(p,q)a=-0.0000-0.3536i-0.0000+0.3536i0.0000-0.3536i0.0000+0.3536ib=0.7071+0.7071i0.7071-0.7071i-0.7071+0.7071i-0.7071-0.7071ir=[](2):p=[1];q=[10001];[a,b,r]=residue(p,q)a=-0.1768-0.1768i-0.1768+0.1768i0.1768-0.1768i0.1768+0.1768ib=0.7071+0.7071i0.7071-0.7071i-0.7071+0.7071i-0.7071-0.7071ir=[](3):p=[101];q=[11-1-1];[a,b,r]=residue(p,q)a=0.5000-1.00000.5000b=-1.0000-1.00001.0000r=[](4):p=[11000-8];q=[10-10];[a,b,r]=residue(p,q)a=-4-38b=-110r=111练习4.21：（1）：D=[2131;3-121;1232;5062];det(D)ans=6（2）：symsabcdD=[a100;-1b10;0-1c1;00-1d];det(D)ans=a*b*c*d+a*b+a*d+c*d+12：（1）：symsabcdD=[1111;abcd;a^2b^2c^2d^2;a^3b^3c^3d^3]