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1、习题2.1画出下列常见曲线的图形（1） 立方抛物线 命令：syms x y; ezplot(x.(1/3)(2)高斯曲线y=e(-X2);命令：clearsyms x y;ezplot(exp(-x*x)(3)笛卡尔曲线命令： clear syms x y; a=1; ezplot(x3+y3-3*a*x*y)(4) 蔓叶线命令： clear syms x y; a=1ezplot(y2-(x3)/(a-x)(5) 摆线:命令： clear t=0:0.1:2*pi; x=t-sin(t);y=2*(1-cos(t); plot(x,y)7螺旋线命令： clear t=0:0.1:2*pi;
2、x=cos(t); y=sin(t); z=t;plot3(x,y,z)(8) 阿基米德螺线命令：clear theta=0:0.1:2*pi; rho1=(theta); subplot(1,2,1),polar(theta,rho1)(9) 对数螺线命令：cleartheta=0:0.1:2*pi;rho1=exp(theta);subplot(1,2,1),polar(theta,rho1)(12) 心形线命令： clear theta=0:0.1:2*pi; rho1=1+cos(theta); subplot(1,2,1),polar(theta,rho1)练习2.21. 求出下列极
3、限值（1）命令：syms nlimit(n3+3n)(1/n) ans =3（2）命令：syms nlimit(n+2)(1/2)-2*(n+1)(1/2)+n(1/2),n,inf) ans = 0（3）命令：syms x； limit(x*cot(2*x),x,0) ans =1/2（4）命令：syms x m；limit(cos(m/x)x,x,inf)ans =1（5）命令：syms x limit(1/x-1/(exp(x)-1),x,1)ans =(exp(1)-2)/(exp(1)-1)（6）命令：syms x limit(x2+x)(1/2)-x,x,inf)ans =1/2
4、练习2.41. 求下列不定积分，并用diff验证：（1）Clear syms x y 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 (2)clearsyms x yy=1/(1+exp(x);f=int(y,x)f = -log(1+exp(x)+log(exp(x)syms x yy=-log(1+exp(x)+log(exp(x);yx=diff(y,x);y1=simple(yx)y1 = 1/(1+exp(x)(3)s
5、yms x yy=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*x2 clearsyms x y y=x*(-1/2*cos(x)*sin(x)+1/2*x)-1/4*cos(x)2-1/4*x2;yx=diff(y,x); y1=simple(yx) y1 =x*sin(x)2(4) syms x yy=sec(x)3;f=int(y,x)f =1/2/cos(x)2*sin(x)+1/2*log(sec(x)+tan(x) clearsyms x yy=1/2/cos(x)2*sin(x)+1/2
6、*log(sec(x)+tan(x);yx=diff(y,x);y1=simple(yx)y1 = 1/cos(x)32. 求下列积分的数值解1）clearsyms xy=int(x(-x),x,0,1)y =int(x(-x),x = 0 . 1)vpa(y,10)ans =1.2）clear syms xy=int(exp(2*x)*cos(x)3,x, clearsyms xy=int(1/(2*pi)(1/2)*exp(-x2/2),x,0,1)y = 32913/*erf(1/2*2(1/2)*2(1/2)*pi(1/0,2*pi)y = 22/65*exp(pi)4-22/65vp
7、a(ans,10)(3) clear syms x y=int(1/(2*pi)(1/2)*exp(-x2/2),0,1); vpa(y,14)ans =.855 2（4） clear syms x y=int(x*log(x4)*asin(1/x2),1,3);Warning: Explicit integral could not be found. In sym.int at 58 vpa(y,14)ans =2.75 2（5） clear syms x y=int(1/(2*pi)(1/2)*exp(-x2/2),-inf,inf); vpa(y,14)ans =.999 练习2.51
8、判断下列级数的收敛性，若收敛，求出其收敛值。1）syms ns1=symsum(1/n(2n),n,1,inf)s1 = sum(1/(n(2n),n = 1 . Inf)vpa(s1,10)ans = 1.因此不收敛2）syms ns1=symsum(sin(1/n),n,1,inf) s1 =sum(sin(1/n),n = 1 . Inf)vpa(s1,10) ans =sum(sin(1/n),n = 1 . Inf)不收敛(3) clear syms n s=symsum(log(n)/n3,n,1,inf)s =-zeta(1,3)收敛(4) syms n s1=symsum(1/
9、(log10(n)n,n,3,inf)s1 =sum(1/(log(n)/log(10)n),n = 3 . inf)不收敛(5) syms ns1=symsum(1/n*log10(n),n,2,inf)s1 =sum(1/n*log(n)/log(10),n = 2 . Inf)不收敛(6) clear syms n s=symsum(-1)n*n/n2+1,n,1,inf)s =sum(-1)n/n+1,n = 1 . Inf)不收敛 习题3.11）clear;x,y=meshgrid(-30:0.3:30);z=10*sin(sqrt(x.2+y.2)./sqrt(1+x.2+y.2)
10、; meshc(x,y,z)clear x,y=meshgrid(-30:0.1:30); z=10*sin(x2+y2)(1/2)/(1+x2+y2)(1/2)mesh(x,y,z)1.2.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 onmesh(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
11、(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3.2P49/例3.2.1命令:syms x y limit(limit(x2+y2)/(sin(x)+cos(y),0),pi),ans =-pi2 limit(limit(1-cos(x2+y2)/(x2+y2),0),0),ans =0P49/例3.2.2命令：clear;syms x y z dx dy dz zxz zy zxx zxyz=atan(x2*y) z =atan(x2*y) zx=diff(z,x),zy=di
12、ff(z,y)zx 2*x*y/(1+x4*y2)zy =x2/(1+x4*y2) dz=zx*dx+zy*dy,dz =2*x*y/(1+x4*y2)*dx+x2/(1+x4*y2)*dzxx=diff(zx,x),zxy=diff(zx,y)zxx =2*y/(1+x4*y2)-8*x4*y3/(1+x4*y2)2zxy =2*x/(1+x4*y2)-4*x5*y2/(1+x4*y2)2 3.2.1作图表示函数z=x*exp(-x2-y2) (-1x1,0y 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3.41. 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 3x = 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)=2.8,0t10,做相平面图新建M函数function dy=weifen1(t,y)dy=zeros(2,1);dy(1)=2*y(1)+3
