matlab实验作业.docx
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matlab实验作业.docx
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matlab实验作业
第二题:
>>A=[1,2,3,4;4,3,2,1;2,3,4,1;3,2,4,1]
A=
1234
4321
2341
3241
>>B=[1+4j,2+3j,3+2j,4+1j;4+1j,3+2j,2+3j,1+4j;2+3j,3+2j,4+1j,1+4j;3+2j,2+3j,4+1j,1+4j]
B=
1.0000+4.0000i2.0000+3.0000i3.0000+2.0000i4.0000+1.0000i
4.0000+1.0000i3.0000+2.0000i2.0000+3.0000i1.0000+4.0000i
2.0000+3.0000i3.0000+2.0000i4.0000+1.0000i1.0000+4.0000i
3.0000+2.0000i2.0000+3.0000i4.0000+1.0000i1.0000+4.0000i
>>A(5,6)=5
A=
123400
432100
234100
324100
000005
第三题
>>A=magic(8)
A=
642361606757
955541213515016
1747462021434224
4026273736303133
3234352928383925
4123224445191848
4915145253111056
858595462631
>>B=A(:
2:
2:
end)
B=
261657
55125116
47204324
26373033
34293825
23441948
15521156
585621
第四题
>>s=sum(2.^(0:
63))
s=
1.8447e+019
>>s=sum(sym
(2).^(0:
63))
s=
184********709551615
第五题
(1)x=[-1:
0.01:
1];
y=sin(1./x);plot(x,y)
(2)x=[-pi:
0.00001:
pi];
y=sin(tan(x))-tan(sin(x));
plot(x,y)
第六题
xx=[-2:
0.1:
-1.2,-1.1:
0.01:
-0.7,-0.7:
0.1:
0.7,0.8:
0.01:
1.2,1.3:
0.1:
2];
[x,y]=meshgrid(xx,yy);
z=1./sqrt((1+x).^2+y.^2)+1./sqrt((1-x).^2+y.^2);
subplot(224),surf(x,y,z),shadingflat
subplot(223),surf(x,y,z),shadingflat,view(0,90);title('俯视图');
subplot(222),surf(x,y,z),shadingflat,view(90,0);title('侧视图');
subplot(221),surf(x,y,z),shadingflat,view(0,0);title('正视图')
第7题
(1)
>>symsxy;y=(3.^x+9.^x).^(1./x);L=limit(y,x,inf)
L=
9
(2)
symsxy;f=x.*y./(sqrt(x.*y+1)-1);L=limit(limit(f,x,0),y,0)
L=
2
(3)
symsxy;f=(1-cos(x.^2+y.^2))./((x.^2+y.^2).*exp(x.^2+y.^2));L=limit(limit(f,x,0),y,0)
L=
0
第8题
(1)
symsxyt;x=log(cos(t));y=cos(t)-t.*sin(t);a=diff(x,t);b=diff(y,t);f=b./a
f=
(cos(t)*(2*sin(t)+t*cos(t)))/sin(t)
(2)
symsxyt;
x=log(cos(t));y=cos(t)-t.*sin(t);a=diff(x,t);b=diff(y,t);f=b./a;f1=diff(f,t);f2=simple(f1./a);
c=subs(f2,t,pi./3)
c=
1.5387
第9题
symsxytf1f2f3f4f5;f1=exp(-t.^2);f2=int(f1,t,0,x.*y);f3=diff(diff(f2,x),x);f4=diff(diff(f2,x),y);f5=diff(diff(f2,y),y);...
f6=simple((f3.*x)./y-2.*f4+f5)
f6=
-2*exp(-x^2*y^2)*(x^3*y-x^2*y^2+1)
第10题
(1)
symsn;f=limit(symsum(1./((2.*n).^2-1),n),n,inf)
f=
0
(2)
symsnf;f=symsum(1./(n.^2+pi.*n),n);L=simple(limit(f.*n,n,inf))
L=-1/(2*pi)-(pi-1/2)/pi=-1
第11题
(1)
symsxyta;x=a.*(cos(t)+t.*sin(t));
y=a.*(sin(t)-t.*cos(t));
I=simple(int((x.^2+y.^2)*sqrt(diff(x,t).^2+diff(y,t).^2),t,0,2*pi))
I=
pi^2*(4*pi^2+2)*(a^2)^(3/2)
(2)
symsabct;
symsabcpositive;
x=(c.*cos(t))./a;y=(c.*sin(t))./b;F=[(y.*x.^3+exp(y)),(x.*y.^3+x.*exp(y)-2*y)];ds=[diff(x,t);
diff(y,t)];I=simple(int(F*ds,t,pi,0))
I=
(2*c)/a-(4*c^5)/(15*a*b^4)
第12题
symsabcdey;A=[a.^4,a.^3,a.^2,a,1;b.^4,b.^3,b.^2,b,1;c.^4,c.^3,c.^2,c,1;d.^4,d.^3,d.^2,d,1;e.^4,e.^3,e.^2,e,1];
y=simple(det(A))
y=
(a-b)*(a-c)*(a-d)*(b-c)*(a-e)*(b-d)*(b-e)*(c-d)*(c-e)*(d-e)
第13题
A=[-2,0.5,-0.5,0.5;0,-1.5,0.5,-0.5;2,0.5,-4.5,0.5;2,1,-2,-2];J=jordan(A)
J=
-4000
0-210
00-21
000-2
第14题
A=[3-6-405;142-24;-63-673;-13100-110;04034];...
B=[3-21;-2-92;-2-19];C=[2-11;-4-1-2;-56-1;-644;6-63];X=lyap(A,B,C)
X=
4.056914.5128-1.5653
-0.0356-25.07432.7408
-9.4886-25.93234.4177
-2.6969-21.64502.8851
-7.7229-31.91003.7634
第15题
(1)
symst;A=[-4.5,0,0.5,-1.5;-0.5,-4,0.5,-0.5;1.5,1,-2.5,1.5;0,-1,-1,-3];B=simple(expm(A*t))
B=
[(exp(-5*t)*(exp(2*t)-t*exp(2*t)+t^2*exp(2*t)+1))/2,(exp(-5*t)*(2*t*exp(2*t)-exp(2*t)+1))/2,(t*exp(-3*t)*(t+1))/2,-(exp(-5*t)*(exp(2*t)+t*exp(2*t)-t^2*exp(2*t)-1))/2]
[(exp(-5*t)*(t*exp(2*t)-exp(2*t)+1))/2,(exp(-5*t)*(exp(2*t)+1))/2,(t*exp(-3*t))/2,(exp(-5*t)*(t*exp(2*t)-exp(2*t)+1))/2]
[(exp(-5*t)*(exp(2*t)+t*exp(2*t)-1))/2,(exp(-5*t)*(exp(2*t)-1))/2,(exp(-3*t)*(t+2))/2,(exp(-5*t)*(exp(2*t)+t*exp(2*t)-1))/2]
[-(t^2*exp(-3*t))/2,-t*exp(-3*t),-(t*exp(-3*t)*(t+2))/2,-(exp(-3*t)*(t^2-2))/2]
(2)
symst;A=[-4.5,0,0.5,-1.5;-0.5,-4,0.5,-0.5;1.5,1,-2.5,1.5;0,-1,-1,-3];f=simple((expm(A*t*j)-expm(-A*t*j))/(2*j))
f=
[(t^2*sin(3*t))/2-sin(5*t)/2-(t*cos(3*t))/2-sin(3*t)/2,sin(3*t)/2-sin(5*t)/2+t*cos(3*t),(t*cos(3*t))/2+(t^2*sin(3*t))/2,sin(3*t)/2-sin(5*t)/2-(t*cos(3*t))/2+(t^2*sin(3*t))/2]
[sin(3*t)/2-sin(5*t)/2+(t*cos(3*t))/2,-4*sin(t)*(2*sin(t)^4-3*sin(t)^2+1),(t*cos(3*t))/2,sin(3*t)/2-sin(5*t)/2+(t*cos(3*t))/2]
[sin(5*t)/2-sin(3*t)/2+(t*cos(3*t))/2,sin(t)+8*sin(t)^3*(sin(t)^2-1),(t*cos(3*t))/2-sin(3*t),sin(5*t)/2-sin(3*t)/2+(t*cos(3*t))/2]
[-(t^2*sin(3*t))/2,-t*cos(3*t),-t*cos(3*t)-(t^2*sin(3*t))/2,-(sin(3*t)*(t^2+2))/2]
(3)
symst;A=[-4.5,0,0.5,-1.5;-0.5,-4,0.5,-0.5;1.5,1,-2.5,1.5;0,-1,-1,-3];
f=simple(expm(A*t)*(expm(A^2*expm(A*t)*t*j)-expm(-A^2*expm(A*t)*t*j))/(2*j))
f=
[(exp(-5*t)*sin(25*t*exp(-5*t)))/2+exp(-9*t)*sin(9*t*exp(-3*t))*(t^4*((81*i)/4)+t^3*(-27*i)+t^2*(9*i))*2*i-exp(-3*t)*sin(9*t*exp(-3*t))*(t^2*(i/4)+t*(-i/4)+i/4)*2*i+2*exp(-6*t)*cos(9*t*exp(-3*t))*((27*t^3)/4-(33*t^2)/4+2*t),(exp(-5*t)*sin(25*t*exp(-5*t)))/2-exp(-3*t)*sin(9*t*exp(-3*t))*((t*i)/2-i/4)*2*i-2*exp(-6*t)*cos(9*t*exp(-3*t))*(3*t-(9*t^2)/2),54*t^3*exp(-9*t)*sin(9*t*exp(-3*t))-18*t^2*exp(-9*t)*sin(9*t*exp(-3*t))-(81*t^4*exp(-9*t)*sin(9*t*exp(-3*t)))/2-(t*exp(-3*t)*sin(9*t*exp(-3*t))*(t*i+i)*i)/2-(t*exp(-6*t)*cos(9*t*exp(-3*t))*(-27*t^2+15*t+4))/2,(exp(-5*t)*sin(25*t*exp(-5*t)))/2+exp(-9*t)*sin(9*t*exp(-3*t))*(t^4*((81*i)/4)+t^3*(-27*i)+t^2*(9*i))*2*i+exp(-3*t)*sin(9*t*exp(-3*t))*((t*i)/4-(t^2*i)/4+i/4)*2*i+2*exp(-6*t)*cos(9*t*exp(-3*t))*((27*t^3)/4-(33*t^2)/4+2*t)]
[(exp(-5*t)*sin(25*t*exp(-5*t)))/2-exp(-3*t)*sin(9*t*exp(-3*t))*((t*i)/4-i/4)*2*i-2*exp(-6*t)*cos(9*t*exp(-3*t))*((3*t)/2-(9*t^2)/4),(exp(-3*t)*sin(9*t*exp(-3*t)))/2+(exp(-5*t)*sin(25*t*exp(-5*t)))/2,(t*exp(-6*t)*(exp(3*t)*sin(9*t*exp(-3*t))-6*cos(9*t*exp(-3*t))+9*t*cos(9*t*exp(-3*t))))/2,(exp(-5*t)*sin(25*t*exp(-5*t)))/2-exp(-3*t)*sin(9*t*exp(-3*t))*((t*i)/4-i/4)*2*i-2*exp(-6*t)*cos(9*t*exp(-3*t))*((3*t)/2-(9*t^2)/4)]
[-(exp(-5*t)*sin(25*t*exp(-5*t)))/2-exp(-3*t)*sin(9*t*exp(-3*t))*((t*i)/4+i/4)*2*i-2*exp(-6*t)*cos(9*t*exp(-3*t))*((3*t)/2-(9*t^2)/4),(exp(-3*t)*sin(9*t*exp(-3*t)))/2-(exp(-5*t)*sin(25*t*exp(-5*t)))/2,(9*t^2*exp(-6*t)*cos(9*t*exp(-3*t)))/2-3*t*exp(-6*t)*cos(9*t*exp(-3*t))-exp(-3*t)*sin(9*t*exp(-3*t))*((t*i)/4+i/2)*2*i,-(exp(-5*t)*sin(25*t*exp(-5*t)))/2-exp(-3*t)*sin(9*t*exp(-3*t))*((t*i)/4+i/4)*2*i-2*exp(-6*t)*cos(9*t*exp(-3*t))*((3*t)/2-(9*t^2)/4)]
[18*t^2*exp(-9*t)*sin(9*t*exp(-3*t))-(t^2*exp(-3*t)*sin(9*t*exp(-3*t)))/2-54*t^3*exp(-9*t)*sin(9*t*exp(-3*t))+(81*t^4*exp(-9*t)*sin(9*t*exp(-3*t)))/2-(t*exp(-6*t)*cos(9*t*exp(-3*t))*(27*t^2-24*t+2))/2,-t*exp(-6*t)*(exp(3*t)*sin(9*t*exp(-3*t))-6*cos(9*t*exp(-3*t))+9*t*cos(9*t*exp(-3*t))),18*t^2*exp(-9*t)*sin(9*t*exp(-3*t))-54*t^3*exp(-9*t)*sin(9*t*exp(-3*t))+(81*t^4*exp(-9*t)*sin(9*t*exp(-3*t)))/2+(t*exp(-3*t)*sin(9*t*exp(-3*t))*(t*i+2*i)*i)/2+(t*exp(-6*t)*cos(9*t*exp(-3*t))*(-27*t^2+6*t+10))/2,18*t^2*exp(-9*t)*sin(9*t*exp(-3*t))+exp(-3*t)*sin(9*t*exp(-3*t))*(t^2*(i/4)-i/2)*2*i-2*exp(-6*t)*cos(9*t*exp(-3*t))*((27*t^3)/4-6*t^2+t/2)-54*t^3*exp(-9*t)*sin(9*t*exp(-3*t))+(81*t^4*exp(-9*t)*sin(9*t*exp(-3*t)))/2]
第一题(第二部分)
(1)
symsat;f=sin(a.*t)./t;F=laplace(f,t)
F=
atan(a/t)
(2)
symsat;f=(t.^5).*(sin(a.*t));F=simple(laplace(f,t))
F=
(240*a*t*(a^2-3*t^2)*(3*a^2-t^2))/(a^2+t^2)^6
(3)
symsat;f=(t.^8).*(cos(a.*t));F=simple(laplace(f,t))
F=
(40320*t*(9*a^8-84*a^6*t^2+126*a^4*t^4-36*a^2*t^6+t^8))/(a^2+t^2)^9
第二题(第二部分)
(1)
symsabs;f=1./(s.*(s.^2-a.^2).*(s+b));F=simple(ilaplace(f,s,t))
F=
exp(a*t)/(2*a^2*(a+b))-1/(a^2*b)+exp(-b*t)/(b*(a^2-b^2))-exp(-a*t)/(2*a^2*(a-b))
(2)
symsasbt;f=sqrt(s-a)-sqrt(s-b);f=simple(ilaplace(f,s,t))
f=
1/2/t/(pi*t)^(1/2)*(exp(b*t)-exp(a*t))
(3)
symsasbt;f=log((s-a)./(s-b));f=simple(ilaplace(f,s,t))
f=
(exp(b*t)-exp(a*t))/t
第三题
(1)
symswtj;j=sqrt(-1);f=(t.^2).*(3*pi-2.*t).*exp(-j.*w.*t);f1=simple(int(f,t,0,2*pi))
f1=
2*(-6*w^2*pi^2+9*sqrt(-1)*w*pi-2*sqrt(-1)*w^3*pi^3+6+3*sqrt(-1)*exp(sqrt(-1)*w*pi)^2*w*pi-6*exp(sqrt(-1)*w*pi)^2)/exp(sqrt(-1)*w*pi)^2/w^4
(2)
symswt;f=t.^2.*(t-2*pi).^2.*exp(-j.*w.*t);f1=simple(int(f,t,0,2*pi))
f1=
-8*(-3*sqrt(-1)*exp(-2*sqrt(-1)*pi*w)+sqrt(-1)*exp(-2*sqrt(-1)*pi*w)*pi^2*w^2+3*exp(-2*sqrt(-1)*pi*w)*pi*w+3*sqrt(-1)-sqrt(-1)*pi^2*w^2+3*pi*w)/w^5
第四题(第二部分)
(1)
symsKTa;f=cos(K.*a.*T);f1=ztrans(f),f2=iztrans(f1,z,K)
f1=
(z*(z-cos(K*T)))/(z^2-2*cos(K*T)*z+1)
f2=
cos(K*T*a)
(2)
>>symsKTa;f=(K.*T).^2.*exp(-K.*T*a);f1=ztrans(f),f2=simple(iztrans(f1,z,K))
f1=
(K^2*T^2*z)/(z-exp(-K*T))
f2=
K^2*T^2*exp(-K*T*a)
(3)
symsaTKz;f=(a.*K.*T-1+exp(-a.*K.*T))./a;f1=simple(ztrans(f,K,z)),f2=simple(iztrans(f1,z,K))
f1=
T*z/(z-1)^2-1/a*z/(z-1)+1/a*z*exp(a*T)/(z*exp(a*T)-1)
f2=
(a*K*T-1+exp(-a*T)^K)/a
第五题
(1)
[x]=solve('exp(pi/2-(x-1)^2)*sin(5*x+2)=0'),y=[eval('exp(pi/2-(x-1)^2)*sin(5*x+2)')]
x=
-2/5
y=
0
(2)
[x]=solve('(x^2+y^2+x*y)*exp(-x^2-y^2+x*y)=0','x'),a=[eval('(x^2+y^2+x*y)*exp(-x^2-y^2+x*y)')]
x=
(-1/2+1/2*sqrt(-1)*3^(1/2))*y
(-1/2-1/2*sqrt(-1)*3^(1/2))*y
第9题
>>symsx;
y=dsolve('D2y-(2-1/x)*Dy+(1-1/x)*y=x^2*exp(-5*x)','x')
y=1/1296*exp(-5*x)*(6*Ei(1,6*x)*exp(6*x)+11+30*x+36*x^2)+C1*exp(x)+C2*log(x)*exp(x)
symsx;y=dsolve('D2y-(2-1/x)*Dy+(1-1/x)*y=x^2*exp(-5*x)',...
'y
(1)=sym(pi)','y(sym(pi))=1','x');y
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