高等应用数学问题的MATLAB求解习题解

MATLAB122MATLAB5317429543653771893911410127AScilab13614211MATLABdemoMATLABMATLABdemo1-11-1MATLABMATLAB!Graphics!VolumeVlsulization1-2Runthisdemo1-32MATLABtype131-2MATLAB1.1c1ex1.mMATLAB1.2c1ex2.mMATLAB1.3c1ex3.mMATLABHilbert1.4c1ex4.mx1=y;x2=_yode45()dde23()Simulink1.5c1ex5.mlinprog()ipslvmex()411-3MATLAB2MATLAB1MATLABtic,A=rand(500);B=inv(A);norm(A*B-eye(500)),tochelpMATLAB500£50010¡12tic,A=rand(500);B=inv(A);norm(A*B-eye(500)),tocans=1.2333e-012Elapsedtimeis1.301000seconds.2f(x)=x5+3x4+4x3+2x2+3x+6x=s¡1s+1f(x)sfsubs()xssymssxf=x^5+3*x^4+4*x^3+2*x^2+3*x+6;F=subs(f,x,(s-1)/(s+1))F=(s-1)^5/(s+1)^5+3*(s-1)^4/(s+1)^4+4*(s-1)^3/(s+1)^3+2*(s-1)^2/(s+1)^2+3*(s-1)/(s+1)+63MATLABABA=266412344321234132413775;B=26641+4j2+3j3+2j4+1j4+1j3+2j2+3j1+4j2+3j3+2j4+1j1+4j3+2j2+3j4+1j1+4j37754£4A(5;6)=5A=[1234;4321;2341;3241]A=123462MATLAB432123413241A(5,6)=5BA(5,6)=5A=123400432100234100324100000005B=[1+4i2+3i3+2i4+1i;4+1i3+2i2+3i1+4i;2+3i3+2i4+1i1+4i;3+2i2+3i4+1i1+4i];B=1.0000+4.0000i2.0000+3.0000i3.0000+2.0000i4.0000+1.0000i4.0000+1.0000i3.0000+2.0000i2.0000+3.0000i1.0000+4.0000i2.0000+3.0000i3.0000+2.0000i4.0000+1.0000i1.0000+4.0000i3.0000+2.0000i2.0000+3.0000i4.0000+1.0000i1.0000+4.0000i4AMATLABBA=magic(8)Amagic()A=magic(8),B=A(2:2:end,:)A=64236160675795554121351501617474620214342244026273736303133323435292838392541232244451918484915145253111056858595462631B=9555412135150162MATLAB7402627373630313341232244451918488585954626315MATLABy=f(x)=8:h;xDh=Dx;jxj6D¡h;x¡Dy=h*(xD)+h/D*x.*(abs(x)=D)-h*(x-D);fori=1:length(x)ifx(i)D,y(i)=h;elseifabs(x(i))=D,y(i)=h/D*x(i);else,y(i)=-h;endendxx6S=63Xi=02i=1+2+4+8+¢¢¢+262+263doublesum(sym(2).^[1:63])ans=1844674407370955161419double162001000sum(sym(2).^[1:200])ans=3213876088517980551083924184682325205044405987565585670602750sum(sym(2).^[1:1000])ans=21430172143725346418968500981200036211228096234110672148875007767407021022498722449863967576313917162551893458351062936503742905713846280882MATLAB719691551493971496078691355496484619708421492101247422837559083643060929499671638825347975351183310878921541258291423929553730843353208596633052487736744113361387507matadd()A=matadd(A1,A2,A3,¢¢¢)vararginfunctionA=mat_add(varargin)A=0;fori=1:length(varargin),A=A+varargin{i};endtry,catchfunctionA=mat_add(varargin)tryA=0;fori=1:length(varargin),A=A+varargin{i};endcatch,error(lasterr);end8MATLABm£mHankelv=[h1;h2;hm;hm+1;¢¢¢;h2m¡1];H=myhankel(v)Hi;j=hi+j¡1functionH=myhankel(v)m=(length(v)+1)/2;%fori=1:m,forj=1:mH(i,j)=v(i+j-1);end,end()ai=[hi;hi+1;¢¢¢;hi+m¡1]HankelfunctionH=myhankel(v)m=(length(v)+1)/2;%fori=1:m,H(i,:)=v(i:i+m-1);endhankel()functionH=myhankel(v)m=(length(v)+1)/2;%H=hankel(v(1:m),v(m:end));2MATLAB99Fibonacciak=ak¡1+ak¡2;k=3;4;¢¢¢a1=a2=1FibonacciMATLABy=fib(k)kkakyfib(n)Fibonaccinn3k=fib(n¡1)+fib(n¡2)n+11M-functiony=fib(n)ifround(n)==n&n=1ifn=3y=fib(n-1)+fib(n-2);else,y=1;endelseerror('nmustbepositiveinteger.')endn=10fib(10)ans=55tic,fib(20),tocans=832040elapsed_time=62.0490tic,a=[11];fori=3:30,a(i)=a(i-1)+a(i-2);end,a(30),tocans=832040elapsed_time=0.0100102MATLAB10MM=A+BCBT,A,B,CMM¡1=³A+BCBT´¡1=A¡1¡A¡1B³C¡1+BTA¡1B´¡1BTA¡1MATLABMfunctionMinv=part_inv(A,B,C)Minv=inv(A)-inv(A)*B*inv(inv(C)+B'*inv(A)*B)*B'*inv(A);M=2664515036165077603236608748163248683775A=266410000200003000043775;B=266412342340340040003775;C=266440000300002000013775M=[51503616;50776032;36608748;16324868];iM=inv(M);%iM=0.0553-0.03890.00170.0041-0.03890.0555-0.0210-0.00210.0017-0.02100.0328-0.01370.0041-0.0021-0.01370.0244A=diag([1234]);B=hankel([1234]);C=diag([4321]);iM1=part_inv(A,B,C)%iM1=0.0553-0.03890.00170.0041-0.03890.0555-0.0210-0.00210.0017-0.02100.0328-0.01370.0041-0.0021-0.01370.02442MATLAB11M1=sym(M);iM0=inv(M1)iM0=[10713/193751,-7546/193751,332/193751,796/193751][-7546/193751,10759/193751,-4068/193751,-416/193751][332/193751,-4068/193751,19075/581253,-2652/193751][796/193751,-416/193751,-2652/193751,18919/775004]norm(double(iM0)-iM)%ans=2.7990e-017norm(double(iM0)-iM1)%ans=3.6583e-016inv()11(xk+1=1+yk¡1:4x2kyk+1=0:3xkM-x0=0,y0=030000xyxkyk()Henon2-1Henonx=0;y=0;fori=1:29999x(i+1)=1+y(i)-1.4*x(i)^2;y(i+1)=0.3*x(i);endplot(x,y,'.')xyx=zeros(1,30000)12MATLAB122MATLAB−1.5−1−0.500.511.5−0.4−0.3−0.2−0.100.10.20.30.42-1Henonµ2-2a(cosµ;sinµ),(cos(µ+120±);sin(µ+120±)),(cos(µ+240±);sin(µ+240±))2-2b¢µ=2;1;0:1.............................................................µxy-6(a)−1−0.500.51−1−0.500.51(b)2-2t=[0,120,240,0]*pi/180;%xxx=[];yyy=[];fori=0:5:360tt=i*pi/180;xxx=[xxx;cos(tt+t)];yyy=[yyy;sin(tt+t)];end2MATLAB13plot(xxx',yyy','r'),axis('square')13sinµ1t¶t2(¡1;1)2-3ax=0t=-1:0.03:1;y=sin(1./t);plot(t,y)2-3bt=[-1:0.03:-0.25,-0.248:0.001:0.248,0.25:.03:1];y=sin(1./t);plot(t,y)−1−0.500.51−1−0.500.51(a)−1−0.500.51−1−0.500.51(b)2-3sin(1=t)14µ½=1:0013µ2½=cos(7µ=2)½=sin(µ)=µ½=1¡cos3(7µ)polar(µ,½)2-4t=0:0.01:2*pi;subplot(221),polar(t,1.0013*t.^2),%(a)subplot(222),t1=0:0.01:4*pi;polar(t1,cos(7*t1/2))%(b)subplot(223),polar(t,sin(t)./t)%(c)subplot(224),polar(t,1-(cos(7*t)).^3)15x