1、 5MATLAB p5 Is“ c1c9 22cMATLAB !9$53cs59 p174cL 59 p295csMMf 59 p436c ZK59 p537csZ59 p718c af /59 p939c q d959 p11410c 5d.dE127Ac1 Scilabe136 ID1421c9 1 F MATLABio demo 7“d U 5 MATLAB p 5Z ? ZEb pMATLAB4 U/o demo 75|u 7 m1-1 U3 g3 gP V V4F U = bm1-1 MATLAB U 4MATLAB ! Graphics ! Volume Vlsulization
2、U5| m1-2 U U Run this demo “5| m1-3 U U b V / f UM1 = 7 LC“ U | /3 gb2TMATLABI 0 V1-type B/v 5 clI /V b1c9 3m1-2 MATLAB U |q 1.1 c1ex1.m MATLAB| Q ps51.2 c1ex2.msY MATLAB| Q ? p TZ ZET1.3 c1ex3.msY MATLAB| Q ?9 Hilbert T ZETv1.4 c1ex4.m 7x1 = y;x2 = _y5 V| =sZBsZF V psZ Z dLsZ#ibode45()f V psZF7dde2
3、3() V psZ4Simulink p mb1.5 c1ex5.mL?5K Qlinprog()f V T X p ?551 n5 ?ipslv mex()b41c9 m1-3 MATLAB8 j U 2cMATLAB !9$1 MATLABi tic, A=rand(500); B=inv(A); norm(A*B-eye(500),toc k 4Ti help 7 F H T db pMATLAB( / 5 V A p500500 Iip I S bB “ I Vr1012b tic, A=rand(500); B=inv(A); norm(A*B-eye(500), tocans =1
4、.2333e-012Elapsed time is 1.301000 seconds.2 k| QZ TVr Tf(x) = x5 + 3x4 + 4x3 + 2x2 + 3x + 6i 7x = s1s+1|f(x)9sf b p V5lff 5subs()f |x9sf syms s xf=x5+3*x4+4*x3+2*x2+3*x+6;F=subs(f,x,(s-1)/(s+1)F =(s-1)5/(s+1)5+3*(s-1)4/(s+1)4+4*(s-1)3/(s+1)3+2*(s-1)2/(s+1)2+3*(s-1)/(s+1)+63MATLAB AB A =26641 2 3 44
5、 3 2 12 3 4 13 2 4 13775;B =26641+4j 2+3j 3+2j 4+1j4+1j 3+2j 2+3j 1+4j2+3j 3+2j 4+1j 1+4j3+2j 2+3j 4+1j 1+4j3775- 44 TA(5;6) = 5 7| I T$ p ZE V A=1 2 3 4; 4 3 2 1; 2 3 4 1; 3 2 4 1A =1 2 3 462cMATLAB !9$4 3 2 12 3 4 13 2 4 1A(5,6)=5 7 H (vB - V A(5,6)=5A =1 2 3 4 0 04 3 2 1 0 02 3 4 1 0 03 2 4 1 0 0
6、0 0 0 0 0 5 9 V4 B=1+4i 2+3i 3+2i 4+1i; 4+1i 3+2i 2+3i 1+4i;2+3i 3+2i 4+1i 1+4i; 3+2i 2+3i 4+1i 1+4i;B =1.0000 + 4.0000i 2.0000 + 3.0000i 3.0000 + 2.0000i 4.0000 + 1.0000i4.0000 + 1.0000i 3.0000 + 2.0000i 2.0000 + 3.0000i 1.0000 + 4.0000i2.0000 + 3.0000i 3.0000 + 2.0000i 4.0000 + 1.0000i 1.0000 + 4.
7、0000i3.0000 + 2.0000i 2.0000 + 3.0000i 4.0000 + 1.0000i 1.0000 + 4.0000i4L !X A kMMATLAB 7| 4 | B A =magic(8) 7 3A 7_B/T b p Z Vmagic() 30 9 V4 | A=magic(8), B=A(2:2:end,:)A =64 2 3 61 60 6 7 579 55 54 12 13 51 50 1617 47 46 20 21 43 42 2440 26 27 37 36 30 31 3332 34 35 29 28 38 39 2541 23 22 44 45
8、19 18 4849 15 14 52 53 11 10 568 58 59 5 4 62 63 1B =9 55 54 12 13 51 50 162cMATLAB !9$740 26 27 37 36 30 31 3341 23 22 44 45 19 18 488 58 59 5 4 62 63 15MATLAB LC/ s f y = f(x) =8 Dh=Dx; j x j6 Dh; x y=h*(xD) + h/D*x.*(abs(x) for i=1:length(x)if x(i)D, y(i)=h;elseif abs(x(i) sum(sym(2).1:63)ans =18
9、446744073709551614T19 double ? V UT KV U16r3b L| Z T V i =r 3 V p2001000 V/ b sum(sym(2).1:200)ans =3213876088517980551083924184682325205044405987565585670602750 sum(sym(2).1:1000)ans =2143017214372534641896850098120003621122809623411067214887500776740702102249872244986396757631391716255189345835106
10、2936503742905713846280882cMATLAB !9$719691551493971496078691355496484619708421492101247422837559083643060929499671638825347975351183310878921541258291423929553730843353208596633052487736744113361387507IB MFf mat add() P 8 TA=mat add(A1,A2,A3,)1 pf ? s i E b p VI/ f vararginM V U VM M function A=mat_
11、add(varargin)A=0;for i=1:length(varargin), A=A+varargini; endTX apA U5 V ktry, catchbfunction A=mat_add(varargin)tryA=0;for i=1:length(varargin), A=A+varargini; endcatch, error(lasterr); end81-IBMATLABf P ?1 3BmmHankel i P Tv=h1;h2;hm;hm+1; ;h2m1; H=myhankel(v)b p %“5 VZEKZEHi;j = hi+j1 function H=m
12、yhankel(v)m=(length(v)+1)/2; % _ for i=1:m, for j=1:mH(i,j)=v(i+j-1);end,end I n B( )ai = hi;hi+1; ;hi+m1 V 3Hankel function H=myhankel(v)m=(length(v)+1)/2; % _ for i=1:m, H(i,:)=v(i:i+m-1); end Chankel()f 5function H=myhankel(v)m=(length(v)+1)/2; % _ H=hankel(v(1:m),v(m:end);2cMATLAB !9$99XFibonacc
13、i Tak = ak1+ak2; k = 3;4; V 3 a1 = a2 = 1kI 3 Fibonacci MATLABf 1 pf Ty=fib(k)k ? pkakiy_ I a M _ f ? BZ TINf b pL !fib(n) V pFibonacci n n 35 Vk=fib(n1)+fib(n2) V p n+1 V PB ?7B g1b8 VIM-f bfunction y=fib(n)if round(n)=n else, y=1; endelseerror(n must be positive integer.)end n = 10 V pM fib(10)ans
14、 =55C11 B/B LC LC tic, fib(20), tocans =832040elapsed_time =62.0490 tic, a=1 1; for i=3:30, a(i)=a(i-1)+a(i-2); end, a(30), tocans =832040elapsed_time =0.0100BZ T 1 +Y1“5A1BZ Tb102cMATLAB !9$10 V TB M VM = A+BCBT,i O A, B, CM 5M I V/ E pM1 =A+BCBT1= A1 A1BC1 +BTA1B1BTA1k EMATLAB IBf M p IiYVBl 0 _i
15、p IZE 1 b pIf function Minv=part_inv(A,B,C)Minv=inv(A)-inv(A)*B*inv(inv(C)+B*inv(A)*B)*B*inv(A);L ! M =266451 50 36 1650 77 60 3236 60 87 4816 32 48 683775OX VsA =26641 0 0 00 2 0 00 0 3 00 0 0 43775; B =26641 2 3 42 3 4 03 4 0 04 0 0 03775; C =26644 0 0 00 3 0 00 0 2 00 0 0 13775 0b V M=51 50 36 16
16、; 50 77 60 32; 36 60 87 48; 16 32 48 68;iM=inv(M); % IEiM =0.0553 -0.0389 0.0017 0.0041-0.0389 0.0555 -0.0210 -0.00210.0017 -0.0210 0.0328 -0.01370.0041 -0.0021 -0.0137 0.0244 A=diag(1 2 3 4); B=hankel(1 2 3 4); C=diag(4 3 2 1);iM1=part_inv(A,B,C) %s v pZEiM1 =0.0553 -0.0389 0.0017 0.0041-0.0389 0.0
17、555 -0.0210 -0.00210.0017 -0.0210 0.0328 -0.01370.0041 -0.0021 -0.0137 0.0244H AT = B L= E uYb ZE I / 1 T2cMATLAB !9$11 M1=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, -2652/1
18、93751 796/193751, -416/193751, -2652/193751, 18919/775004 norm(double(iM0)-iM) % pS ans =2.7990e-017 norm(double(iM0)-iM1) %W pS ans =3.6583e-016VnWZE I vy If inv()f PQN 3v.bN V T 5i5 YPWZEFv.b11/ B (xk+1 = 1+yk 1:4x2kyk+1 = 0:3xk p M-f T |x0 = 0,y0 = 0 * h30000Q pBFxy_ xkykUS)B(i1 L)K mb4 U“mHenon
19、Lm | BK : Lmb p T %N5 V m2-1 UHenon Lmb x=0; y=0;for i=1:29999x(i+1)=1+y(i)-1.4*x(i)2;y(i+1)=0.3*x(i);endplot(x,y,.) E lxy B1“S h HW F y V I n5l M x=zeros(1,30000)b12MATLAB A V B kIBlBUS“/ B“ V 4rTb122cMATLAB !9$1.5 1 0.5 0 0.5 1 1.50.40.30.20.100.10.20.30.4m2-1 Henon Lm pL ! I H 5 V m2-2a U Uim (co
20、s ;sin ), (cos( +120);sin( +120), (cos( +240);sin( +240) V wL m2-2b U khl 4 = 2;1;0:14rTb.xy-6(a) Uim1 0.5 0 0.5 110.500.51(b) wLrTm2-2 wL t=0,120,240,0*pi/180; %Mxxx=; yyy=;for i=0:5:360tt=i*pi/180;xxx=xxx; cos(tt+t); yyy=yyy; sin(tt+t);end2cMATLAB !9$13plot(xxx,yyy,r), axis(square)134 a / msin1t t
21、 2 (1;1)b p Ym T4W m2-3a U wL x = 0PAYb t=-1:0.03:1; y=sin(1./t); plot(t,y)4W ZE V m2-3b U wLb t=-1:0.03: -0.25, -0.248:0.001:0.248, 0.25:.03:1; y=sin(1./t); plot(t,y)1 0.5 0 0.5 110.500.51(a)W wL1 0.5 0 0.5 110.500.51(b)W wLm2-31M |/sin(1=t) wL14 a S |sY/ USm = 1:0013 2 = cos(7 =2) = sin( )= = 1cos
22、3(7 ) pUS wLZEepolar( ,) VUSm m2-4 Ubim H t=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)15mZ Ts/ Z Z bx2 +y2 = 3xy2; x3 x2 = y2 y p Z TZf ezplot() Z m2-5a Ub142cM
23、ATLAB !9$2040302106024090270120300150330180 00.51302106024090270120300150330180 00.51302106024090270120300150330180 012302106024090270120300150330180 0m2-4USm ezplot(x2+y2-3*x*y2);hold onezplot(x3-x2=y2-y)V bvZE p m2-5b UbVm V (0:4012;0:8916)(1:5894;0:8185)b k| sY SZb6 4 2 0 2 4 66420246xyx3x2=y2y =
24、 0(a) Z wL1.58941.58941.58941.58941.58941.58941.58940.81850.81850.81850.81850.8185xyx3x2=y2y = 0(b) bv um2-5= ZmE2cMATLAB !9$1516 hsYxysin(xy) mLb p(a)/ 7 Vm m2-6aab Ub x,y=meshgrid(-1:.1:1);surf(x,y,x.*y), figure; contour(x,y,x.*y,30)(b)/ 7 Vm m2-6cad Ub x,y=meshgrid(-pi:.1:pi);surf(x,y,sin(x.*y),
25、figure; contour(x,y,sin(x.*y),30)10110110.500.51(a) xy m1 0.5 0 0.5 110.500.51(b) xyL50550510.500.51(c) sin(xy) m3 2 1 0 1 2 33210123(d) sin(xy)Lm2-6 mL17m f TNaN5Ms k ? pz = sinxyV mig M/x2 +y2 6 0:52sb p/ 7 V uf sx2 +y2 6 0:52 uUS| f !NaNK m2-7 U w b162cMATLAB !9$ x,y=meshgrid(-1:.1:1); z=sin(x.*y
26、);ii=find(x.2+y.2 syms x; f=(3x+9x)(1/x); limit(f,x,inf)ans =9 syms x; f=(x+2)(x+2)*(x+3)(x+3)/(x+5)(2*x+5);limit(f,x,inf)ans =exp(-5)2 k p/ Kblimx!1y!2x2y +xy3(x+y)3limx!0y!0xypxy +11limx!0y!01cosx2 +y2x2 +y2ex2+y2b pK5 V/ pb syms x yfa=(x2*y+x*y3)/(x+y)3; limit(limit(fa,x,-1),y,2)ans =-6 fb=x*y/(s
27、qrt(x*y+1)-1); limit(limit(fb,x,0),y,0)ans =2 fc=(1-cos(x2+y2)*exp(x2+y2)/(x2+y2);limit(limit(fc,x,0),y,0)ans =03 p/ f by(x) =qxsinxp1exy = 1pcosaxx(1cospax)atanyx = ln(x2 +y2)y(x) = 1na ln xn +axn ; n 0183cs59 p p pf diff() V /T f #1 f p T b syms x;f=sqrt(x*sin(x)*sqrt(1-exp(x); simple(diff(f)ans =
28、1/2/(x*sin(x)*(1-exp(x)(1/2)(1/2)*(sin(x)*(1-exp(x)(1/2)+x*cos(x)*(1-exp(x)(1/2)-1/2*x*sin(x)/(1-exp(x)(1/2)*exp(x) syms a xy=(1-sqrt(cos(a*x)/(x*(1-cos(sqrt(a*x)simple(diff(y)ans =1/2/cos(a*x)(1/2)*sin(a*x)*a/x/(1-cos(a*x)(1/2)-(1-cos(a*x)(1/2)/x2/(1-cos(a*x)(1/2)-1/2*(1-cos(a*x)(1/2)/x/(1-cos(a*x)
29、(1/2)2*sin(a*x)(1/2)/(a*x)(1/2)*a f=atan(y/x)-log(x2+y2);f1=simple(-diff(f,x)/diff(f,y)f1 =(y+2*x)/(x-2*y) syms n positive; syms a; f=-log(xn+a)/xn)/(n*a); diff(f,x)ans =-(n/x-(xn+a)/(xn)*n/x)/(xn+a)*xn/n/aLATEXV U T51=2sin(x)p1ex +xcos(x)p1ex 1=2 xsin(x)exp1ex 1qxsin(x)p1ex1=2 sin(ax)apcos(ax)x(1co
30、s(pax) 1pcos(ax)x2 (1cos(pax) 1=21pcos(ax)sin(pax)ax(1cos(pax)2paxy +2xx2ynx (xn +a)nxnxxn (xn +a)1 n1a14 k py(t) =s(x1)(x2)(x3)(x4)f 4 b p V/ syms a xf=sqrt(x-1)*(x-2)/(x-3)/(x-4); simple(diff(f,x,4)ans =3cs59 p193*(16*x11-392*x10+4312*x9-28140*x8+121344*x7-364560*x6+783552*x5-1214604*x4+1342560*x3
31、-1015348*x2+474596*x-103741)/(x-1)*(x-2)/(x-3)/(x-4)(7/2)/(x-3)8/(x-4)8316x11392x10+4312x928140x8+121344x7364560x6+783552x51214604x4+1342560x31015348x2+474596x103741(x1)(x2)(x3)(x4)7=2(x3)8 (x4)85 ps0s ( H01 Hs TK H V PLHopitalE5s0s sY p 1 kE5limx!0 ln(1+x)ln(1x)ln(1x2)x4i pKTM1 b pVs A X Px = 0)05 p4 “s0 p4 |x = 0 T“ V PLHopitalE5 pK b syms x; n=log(1+x)*log(1-x)-log(1-x2); d=x4;n4=diff(n,x,4); d4=diff(d,x,4); n4=subs(n4,x,0);L=n4/d4L =1/12C pK V T b limit(
