matlab在高数中的应用

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2012/1/1

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1MATLABᐭ..........................................................41.1MATLABᭆ..........................................................41.2MATLABḄᵨ............................................................51.3ᑁ..............................................................181.4..............................................................182MATLAB...........................................................212.1!"#$Ḅ%&'(ᑴ..................................................212.2*+,-..............................................................232.3*+./0ᦪ..........................................................242.4*+᩽ᙶ᪗..............................................................262.54+,-................................................................272.656,☢................................................................282.74+Ḅ8ᣩ:ᑴ..........................................................302.8;<ᑴ...................................................................302.9ᑖ>?@................................................................322.10ᑁ.............................................................362.11.............................................................363MATLABABCD......................................................413.1MᦻEḄᵨ..............................................................41

23.2ᑁ..............................................................453.3..............................................................454FGᑖḄHIJK........................................................484.1᩽▲......................................................................484.2MᦪNᐸPᵨ..............................................................574.3QAḄᦪRSTQU........................................................624.4VWGᑖ...................................................................654.5WGᑖ.....................................................................674.6*XGᑖ...................................................................744.7YZ[ᦪ...................................................................754.8\FᑖQAḄST..........................................................844.9ᑁ..............................................................884.10].............................................................905-ឋ_ᦪḄHIJK.....................................................995.1`ᑡb.....................................................................995.2c▣NᐸJK.............................................................1055.3c▣Ḅefgᣚ...........................................................1075.4ᔣjkḄ-ឋlᐵឋ.......................................................1145.5lnc▣N*op.........................................................1155.6ᑁN.......................................................119

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39266ᡂᦪzux'ylnxḄs⊤஺(1)ᙠMatLabghijb¶ᓫFi1e—>New->M-fiBLe,ᡭ¢Mᦻ¤¸¹ijIᐭ@A᝞(Bx=-3:0.1:3;[X,Y]=meshgrid(x);z=X.A2+Y.A2.*sin(X);mesh(z);M=moviein(30);axismanualforj=1:30mesh(cos(4*pi*j/30)*z,z)M(:,j)=getframe;endmovie(M,25)(2)ᙠMᦻ¤¸¹ijbFile—>Save,ᙠº»¼½(¾¿ᦻ¤ÀÁdh.m(3)ᙠMatLabghijbIᐭ»dh%ᙠFijs¥27277(1)ᙠMatLabghijbIᐭ>>z=0:0.1:100;>>x=sin(z);>>y=z.*2+exp(z);(2)ᙠMatLabghijbIᐭ

40>>comet3(x,y,z)%ᙠFijs஺¥28Â3ÃMatLab@AÄÅÆÃÇÈḄÉ⌕ËḄB3.ÌÍÎÏMatLab@AÄÅḄÐAஹᑖÑÒÓÔ᪀04.ÌÍÎÏÖÆMᦻ¤×ØÙᦪḄÄÅÚᵨ03.1Mᦻ¤ḄÚᵨ3.1.1Mᦻ¤ḄÛÜÝÞ1ßMatLab2¶ᓫFile-New-M-file,àᐭᦻ¤¸¹ij3ᙠᦻ¤¸¹ijIᐭMᦻ¤ᑁq4mÁ᡽âÀ¾¿ãäᦪᦻ¤Ḅᦻ¤ÀeØᦪÀe᪵஺5ᙠghijbIᐭÖÆᦻ¤ÀᓽÛÜÖÆMᦻ¤ᦪᦻ¤ḄÚᵨᑁçᦪḄÚᵨèée᪵஺3.1.2êëêëÀìíî¢ᜮᵫíîஹᦪí(ᑜñᡂᨬC31|íóᑖᜧõᑏíî஺ãBêë◤⌕øùúûḄüýþÿ
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42ᩩᙽBC2elseᩩᙽBC3end3ᵨforz{ᢣᩭº¬Fibonaccᦪ\¯ᜧ°10000Ḅᐗ¤஺ᦻexample3.mn=100;a=ones(l,n);fori=3:na(i)=a(i-l)+a(i-2);ifa(i)>=10000a(i),break;end;endjᙠᐭexample3,;gV`ans=10946i=212switch-caseV᪀switch⊤JEcase⊤JE1BCᙽ1case⊤JE2BCᙽ2otherwiseBCᙽnend4¼½Ḅᡂ¿Àᳮᦻexample4.mmark=86(n=fix(mark/10)(switchncase10Rank—¥ᑖcase9Rank='ÁÂcase8Rank='ÃÄcase6,7Rank='ÅÆotherwiseRank±.ÅÆ'End

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45»plot(0,funl(O),'*',1,fun1(11.5,funl(1.5),'*')>>fplot(fun,1,2])%1ᵫ12ᔜ%Ḅឋឋ}ᙠ=1.5ᜐ____________________ᙠx=0ᜐ____________________ᙠx=lᜐ____________________2(1)ᙠMatLabopqrs%tuᓫFile->New>M-file,ᡭxMᦻS?᝞|}functionz=fun2(x)z=x(l).3x(2).3+3*x(l).2+3*x(2).29*x(l);end(2)ᙠMᦻSSave,ᙠ~|ᦻSVfun2.m(3)ᙠMatLabopqrsMᐭ᝞|ᢣp}»fun2([l,0])f(l,0)=,»fun2([l,2])f(l,2)=,»fun2([-3,0])f(-3,0)=,»fun2([-3,2])f(-3,2)=,»holdoff»clf»x=-4:0.1:2;»y=-l0.13»[X,Y]=meshgrid(x,y);»Z=X.A3-Y.A3+3*X.A2+3*Y.A2-9*X;»mesh(X,Y,Z)%2»holdon00-1

462»plot3(1,0,fun2([1,0])b**)ᙠ#qrᵨ_ᐹ12%(1,0)ᜐ&᩽'Ḅ5»plot3(1,2,fun2([1,2])r*')ᙠ#qrᵨ_ᐹ12%(1,2)ᜐ&᩽'Ḅ5,ᙠ#qrᵨ_ᐹ12%(-3,0)ᜐ&᩽'Ḅ5,>>plot3(3,2,fun2([3,2]),'y*')ᙠ#qrᵨ_ᐹ12%(32)ᜐ&᩽'Ḅ5,3(1)ᙠMatLabopqrs%tuᓫFile—>New->Mfile,ᡭxMᦻS?᝞|}data(l,:)=l:8;data(2,:)=[8.2510.36.6812.0316.8517.519.310.65];data(3,:)=[15.0016.259.918.2520.8024.1515.5018.25];data(4,:)=data(3,:)-data(2,:);fori=l:7w=data(4,i);k=i;flag=0;forj=i+l:8ifwSave,ᙠ~|ᦻSVfun3.m(3)ᙠopqrMᐭ»fun3%FGᢥᑭC᣸?M᣸?ḄFG?N}41

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ᜧ)X—>aF(x)012xiaF(X)F(x)4.1.4ᨵᐵᦪ᩽▲78ḄMatLab9:(l)limit(F,x,a)᡻<=>?ᦪFᙠ@ABCxaḄ᩽▲(2)limit(F,a)᡻<=>?ᦪFᙠ@ABCfindsym(F)aḄ᩽▲(3)limit(F)᡻<=>?ᦪFᙠ@ABCfindsym(F)0Ḅ᩽▲(4)limit(F,x,aleff)᡻<=>?ᦪFᙠ@ABCxaḄD᩽▲(5)limit(F,x,a,,right,)᡻<=>?ᦪFᙠ@ABCxaḄE᩽▲F:Hᵨ9:limitJ⌕ᵨsymsLMN@ABCOP.R7STᑡ᩽▲

55x2(l)limC0SX72x->0%4ᙠMatLabḄ9:]^_ᐭ:symsxlimit((cos(x)-exp(-xA2/2))/xA4,x,0)a0x4x->0x-0x2x2x22-cosx+l+e2-i-e2x1+(F)I--1lim=lim—------2------Le2x->0xf0ফ212122242)2A1—+o(x4\-)+---1---+o(x4))cosx-e224!22{2lim=limx70x4x->014-----X=lim12x->0x412(2)lim(l+—)3x%BC
ᜧ,ᦪtXT8XᙠMatLabḄ9:]^_ᐭ:symsxtlimit((l+2*t/x)(3*x),x,inf)a00XX->00X(3)limSE᩽▲x->0+xᙠMatLabḄ9:]^_ᐭsymsxlimit(l/x,x,0,9right*)a

564.2ᦪᐸNᵨ4.2.1ᦪᦪឋ(1)ᦪ/(x)ᙠx=aᜐḄᦪ/ভt)dx_XT஺x-axa(2)ᦪḄᦪ/(x)ᙠx=“ᜐᑣᦪᙠx=aᜐᑗᙠ/'(a)¡kᑗḄ¢᳛.R8ᦪy=x2ᙠ(1,1)ᜐḄᑗ{¥.y=2x-l,᝞12ᡠ¨.(3)ᦪ/(x)ᙠx="ᜐ«¬¡ᦪ᜜ᙠx=aᜐḄ⌕ᩩ°.R9ᦪy=|x|ᙠx=0ᜐ«¬²ᙠx=0ᜐ³.᝞13ᡠ¨.12´ᡂ12,13Ḅ¥¶.:elfsubplot(1,2,1)holdonfplot(fx.A2',[0,2])fplot(r2.*x-l\[0,2])pk)t(l,l,'*')subplot(1,2,2)holdonfplot(*abs(x)\[-l,l])

57T☢Ḅ¥¶Ä¨ᦪ)=/ᙠ(],])ᜐḄᑗy=2l-1Ḅ´ᡂÅ¥஺symsxholdonfplotCx.*x[0,2];k')fori=l:9xl=2-0.1*i;yl=xl*xl;y=l+(y1-1)/(X1-1)*(X-1)pauseezplot(y,[0.8,2])endfplot(2*xl',[0.8,2],T)(3)ᦪḄNᵨ:ᦪ஻x)ᙠ(ᑁt▤▤ᑣᙠ(ᑁT☢beÈÉf(x)>0=/(x)ᓫË⌴Í;f(x)<0of(x)ᓫË⌴ÎÏf'(x)>0<=>f(x)¡ÐᦪÏf'(x)<0of(x)¡ÑᦪÏ/(x)ᙠx=aᜐÒᑮ᩽ÔᑣF(x)=04.2.2ᦪᦪ78Ḅ⌕be(1)(x"y=axa~[,(sinx)'=cosx,(cosx)'=-sinx,(tanx)'=sec2x,(cotx)*=-esc2x,(ax\=ax

58a,(e")'=ex,(log^x)'=—!—,(lnx)'=-x

59axফ᝞cᦪu=u(x)v=v(x)ᙠ"Xᐹᨵᦪ01Ö×ḄØஹÚஹÛஹᖪ(◀ᑖß.Ḅ"᜜)ᙠ"Xᐹᨵᦪ(w(x)±y(x))'=/(X)±/(x);[w(x)v(x)]r=u(x)v(x)+u(x)vXx)l/(X)V(X)-H(X)vV)ZX,-----=-------------------------v(x)WUn.v2(x)(3)஻=c(x)ᙠ"xy=f(n)ᙠMNḄ"w=*(x),ᑣàᔠᦪy=f((p(x))ᙠ"Xᜐ~~—f'(—)dx4.2.3ᨵᐵᦪᦪ78ḄMatLab9:(l)diff(F,x)⊤¨⊤jFã@ABCxSt▤ᦪᐕå⊤jFæᨵᐸç@ABCxèḕᑣ⊤¨ãᵫ9:symsḄBCSt▤ᦪ஺(2)diff(F,x,n)⊤¨⊤jFã@ABCxSn▤ᦪ஺R10STᑡᦪḄᦪ

60(1)ëìy=xarcsin>+^4Sy',yব;ᙠMatLabḄ9:]^_ᐭ᝞T9:¶ᑡsymsxy=x*asin(x/2)+sqrt(4-xA2)diff(y,x)%᡻

61dl=diff(y,x)%,-▤(ᦪd2=diff(dl,x)%,/▤(ᦪelfsubplot(1,1,1)holdongridonezplot(y,[-22])gtext('f(x),)ezplot(dl,[-2,2])gtext('f'(x)')ezplot(d2,[-2,2])gtext('f"(x)')title஺(ᦪḄᵨ)gtext('o')gtext('(xl,yl)')gtext('o')gtext('(x2,y2)')gtext('o')gtext('(x3,y3)')fl=char(dl)xi=fzero(fl,0)%,•,▤(ᦪᙠx=0▬3Ḅ4x2=fzero(fl,l)%,•▤(ᦪᙠx=l▬3Ḅ45146514789:ᙢ<ᑮ&>᝞?*2/2@᩽AḄ-▤(ᦪ@4>ᡭ,C?@AḄ/▤(ᦪ@4ᙠᓫDᓣ8,X1UX2+8ᦪḄ-▤(ᦪᜧG4ᙠᓫ#H>@/2ᦪḄ-▤(ᦪJG4ᙠ᩽ᜧ,1ᜐ/▤(ᦪJG4ᙠ᩽J>,L?ᜐ/▤(ᦪᜧG4ᙠ-8,X3ᦪḄ/▤(ᦪ

62JG4ᙠ(x3,+oo)ᦪḄ/▤(ᦪᜧG4஺4.2.4᩽⚪MatLabNOPQR,-ᐗTᐗᦪ᩽U⚪Ḅ&fmin(f,xl,x2),ᦪf(x)ᙠxl

631)ᡭjMatLabNOᓫpqᓫfile,new,m-file,yᐭMᦻO{|஺2)ᙠ{|ᐭfunctiony=fl(x)y=(x(1)*x(1)-4*x(2))A2+120*(1-2*x(2))A2;3)ᓫpqᓫfile,save@fl.m4)ᑮMatLabᐭdl=fmins('fr,-2,2)ᦪḄ᩽J஺᡻]^_&<11=-1.41420.5000ᐭfl(dl)᩽J஺᡻]^_&ans=9.7459e-0094.3Ḅᦪ,1MatLab,3¡Ḅ¢&fzero(tf,,x)%ᙠx=x0▬3,f(x)=0Ḅ3¡஺02{ᑏ$,Ḅ3¡8ᑖ¥gᩭ§&¨-g¢©ª᪷Ḅᜧ¬®஺ᐜ°±©ᙢ²y=f(x)Ḅ5³ᯠµ65Dª
¶x·¸Ḅᜧᭆº»஺ᵫGZ5½ᦪḄ¾¿ÀÁ§ÂÃ᪷ḄıÅḄ3¡Æ-ÇÈ8©ª᪷Ḅ◞Ê஺¨/g¢᪷Ḅ◞ÊḄËZ@᪷ḄÌÍ3¡⌲gᦋᗐ᪷Ḅ3¡Ḅ±©ÅÑÒ,ÂÓÔ±©Å⌕,Ḅ3¡஺ÖᵨḄᨵ/ᑖᑗ஺(1)/ᑖÙf(x)ᙠa,bDÚÛf(a)f(b)<0,Üf(x)=0ᙠ(a,b)ᑁÞᨵ-ßà᪷c,G¢a,bᓽ¢Àß᪷Ḅ-ß◞ÊW7X|=g2,/(/),åfl)=0,æçC=X,å—¶/(«)ëìæçWa1=X,í=5,å/(î)¶f(b)ëìæçWaj=a,Z?j=x,,òóôCWXö8,Â÷Üø--a)ভ÷Z@úḄ◞ÊûüDý§ôCHX2=g(4+÷)ö8,Âa2

64Ḅᑗ1ᩭ`a\1]bcdMNS᪷Ḅ#$%஺᝞ᙠeᙶ᪗h/”(x)iLḄ&V^(^j(X()"(X())))ᑗ1mᑗ1hXnḄoḄpᙶ᪗ᵫqrstu#MNḄ᪷C஺y=f(x)Ḅxyzᨵ{|}~`xn=xn-\-F-----r,஻=1,2,…ᐸX஺Ḅ%ᑖ|}~᝞x16(a)<(a)<0,/<)>0,(b)/(«)>0,/(&)<0,/,(x)>0,/"U)<0,/=a,?ᑖ2MNf=0Ḅ#$ḄᦪerffK᝞{functiony=erff(f,a,b,wch)%ᐸfULᦪa,bU◞X78Ḅ^%wchU⌕Ḅ)*ᦪ#$`ᦪ஺x=a;fa=eval(f);

65x=(a+b)/2;fx=eval(f);n=0;while(b-a)>wchn=n+l;if(fx*fa>0)a=x;elseb=x;endx=a;fa=eval(f);x=(a+b)/2;fx=eval(f)¢endy(l)=a;y(2)=n;ᑗ12MNf=0Ḅ#$ḄᦪqxfK᝞{functiony=qxf(f,a,b,wch)%fULᦪa,bU◞X78Ḅ^%wchU⌕£Ḅ)*ᦪ#$`ᦪ஺dlf=diff(f);d2f=diff(f);x=(a+b)/2;fl=eval(dlf);f2=eval(d2f);n=l;iffl*f2>0z(l)=b;elsez(l)=a;endx=z(n);z(n+1)=z(n)-eval(f)/eval(d1f);whileabs(z(n+l)-z(n))>wchn=n+l;x=z(n);z(n+1)=z(n)-eval(f)/eval(dIf)¢endy(l)=z(n+l);y(2)=n;¤14ᵨMatLabᦪஹ¦N?ᑖ2ஹᑗ12§}M2MN/+1.52+0.9x-1.4=0Ḅ

66S᪷Ḅ#$%©)*ª«¬10-3஺®/(x)=A3+1.lx2+0.9x-1.4,^^f(x)ᙠ(-co,+oo)ᑁ±²஺³/")=3”+2.2x+0.9>0,ᦑf(x)ᙠ(-8,+8)ᑁᓫ¸⌴º/(X)=()»¼ᨵRVS᪷஺ᵫ/(0)=-1.4<0,/(1)=1.6>0,/(x)=0ᙠ[0,1]ᑁᨵQḄS᪷஺a=0,b=l,[0,l]ᓽURV◞X78oᐜÁdᦪf(x)Ḅxy᝞x17,ᙠMatLabḄÅ®ÆÇÈᐭ᝞{Å®f='xA3+l.l*xA2+0.9*x-1.4'fplot(f,[0,l])gridonM21ᙠMatLabḄÅ®ÆÇÈᐭ᝞{Å®:f='xA3+l.l*xA2+0.9*x-1.4'fzero(f,l)ÒÓÔans=0.6707M22?ᑖ2MNḄ#$ᙠMatLabḄÅ®ÆÇÈᐭ᝞{Å®f=,xA3+l.l*xA2+0.9*x-1.4a=0;b=l;wch=0.0001;erff(f,a,b,wch)ÒÓÔans=0.670714.0000?ᑖ2`14#$0.6707oM23ᑗ12MNḄ#$ᙠMatLabḄÅ®ÆÇÈᐭ᝞{Å®f=,xA3+l.l*xA2+0.9*x-1.4a=0;b=l;wch=0.0001;qxf(f,a,b,wch)ÒÓÔans=0.67074.0000ᑗ12×Øᐳ`4#$0.6707஺rÚÔᑗ12ḄᦈÜÝÞß஺4.4ªKàᑖ4.4.1ᑖឋ

67(1)ᙠ78I<ᦪf(x)Ḅâᨵãäåᦪ⚗Ḅçᦪèf(x)ᙠ78I<ḄªKàᑖjJ/(x)dx(2)êëàᑖ⊤^kdx=kx+CíUåᦪ)rxa+l\xadx----+C(a-1)J■—dx=arctanx+Cdx=arcsinx+CJcosxdx=sinx+CJsinxdx=-cosx+Cdx=tanx+Cdx=-cotx+CJsecxtanxdx=secx+Cescxcotxdx=-escx+Cydx?/+C\axdx=—^CJIna(3)3ᦪf(x)Fg(x)ḄçᦪïᙠᑣJ"(x)+g(x)]dx=j/(x)dx+Jg(x)dx(4)3ᦪf(x)Ḅçᦪïᙠᑣj\f(x)dx=k(5)(õRöᣚᐗ2)3ᦪf(u)Ḅçᦪïᙠu=°(x)Aᑣᨵᣚᐗ]7[஺(᜜/(᜜=[J/(஻)ᵲ஻=ü)(6)(õ?öᣚᐗ2)3x=°Q)Uᓫ¸ḄஹAᦪ9()þ0ÿᐹᨵᦪᑣᨵᣚᐗ

68(7)(ᑖᑖ)|i/v*dx=uv-Jw*vdx4.4.2ᨵᐵᦪᑖḄMatLab!"int(f)#ᦪfᐵ%syms)Ḅ*+,-Ḅᑖ;int(f,v)#ᦪfᐵ%,-vḄᑖ஺01MatLabᙠᑖ89:;<=>ᑖ?ᦪC@15ᵨMatLabBCDᑡᑖᙠMatLabḄ!"FGHᐭ᝞D!"1symsxint('xA3:{Jexp(-xA2),,x)᡻<891ans=-l/2*xA2/exp(-xA2)-l/2/exp(-xA2)ᳮ[\]1•ᑖᑖ1ue~lidu)=-(-ue~u+~udu)=-(-«rH-e-H)+c=-(-A-x2-rx2)+cᙠMatLabḄ!"FGHᐭ᝞D!":symsxy=[sin(x),xA3;x*exp(x),tan(x)Jint(y)᡻<891ans=[-cos(x),1/4*XA4][x*exp(x)-exp(x),-log(cos(x))J4.5ᑖ4.5.1ᑖ)gឋiᑖ)1ᦪ/(X)ᙠkl&ᑗoᨵ)pqᵨᑖrQ=X஺

694=max{AXj}f0oḄ᩽▲ᙠᑣᦪ/(x)ᙠklGᔣol0,ᑣ^f(x)dx>o(5)(ᑖ:ᳮ)᝞9ᦪ“X)ᙠklx©oᑣᙠ¨a,ᑗᑁÇÈᙠÉrJÊDᡂË1¨f(x)dx=f^b-a),^>a,b,.ÌwᳮᨵÍÎḄª«q)1ϳÐḄ³ÐÑÒÓᙠ•wÔÕÔ¨“oÉr4ḄÖᙶ᪗/(ÙÚḄÛÒᐸ☢ÝÞ%³ÐÑÒḄ☢.᝞¬19ᡠ|.

70(6)ÏkloḄᑖ1/(x)ᙠoᑣᨵ/(᜜᜻ᦪᑣä/஺)=0¡La/(X)Ꮤᦪᑣ£fWx=2/f(x)dx.ᑖḄæ(1)çèߟêëì₈᝞9ᦪî(x)ïᦪᙠkl©oḄÉwᦪᑣj/(x)dx=Fg)-F(a)(2)ᑖᣚᐗᎷ(a)ᦪ/(x)ᙠkl¨%ᑗo¡(b)ᦪx=°óᙠkl¨a,0oᨵ¤,+Ḅ]ᦪ¡(c)tᙠ¨a,᜛,ᓄ,x=e(t)Ḅᙠ¨a,o,ᓄ,¤s(a)=”,஺(᜛)=/?,jf(x)dx=ᑣᨵ(3)ᑖḄᑖᑖᦪ“(X)Ùv(x)ᙳᙠkl3,6oᨵḄ]ᦪᑣudv=(MV)vdu4.5.2ᨵᐵ!"#ᦪᑖḄMatLab$%int(f,a,b)#ᦪfᐵ%syms)Ḅ*+,-ùaᑮbḄᑖ¡int(f,v,a,b)#ᦪfᐵ%,-vùaᑮbḄᑖ஺@16ᑭᵨMatLabBCüýjJ1-x2þÿ
ᑖᳮḄ"-Ji-x2dx=-^1-^2oᙠMatLabḄᐭ᝞ᑡsymsxy=sqrt(l-xA2);zhi=int(y,O,l)%34(Jl_x2dx=,z=y-zhi;zf=char(z);fzero(zf,0.5)%?@AfAT-x2dx=Jl-┐ḄJBCDEans=0.6190

71I17ᵨMatLabKL?ᑡ
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74v2ᦪ
ᑖvYxᑖᦪÐ10,100,500஺ᙠMᦻLàòᐭ«ó]ᦪYᑖôõöÐzjx.m,djx.m,rjx.m,txf.m,smp.mᙠMatLabḄᐭformatlongdigits(20)symsxy=sin(x)/x;zjx(y,0,l,10)zjx(y,0,l,100)zjx(y,0,1,500)rjx(y,0,l,10)rjx(y,0,l,100)rjx(y,0,1,500)djx(y,0,l,10)djx(y0,U00);djx(y,0J,500)smp(y,0,l,10)smp(y,0,1,100)smp(y,0,l,500)÷øDE᝞n10100500³v0.953758522626510.946873205701690.94624149899281v0.946208578843150.946084325238830.94608312056197µv0.937905621107300.945287915549770.94592444096243v0.945832071866910.946080560625730.94608296997762`av0.946083076517730.946083070367800.94608307036718ùú«óDEYÕûnᜧYý
ᑖḄÁÂ1=0.9460831ùú,`aᦈÿḄ
ᨬ஺3ᦪ,ᑖᵨ5▤,10▤,20▤.ᙠMatLabḄ!"#$ᐭ&ty=taylor(sin(x)/x,0,5);int(ty,O,l)ty=taylor(sin(x)/x,0,10);int(ty,O,l)ty=taylor(sin(x)/x,0,20);int(ty,O,l)'()*᝞,&n51020ᦪ0.946II11II11I1I0.946083072632350.94608307036718-./)*0123ᑮ10▤Ḅ)*567.

754.69:;ᑖ<=,MatLab>?ᨵA9:;ᑖḄ!ᡃCᵨD;ᑖḄint!)ᔠᦪFGḄ23HᡂJ9:;ᑖḄ.K19NOPஹᐸSDTUVW=2ᑮX=ZX=12-[\ᡂ]^.ᐹ`ab᝞,&(1)ᑜD;ᑖ]^&yl=2*x;y2=x/2;y3=12-x;ezplot(yl,[-2,12])holdonezplot(y2,[-2,12])ezplot(y3,[-2,12])title஺;ᑖ]^))*᝞F20eᩩUVghᡠ\]^ᓽT;ᑖ]^.(2)kDhlḄmᙶ᪗&xa=fzero('2*x-x/2\0)xb=fzero(*2*x-l2+x\4)xc=fzero(,l2-x-x/2',8))*T&xa=0xb=4xc=8বᓄ&:rᑖTst;ᑖ[dxgNdy+fdxguvᙠMatLabḄ!"#$ᐭ&symsxyzz=xA2/yA2;dx1=int(z,y,x/2,2*x);jl=int(dx1,0,4);dx2=int(z,y,x/2,12-x);j2=int(dx2,4,8);

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84qä஺®%=0?3'ᦪ/5)=/(0)+7(0å+½*+ߟ+*/+--.(-/?⚗*'@ᙠBᦪCDEFGHIJ'ᡠLMHᵨN᪵Ḅ>⚗*ᩭQ-⊤S

85/ᩖḄ#ᦪ.N᪵UVḄWXYLᵨZ⚗ᩭ[D.\24]#ᦪy=sinxḄ5^▤ᦪḄ`ab᪍$*'defgh5^▤ᦪ$*i#ᦪḄQ-jk'DEsinlḄQ-C.8symsxsin3sin5sin7sin9sin3=taylor(sin(x),3);sin5=taylor(sin(x),5);sin7=taylor(sin(x),7);sin9=taylor(sin(x),9)%sin9=x-l/6*xA3+l/120*xA5-l/5040*xA7elfholdonezplot(sin(x))gtext('sinx')ezplot(sin3)gtext('3▤')ezplot(sin5)gtext('5▤')ezplot(sin7)gtext('7▤')ezplot(sin9)gtext('9▤')title(*y=sinxnᐸop$*qr)sin(pi/8)x=pi/8;zhi3=eval(sin3)zhi5=eval(sin5zhi7=eval(sin7)zhi9=eval(sin9)

86f21sin-ḄstC0382683432365098n3579sin(x)0.392699081698720.382605892675190.382683717505510.38268343175391ᵫf);ᦪvYw▤ᦪxyQ-zkxy.\25DEeḄQ-C'ztᑮ{eḄC|<᮱Ḅ$%*ᙠx=lᜐḄ#ᦪC'ᓽe=>—=1+1+—+•••+—+•••«1+1+——+…-F——£“2!஻2!ᐸWXR\-----------1---------------1-…H-----------------F…11(஻+1)!(஻+2)!(஻+111(஻+1)!(n+l)!(n+l)(n+1)!(n+1/-11F,111'=---------1H--------1---------------1--------------p(n+l)![n+l("+1)2(n+1)J111+-±nln⌕ztᑮ1()T°—ᓽ஻>10ᵫ1313>1஺1°,ᦑ஻=13,nlne«l+—+••■+—»2.7182818285.2!13!ᵨMatLab#ᦪedejs.mᦻ,wch⊤WX.functionzhi=edejs(wch)symsxsn=5;s=taylor(exp(x),n);x=l;zhil=eval(s);n=n+l;

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88᝞»¼⚗Ḅ;e8ln2ḄQ-C'ᐸWX½=2¾"+ÀÁ++,*+",)(|"Id)Ã2i11144-4=--------==--------<—x10<1i0n.3"1-14-39787322<ᨵ,Inc2a2C(/1—I--1--1--+J__L_LJ_«0.6931.33335¥7?-ᵨMatLab#ᦪln2jsl.mᦻ4ÅI1iln2BQ-'#ᦪIn2js2.mᦻ4ÅI2iln2BQ-,n⊤op$%▤ᦪ'functionzhi=ln2jsl(n)symsxstt=log(l+x);s=taylor(t,n);x=l;zhi=eval(s);functionzhi=ln2js2(n)symsxstt=log((l+x)/(l-x));s=taylor(t,n);x=l/3;zhi=eval(s);ᙠMatLabᐭformatlongln2jsl(5)ln2jsl(10)ln2jsl(50)ln2jsl(1000)logফIn2js2(5)ln2js2(10)ln2js2(50)᡻Ç©᝞È:ln2ḄstC8069314718055995I5105010000I10.583333333333330.745634920634920.703247160575920.69319718305996I20.691358024691360.693146047390830.69314718055995

89ghL+ᦪvw:I2ᦈ¨ÊkÇI1ª>'7ËᙠQ-DE!ាÍᙢ⌱Q-Ð*'ᦈ¨Ḅ^F'ÑÒᦈ¨ḄÊk.4.8HÓᑖIjḄ]{4.8.1ÔᭆÖ®×ᙢ'Ø⊤ÙÚw#ᦪஹÚw#ᦪḄÛᦪÜÝÞ¡ßàḄᐵâᑮḄIj'ãÓᑖIj•Úw#ᦪ<®ᐗ#ᦪḄIjãHÓᑖIjæÚw#ᦪ<>ᐗ#ᦪḄIj'nqèÓᑖIj஺ÔéêëìHÓᑖIj஺ÓᑖIjᡠ¸ÅḄ]w#ᦪḄᨬy▤ÛᦪḄ▤ᦪ'ãÓᑖIjḄ▤஺®×ᙢ'஻▤ÓᑖIjḄ)*<ᐸU<=஻+2Þ¡Ḅ#ᦪ஺᝞ÓᑖIjḄ{²ᨵîÒHᦪ'ïîÒHᦪḄ=ᦪÜÓᑖIjḄ▤ᦪ°^'N᪵Ḅ{ãÓᑖIjḄð{஺tñ2ð{ḄîÒHᦪL'|ᑮ2ÓᑖIjḄᱯ{.4.8.2HÓᑖIjḄ{(1)YᑖóÞ¡ḄÓᑖIj.®×ᙢ'᝞®=®▤ÓᑖIjôᑏᡂg(y)dy=f(x)dxḄ)*'|<ö'ô÷ÓᑖIjᑏᡂ®øê²yḄ#ᦪ;ú'û®øê²xḄ#ᦪ;dx,üýþIj|ÿ
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:D⊤Ḅ,Dy⊤y•▤ᦪDny⊤n▤ᦪ.dsolve(ldiff_equation')%diff_equation)*Ḅ+,ᑖ./t,0.Ḅ1*dsolve(1diff_equation,,,var,)%diff_equation)*Ḅ+,ᑖ./vardsolve(idiff_equation,,,condl,cond2,var')%678ᩩ:Ḅ+,ᑖ.

93;27*+,ᑖ.y”+y=xcos2xsymsxdiff_equ='D2y+y=x*cos(2*x)';y=dsolve(diff_equ,*x')*0DEFy=(l/2*cos(x)+l/2*x*sin(x)+l/18*cos(3*x)+l/6*x*sin(3*x))*sin(x)+(-l/18*sin(3*x)+l/6*x*cos(3*x)+1/2*sin(x)-1/2*x*cos(x))*cos(x)+C1*sin(x)+C2*cos(x);28+,ᑖ.y"'-y"=xNOyপ=8,),প=7,)”প=4Ḅᱯ*.symsxdiff_equ='D3y-D2y=x';y=dsolve(diff_equ,^(1)=8\'Dy(l)=7\,D2y(l)=4,,,x,)*0DEFy=-l/2*xA2-l/6*xA34-l/6+5/2*x+6/exp(1)*exp(x)4.9XYZ[ᑁ]\YITT1ᵨ_`aᑡcᦪᑡdXCOSghij1⚗ᑮj1000⚗noᦪᑡḄ᩽▲rn2£=0.001,Nuvwxyz2{|no}x72~y=/Ḅ᩽▲r£=0.001,5wxy,}0<—2]<3~,|y-4|<0.001?

942v-ln2v-l3ᵨMatLab:᩽▲(RikᳮX.4ᵨMatLab:ᑡᦪḄᦪFপ(2)y=e'cosx,yভ(3)z=111(+)2)*/,ᒹ,^^,~^-^dxdx2dxdy5ᦪy=x2sin(x2-x-2),xe[-2,2],ᢥ⌕£ᡂ☢Ḅ¦§:(1)ᵨMatLab:ᦪḄ¨▤©▤ᦪ(2)ªcᦪy«ᐸ¨▤ஹ©▤ᦪ®¯noᓫ±²³´µ²³v«᩽¶`·`(3)ᵨ{|noa¸cᦪḄ¹º»`¹º᩽¶`¼¹º·`½ᐸ¾¿Ḅᳮ¶ÀÁ஺(⌕DEÃᶇÅÆÇᦪ)6ᵨMatLab:ᑡÈᑖFxᑍপᡂ'ফ'বËÇ"ভÌ7ᵨMatLab:©ÍÈᑖFJ[(x2+y2)db,ᐸÏDÐÑᙊᕜ¨+),2=[«ᙶ᪗ÖᡠØᡂḄᙠj¨Ú▲ᑁḄÛ²Ü8ᵨ☢ÝÞaßàḄ¶¼áâ¶ÀÁ.„3J,2»-lra1ᑭᵨarctanxax---+—H----i-(-l)n-----¼arctanl=—ßæḄ¶.352n-l428ᑭᵨ©=£¨©a28ç(2-1)2"28/T-lna3ᑭᵨ©12ç஻2ᑭᵨÇêëa4ᑭᵨW-1-=ysin(2஻-1)a58£NT_/ix^-1_n_(1a6íIJᵨï16V(--1-4Y-(¨)ç(2ò-1»21£(2^-1)23921

959*,ᑖ.xy'=yk)g(y/x)y(10)=14.10XYõ{ö÷1ᙠMatLabḄøùúËûᐭ᝞øùþᑡFelfsubplot(1,2,1)holdongridonn=l:1000;m=l./n.*cos(n*pi/2);plot(n,m,'k.')ᦪᑡḄᦣ!"22,#n$%&'ᜧ)*ᦪᑡ$%subplot஺,2,2)holdongridonn=500:10000;m=l./n.*cos(n*pi/2);plot(n,m,'k.')fplot('0.00r,[500J0000J)fploK'-O.OOT,[500,10000])axis(l500J0000,-0.005,0.005])"23,#£=0.001),<=>N=*#n>N)ᨵ_£Jcos"

96holdongridonfplot('x.*x',[l,3])Rᦪ"24,#x->2),y=/Ḅ᩽▲Usubplot(l,2,2)holdongridonfplotCx.*xV[1.9,2.1])fplol('4.00W,[1.9,2.1])fplot(3999',[1.9,2.U)axis([l.9997,2.0005,3.9989,4.0011])%Y᦮[\"]Ḅ_U`abḄc!"25,#£=0.001)*3>*d#001-COSX4ᙠMatLabḄHIJKLᐭ᝞OHIPᑡV(1)symsxy=sqrt(x+2)*(3-x)A4/(x+1)A5diff(y,x)%vw▤yᦪfghi/=______________________________________x=l;eval(y)%vyᦪᙠx=lᜐḄ{

97fghi),L=]=________________________(2)symsxy=exp(x)*cos(x)diff(y,x,4)%v~ভfghiyভ=________________________(3)z=ln(x+?2)*/,vᒹ,dxdxdxdyᙠMatLabḄHIJKLᐭ᝞OHIPᑡVsymsxyzz=log(x+yA2)*xAydiff(z,x)fghi—=__________________dxdiff(z,x,2)d27fghi=____________________dx2diff(diff(z,x),y)2fghid^z^=_____________________dxdy5(1)Rᦪf(x)Ḅ*vf(x)Ḅ!஺ᙠMatLabḄHIJKLᐭ᝞OHIPᑡVsymsxy=xA2*sin(xA2-x-2);dl=diff(y,x)%vw▤yᦪd2=diff(dl,x)%v▤yᦪsubplot஺,3,1)holdongridonezplot(y,[-22])%Rᦪf(x)Ḅtitle(,f(x),)O☢ᵨ"rvRᦪf(x)Ḅᔜ!:"26,{_*ᙠ-2,—1mvRᦪf(x)Ḅ!*LᐭHIPᑡ:axis([-2,-1.5,-0.1,0.1])%£"27axis([-1.9,-1.8,-0.01,0.01])%£"28axis(l-l,85,-1.8,-0.001,0.001])%£"29axis([-l.84,-1.82,-0.001,0.001])%£"30

98axis([-l.825,-1.82,-0.001,0.001])%£"31axis([-l.823,-1.821,-0.001,0.001])%£"32axis([-1.822,-1.8215,-0.001,0.001])%£"33axis([-1.8218,-1.8216,-0.0001,0.0001])%£"34ᵨ"r¥!Ḅ¦§{jV"29"30"31-1-1.8218-1.8217-1.8216"32"33"34¨r2ᙠ-2,-2
mᵨv᪷ª«v!*ᙠHIJKLᐭ᝞OHI:fl=char(y);fzero(fl,-2)fghi¥¦§!j

99fzero(f1,-1)fghi______________fzero(fl,0)fghi______________fzero(fl,2)fghi_________________¬"r®v᪷ª«r*hlU஺(2)Rᦪw▤yᦪḄ*v¯!஺ᙠMatLabḄHIJKLᐭ᝞OHIPᑡVsubplot(l,3,2)holdongridonezplot(dl,[-2,2])title(*w▤yᦪF(x),)"36,

100f(x)w▤yᦪ&)•▤yᦟ&)(3)Rᦪ▤yᦪḄ*vÀ!஺ᙠMatLabḄHIJKLᐭ᝞FHIPᑡVsubplot஺,3,3)holdongridonezplot(d2,[-2,2])title(▤yᦪ"(x)*)"37,<▤yᦪᙠ[2,2]ᨵ4!,¦§{j-1.9,-1.3,0.5Á.2,O☢ᵨv᪷ª«tu°±Ḅ!{*LᐭHIVf3=char(d2);x=fzero(f3,-1.9)eval(y)fghi*²`!jx5=,f(x5)=x=fzero(f3,-1.3)eval(y)fghi*²`!jx6=,f(x6)=x=fzero(f3,0.5)eval(y)fghi*²`!jx7=,f(x7)=x=fzero(f3J.2)eval(y)fghi*²`!jx8=,f(x8)=᪷³RᦪÂÃឋ¶▤yᦪḄᐵ¸*<¥Rᦪf(x)ḄÂj,Ãj஺᪷³Rᦪ"]37,<ᑨRᦪḄÀ!jc6dᵨMatLabÄÅvOᑡÆᑖVXᑍ(1)(2)J:edx(3)f^2'cos^Jsin3xJ(e+1)J)

101ᙠMatLabḄHIJKLᐭ᝞OHIPᑡV(1)symsx;y=x*cos(x)*(sin(x))A(-3);int(y)fghi:ans=__________________________________(2)symsx;y=x*exp(x)*(exp(x)+l)A(-2);int(y)fghi:ans=__________________________________(3)symsx;y=exp(2*x)*cos(x);int(y,0,pi/2)fghi:ans=__________________________________(4)quad('exp(-x.A2)',0,1)fghi:ans=__________________________________.227272db*ᐸÈDUᵫᙊᕜw+y2=iÍᙶ᪗Ðᡠ_ᡂḄᙠÓwÔ▲ᑁḄÖ×.ᐹÙÚÛ᝞OVপᑜÞÆᑖ×Vezplot('xA2+yA2-r,[0,l,0,l])hi᝞"38,DjÆᑖ×.(2)ᓄcÆᑖH,(x2+y2)dbjáâÆᑖᙠMatLabḄHIJKLᐭ᝞OHIsymsxyzz=xA2+yA2;dxl=int(z,y,O,sqrt(l-xA2));jf=int(dxl,O,l);hijVjf=_________________8ᵨMatLabãäRᦪpii.mᦻÅaæ¨riçèég¦§*nê⊤ìí▤ᦪ,i=1,…,6,functionzhi=pil(n)symsxst

102t=atan(x);s=taylor(t,n);x=l;zhi=4*eval(s);functionzhi=pi2(n)symsxtt=l/(2*x-l)A2;zhi=symsum(t,l,n);functionzhi=pi3(n)symsxtt=(-l)A(x-l)/xA2;zhi=sqrt(12*symsum(t,x,1,n));functionzhi=pi4(n)symsxtt=(-l)A(x-l)/(2*x-l)A3;zhi=(32*symsum(t,x,l,n))A(l/3);functionzhi=pi5(n)symsxtt=sin(2*x-l)/(2*x-l)A3;zhil=8*symsum(t,x,l,n);zhi=(l+sqrt(l+4*zhi1))/2;functionzhi=pi6(n)symsxtt=(-l)A(x-l)/((2*x-l)*5A(2*x-l));zhi1=symsum(t,x,l,n);t=(-l)î(x-l)/((2*xl)*239A(2*xl));zhi2=symsum(t,x,1,n);zhi=16*zhil-4*zhi2;ᙠMatLabHIJKLᐭformatlongPipil(IO)pil(lOO)piI(1000)pi2(10)numeric(ans)%ïhiᵫᑖ«⊤q]«ðᡂᦪ]«pi2(100)numeric(ans)

103pi2(1000)numeric(ans)pi3(10)numeric(ans)pi3(100)numeric(ans)pi3(1000)numeric(ans)pi4(100)numeric(ans)pi4(1000)numeric(ans)pi4(100)numeric(ans)pi5(1000)numeric(ans)pi5(100)numeric(ans)pi5(1000)numeric(ans)pi6(10)numeric(ans)pi6(100)numeric(ans)pi6(1000)numeric(ans)᡻ghiòᐭO⊤VóḄô±{j:_____________________________101001000PilPi2pi3pi4pi5pi6=mᦪ³¥:________________________________________________________________9ᙠMatLabHIJKLᐭsymsxdiff_equ='x*Dy=y*log(y/x),;y=dsolve(diff_equ,'y(10)=l','x')

104õ¥hij:_______________________________Ó5öឋêᦪḄ÷øfuøöùúḄû⌕ýḄV1þúឋêᦪÈᨵᐵgᑡ«ஹ▣ஹ▣ᣚஹᔣḄឋᐵឋஹឋḄஹ▣Ḅᐵ.2ᵨMatLab$%&''ᑡ)Ḅ*+ஹ▣Ḅ,-.+ஹ▣ᣚஹᔣḄឋᐵឋḄᑨ0ஹឋḄஹᓄ᪗34Ḅ.+.5.1'ᑡ)5.1.1n▤'ᑡ)78ᵫ"2;ᐗ=>(i,j=1,2,.,")ᡂḄGHIJn▤'ᑡ).ᐸMNᡠᨵQRST'STᑡḄn;ᐗ=ḄUVa]pY2p,…anpnḄ[ᦪ],ᔜ⚗Ḅ`Hᵫna᣸ᑡP1P2…P”e7fᓽD-V…j'„.....Dij(1)dlP1d2P…anpnf2P\P2-PnᐸoZ⊤rsᡠᨵna᣸ᑡ]fr(P|,P2,…,P")N᣸ᑡPM2…P”Ḅ⌮wᦪ.P\P2-Pn5.1.2'ᑡ)Ḅឋx(1)'ᑡ)>yḄz{'ᑡ).(2)|ᣚ'ᑡ)Ḅ}'(ᑡ)f'ᑡ)H.(3)'ᑡ)ᨵ}'(ᑡ)ᐰTfᑣ'ᑡ)J.(4)'ᑡ)Ḅi'(ᑡ)oᡠᨵḄᐗ=UTiᦪk,ᵨᦪkU'ᑡ).(5)'ᑡ)ᨵ}'(II)ᐗ=ᡂfᑣ'ᑡ)J.(6)'ᑡ)Ḅiᑡ(')Ḅᐗ=N}ᦪḄ]fᑣ'ᑡ)s};'ᑡ)].ᓽ

105(7)'ᑡ)Ḅi'(ᑡ)Ḅᔜᐗ=UTiᦪᑮi'(ᑡ)sḄᐗ=f'ᑡ)S.(8)'ᑡ)yḄi'(ᑡ)Ḅᔜᐗ=>ᐸsḄ[ᦪ)UV]fᓽD,i=kO=Z>=QixkC=L2,…f஻)fj=lDJ=kᡈO=Z5'A=d(j=1,2,.••,/!)0,-ki=l¦§A,BNn▤▣fᑣ|ª=,],|kA|=kn|A|,|AB|=|A||B|.(10)ANn▤¬⌮▣fᑣ|40n(11)§4f®…4Nn▤▣AḄᱯ°Mfᑣ±=FI4,1=1(12)§A*Nn▤▣AḄ´µ▣fᑣ|4*|=|A|"in>2(13)·¸ᱯ¹'ᑡ)Ḅ*+:00a\2000a22=a\\a22…J"=஻11஽22…00ann0000஺12…a

106a220/7(n-l)a\\a22…஺22…0=(-1)2aa_\in2nan\an2005.1.3MatLab*+'ᑡ)Ḅ½¾det(var)%*+▣varḄ'ᑡ)1-322-34091*+'ᑡ)ḄM2-2623-383ᙠMatLab½¾ÂÃÄᐭÆA=[l,-3,2,2;3,4,0,9;2,-2,6,2;3,3,8,3]

107det(A)᡻'ÈÉ:A=1-322-34092-2623-383ans=-50a1002*+'ᑡ)-b1஺ḄMfᐸoa,b,c,dNËᦪ.0-1c100-1dᙠMatLab½¾ÂÃÄᐭÆsymsabedA=[a,l,0,0;-l,b,l,0;0,-l,c,l;0,0,-l,d]det(A)᡻'ÈÉÆA=[a,1,0,0][-1,b,1,0][0,-1,c,1][0,0,-1,d]ans=a*b*c*d+a*b+a*d+c*d+l11111-22x,3,=0Ḅ᪷.144x21-88x3(1)ᐜ'ᑡ)ḄMᙠMatLab½¾ÂÃÄᐭÆsymsxA=[l,l,l,l;l,-2,2,x;l,4,4,x*x;l,-8,8,xA3]y=det(A)᡻'ÈÉÆA=[1,1,1,1][1,-2,2,x][1,4,4,xA2][1,-8,8,x^3]y=-12*xA3+48*x+12*xA2-48(2)3Ḅ᪷.✌ᐜÏÐÑᦪḄÒ4Ó7᪷ḄᜧÕ×fᙠMatLab½¾ÂÃÄᐭÆgridon

108ezplot(y)Ò1ØÙÒ1,¬3;᪷ᜧÕᙠ-2,0,4▬ÛfÜ☢ÞÓM,ᙠMatLab½¾ÂÃÄᐭÆyf=char(y);gl=fzero(yf,-2)g2=fzero(yf,0)g3=fzero(yf,4)᡻'ÈÉÆgl=-2g2=1.0000g3=2.0000¬Ḅ3;᪷ᑖ0J-2,1,2.5.1.4ᵨMatLab=>?@ABᑣ(1)àáâãᑣäåឋ011æ+42*2+…+=஺21ᱏ+஺22é2+…=.anlxl+an2x2+'"+annxn="“11a\2ainêᐸëᦪ'ᑡ)o=%a2n*0ì,ᨵíi,an\an2ann

109î¬⊤rJïᖛ,ñòf“òᐸo0(1=1,2,…Nôëᦪ'ᑡ)஺oõjᑡḄᐗ=ᵨö÷Ḅøᦪ⚗[ùú«11…a\.j-\h\a\,j\a

110+ᡠûᑮḄn▤'ᑡ)fᓽñ=ÆÆÆÆüan\an,j-lbna«j+l…annsåឋa..Xi+a.^XQH------\-a.x„=011112zIn஻a2]x\+a22x2+.i+஺2஻/(°an^\+þ?22+…+Q஻,=0"Il஺12…&5ᐸᦪᑡa2nan\an2…annᨵ;D=0ᨵ.(2)ᑏᦪklm.niᵨᑣ"#$%ឋ.functionx=klm(a,b)%(ᦪa)⊤Ḅᦪ,▣.,▣b)⊤Ḅ/ᦪ011,%12Ḅ[m,n]=size(a);if(m-=n)dispCᑣ3〉ᵨḄ"5)elsed=det(a);if(d==0)dispC78ᨵ5)elsedispC7ᨵ5)fori=l:me=a;e(:,i)=b;f=det(e);x(i)=f/d;endendend

111:4ᵨᑣ;ᑡ:%+9+⌨+=5+2%2—3+4%=-22%]—3^2—?—5%=—23A+2+2X3+154=0BCDEFᙠMatLabHIJKLᐭFA=[5;-2;-2;0];klm(D,A)᡻OPF7ᨵQans=123-1ḄRXj=1,%2=2,3=3,4=-1:5SaTUV#$(5-஺)W+2x2+2^3=0,2xj+(6-ti)x=0ᨵX22W+(4-஺)/3=0᪷[#$ᨵᦪᑡRᵨMatLabBCDE᝞;:ᙠMatLabHIJKLᐭFsymsxA=[5-x,2,2;2,6-x,0;2,0,4-x];yy=det(A)ezplot(yy,l0J0J)gridon᡻OPFᑡḄVRFyy=80-66*x+15*xA2-xA3CᦪyyḄ]^᝞]2_`]2,ab᪷ᜧdᙠ2,5,8▬f,ALᐭHIFyf=char(yy);]2xl=fzero(yf,2)x2=fzero(yf,5)x3=fzero(yf,8)᡻OPFxl=2x2=5x3=8ᓽaT2,5,ᡈ8#$ᨵ஺

1125.2,▣jᐸkl5.2.1D▣Ḅᵫmxnqᦪajj(Z=1,2,m;j=1,2,••஻)᣸ᡂḄmnᑡḄᦪ⊤a\2…a

113a2\a22…a2nam\am\…amn}Rmnᑡ,▣~}mxn,▣.C(a\\a\2…a

1144="22…“2”"஻?1…amn)5.2.2,▣Ḅklᨵqmxn,▣A=(ag)8=(),ᑣপA+B=(aj+b)iijrnxnMatLab",▣ḄBCR“+”(2)ᦪL4=(ka)mxnijMatLab",▣ᦪḄBCR“*”(3),▣,▣,▣4=(a,)mxs,▣8=(bq)sxn,▣,ᑣ,▣A,▣BḄ£qmxn,▣஺=(%),ᐸ¤SCjj=Zaikbkj,(z=l,2,---,w©y=l,2,«••,«)k=l£CC=ABMatLab",▣£ḄBCR“*”(4),▣Ḅ¯°,▣4=(ajj)mxn,▣,,▣AḄᣚᡂ²³ᦪḄᑡ´ᑮqnxm,▣¶

115AḄ¯°,▣CᙠMatLab",▣¯°ḄBCR(5)▣Ḅᑡ,▣A=(ajj)nxn,▣ᵫAḄᐗ¸᪀ᡂḄᑡ(ᔜᐗ¸Ḅ»°3¼),}R▣AḄᑡC²ᡈdetA.MatLab"▣ᑡḄHIRFdet(var)%var)⊤À"ᑡḄ▣(6)▣Ḅ⌮,▣,▣A=Ã)nxn,▣Äᨵqn▤,▣B,ÆAB=BA=EᑣÈ,▣Aa⌮,,▣B}RAḄ⌮,▣.R8=AT⌮,▣ḄᑨÊËᳮFÄ]h0,ᑣ,▣Aa⌮Ï—=5A*,ᐸ¤A*,▣AḄÐÑ,▣ᵫᑡ²\A\‘Ai…4Ḅᔜqᐗ¸Ḅ)ᦪÒÓRᡠ᪀ᡂḄA*=4,2A22-4,2MatLab"▣⌮ḄHIRFinv(var)%var)⊤À"⌮,▣Ḅ▣;☢ᢥ×AT=Ù*,ᵨMatLabᑏ³",▣Ḅ⌮F²functiony=aij(A,i,j)%"▣Aᐗ¸Ḅ)ᦪÒÓA^,C=A;C(i,F)=[];C(:,j)=[];y=(-l)A(i+j)*det(C);functiony=axing(A)%"▣AÐÑ,▣A*fmn]=size(A);fori=l:nforj=l:ny(i,j)=aij(A,j,i);end

116endᑣ▣AḄ⌮áâaxing(A)/det(A)-111]5123-:64=11-1,B=-1-24S3AB-2ATBᔲa⌮XÄ7,▣a⌮"äḄ1-11J[o51⌮.ᙠMatLabåæmᦻèknf.méᡂ7S⚪ḄBCFA=[l,l,l;l,l,-I;l,-I,l];B=[l,2,3;-l,-2,4©0,5,l];C=3*A*B-2*A'*B;dc=det(C);ifdc==OdispC,▣3a⌮5)elsedispC,▣a⌮!ᐸ⌮,▣R:,)inv(C)endᙠMatLabHIJKLᐭknf᡻OPF,▣a⌮!ᐸ⌮,▣RFans=-0.38570.51430.50000.0857-0.114300.07140.071405.3,▣Ḅìá¼ᣚ5.3.1;☢íî¼ᣚ}R,▣AḄìá(ᑡ)¼ᣚF(1)ïi,j(ᑡ)©(2)ðᦪkwO,▣AḄñi(ᑡ)¤ᡠᨵᐗ¸©(3)ñi(ᑡ)ᡠᨵᐗ¸Ḅkòᑮñj(ᑡ)Ḅᐗ¸óô;ᵨMatLabðóìá¼ᣚF(1)A([i,j],:)=A([j,i],:)ফA(i,:)=k*A(i,:)(3)A(j,:)=k*A(i,:)+A(j,:)5.3.2ᵨ,▣ìá¼ᣚᓄ,▣Rᨬ~^.ᨬ~^Ḅᱯù:aÃúᩩ▤ü%%ḄFᐰR0,þqÿ▤
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117ᓽḄᦪ,▤Ḅ☢ḄᐗᐗḄᐗ1,ᐗᡠᙠḄᑡḄᐸᐗ0.MatLab!"ᓄ$▣ᨬ'(Ḅ)*+rref(var)%var,⊤.ᓄᨬ'(Ḅ$▣“221_/70$▣1=21-2-2ᓄᨬ'($▣஺1-1-4-3ᙠMatLab)*456ᐭ+formatrat%9ᑖᦪḄ(;<=>?rref(A)᡻>?+ans=10-2-5/30124/300005.3.3ABCᣚḄ"ᵨ(1)F$▣AḄ⌮$▣+0ᑖᙽ$▣(A,E)IJABCᣚᓄᡂ(E,B),$▣BLMᡠF$▣AḄ⌮$▣.-1-322-3409/8ᵨABCᣚF$▣O+:Ḅ⌮$▣.2-262_3-383_ᙠMatLabQRni.mSᦪᦻUVᡂᵨABCᣚF$▣Ḅ⌮஺functiony=ni(a)da=det(a);ifda==0dispCW$▣XY⌮!,)elsedispCW$▣Y⌮!ᐸ⌮$▣[mn]=size(a);e=eye(n);d=rref([ae]);y=d(:,(n+l):2*n);endᙠMatLab)*456ᐭ+A=[l,-3,2,2;-3,4,0,9;2,-2,6,2;3,-3,8,3];ni(A)᡻>?+W$▣Y⌮!ᐸ⌮$▣+ans=

118-0.5200-0.0400-4.04003.1600-0.48000.0400-0.96000.8400001.5000-1.00000.04000.0800-0.92000.6800(2)F$▣Ḅ\+ᙠmxn$▣A]^_kkᑡ`aᑡbcᜐḄk2ᐗXᦋCfgᙠA]ᡠᜐḄ`hijklᑮḄk▤ᑡ;n$▣AḄk▤o;஺pᙠ$▣A]ᨵXBa0Ḅr▤o;D,ᡠᨵḄr+1▤o;ᐰBa0,rsDn$▣AḄᨬt▤o;ᦪrn$▣Ḅ\uvR(A).ᨵᐵ$▣AḄ\Ḅឋy+(a)$▣Aᨵr▤o;XᑣR(A)2r$▣Aᡠᨵr▤o;BaᑣRG4)4r஺(b)0<7?(A)?+ans=3ans=101/207/201-3/40-1/40001-2AḄᨬ'(ᨵ3Y$▣AḄ\3,ᨬt▤o;Y⌱1,2,31,2,4ᑡ᪀ᡂḄo;஺)*+zishi=A(l:3,[l24])zishi=325

1193-26205det(zishi)ans=-16%¤¥¦o;X(3)Fឋ~§¨AX=bḄ«¬ᳮ1+nᐗ®iឋ~§¨AX=b(i)¯«Ḅᐙᑖ±⌕ᩩUMR(A)

120elsed(m+l,:)=l:n+l;fori=l,raif(d(i,i)==0)j=i+l;while(d(i,j)==O)j=j+lendd(:,[i,j])=d(:,[j,i]);endendx=[-d(l:ra,ra+l:n),d(l:ra,n+1)];x=[x;eye(n-ra,n-ra+1)];y=xfori=l:ny(d(m+l,i),:)=x(i,:);enddisp('thespecialsolutionis:')ss=y(:,n-ra+l)'disp('thebasicsolutionis:*)bs=y(:,l:n-ra)'endelsedisp(,thereisnosolution1)end/10ᑖÏᵨèé~:⌮,◀ABCᣚ(½¾$▣)F®iÅ®iឋ~§¨Ḅ«஺+XQ+3/—=-2ë-4ì2+2X=03x-x4-x=12342X2-x3=0(1)ফ+ð2+2X+2X=4—X]+2ᓰ/=034%1-x+x-x=0234(1)!a~§¨(1),ᐜᑨÏÉᦪᑡ;Ḅô6ᐭ)*+A=[l,-4,2;0,2,-l;-l,2,-l];det(A)᡻>?+ans=0ÆÇ~§¨ḄÉᦪ$▣XY⌮,¦~§¨ᨵ¯õ¸«öᵨSᦪjfchF«6ᐭ)*:B=zeros(3J);jfch(A,B)᡻>?+ra=2thespecialsolutionis:ss=000

121thebasicsolutionis:bs=00.50001.0000ans==000.500001.00000÷0>?YÉᦪ$▣Ḅ\2,~§¨ḄØ«x=c0.5,(c^øùᦪ)2(2)!a~§¨(2),ᐜᑨÏÉᦪᑡ;Ḅô6ᐭ)*:det(A)᡻>?+ans=10ÆÇ~§¨ḄÉᦪ$▣Y⌮ᑣ6ᐭ)*+B=[-2;l;4;0];~1:Xúinv(A)*B᡻>?+X=1.0000-1.00000.00002.0000~2:X=A\B᡻>?+X=1-102~3:Y=rref([A,B]);X=Y(:,5)᡻>?+X=1-102/11Fûᑡ®i~§¨ḄØ«஺2÷+ì2-5ì3+ì4=8,X]ì2ᨵ+¯4=0X]332-6x4-9,

1224.¥|+2x^—3=23x]-2+23=10(5)1Ixj+3ᑍ2=8(1)(3),!ᐭ#$%A=[111,1;11,1,-3;11,-2,3],B=[0;l;-l/2];jfch(A,B)᡻'()%ra=2thespecialsolutionis:ss=0.50000.500000thebasicsolutionis:bs=0-1101201ans=01.00000.5000-1.00002.00000.50001.00000001.00000*()+,-ᦪ/▣Ḅ232,ᨵ5678983:3;<=ᦪ>(2)(4),!ᐭ#$%A=[2,l,-5,1;1,-3,0,-6;0,2,-1,2;14-7,6];B=[8;9;-5;0];jfch(A,B)᡻'()%ans=3-4-11*(),ᨵ?@8%3--4-11ব(5),!ᐭ#$:A=[4,2,-l;3,1,3,0];B=[2;10;8];

123jfch(A,B)᡻'()%thereisnosolutionQRS58.5.4ᔣUḄVឋXᐵឋ5.4.1Z[ᔣUA:,᝞)]ᙠ_ᐰ3aḄᦪb,1<2,…,k,”,gk|a1+k2a2"i---nka=0,mmᑣlᔣUAmVឋXᐵḄᔲᑣlomVឋ5ᐵ.pᨵᔣUA,᝞)ᙠAqr⌱truᔣU…,v,wx(1)ᔣU4()-஺],஺2,…,”rVឋ5ᐵz(ii)ᔣUAq;

124rref(A)᡻'():ans=10-10401-1030001-300000()QRᔣUḄ233,ᑡᔣUḄᨬᜧ5ᐵ3uᔣUµ/▣AḄ¶1,2,4ᑡ3ᑡᔣUḄ@uᨬᜧ5ᐵᐸ¸ᔣUᵨᨬᜧ5ᐵVឋ⊤¡3%஺3=@஺5=4஺]+3஺2—3஺35.5X¹/▣º»¼½5.5.1▣ḄᱯRSᱯRᔣKপ[¿pAmn▤/▣᝞)ᦪ4ÁnÂÃaᑡᔣUxgᐵ-Ä4x=2xᡂÅ,}~,Æ᪵Ḅᦪ4l3▣AḄᱯÉÊÃaᔣUxl3AḄËᱯÉÊ2ḄᱯÉᔣU.(2)ᱯÉÊḄឋÌpn▤/▣4=(ajj)ḄᱯÉÊ3Í…পÎ+Ï2+…+41=a[]+a22+…+annz(ii)Ð22…4n=|A|(iii)Ñm஻ḄᱯÉÊ(iv)ÓA+⌮ÕzmA"ḄᱯÉÊ.(V)X¹/▣ÖᨵX×ḄᱯÉÊ.(3)[ᳮ1:Ë_×ᱯÉÊḄᱯÉᔣUVឋ5ᐵ.[ᳮ2:n▤/▣AÙÚ/▣X¹Ḅᐙ⌕ᩩmAᨵnuVឋ5ᐵḄᱯÉᔣU.[ᳮ3:pAmn▤l▣,ᑣᨵÛÜ▣P,gPTAP=P0P=AᐸqAmAḄnuᱯÉÊ3ÚᐗḄÚ▣.(4)MatLab³/▣ᱯÉÊÙᱯÉᔣUḄ#$%d=eig(A)%Þßᵫ/▣AḄᱯÉÊᡂḄᑡᔣU.[V,D]=eig(A)%ÞßᱯÉÊ/▣DÁᱯÉᔣU/▣V.ᱯÉÊ/▣DmAḄᱯÉÊ3ÚVḄᐗáâᡂḄÚ▣/▣AḄ¶kuᱯÉÊḄᱯÉᔣUm/▣VḄ¶kᑡᔣUᓽwxAV=VD.l/▣,ÞßḄᱯÉᔣU/▣mÛÜ/▣.(5)ᵨMatLabä/▣ÚᓄḄᑨ¤.᪷ç[ᳮ2,▣A+ÚᓄḄᩩm▣AḄèuᱯÉÊᐸéêëᦪìᦪëᦪ,✌ᐜᙠMatLabïðñᦪᦻkdjh.m,ä/▣+ÚᓄḄᑨ¤functiony=kdjh(A)y=l;c=size(A);%▣AḄ▤ᦪifc(1)~=c(2)%ᑨómᔲ3▣

125y=ozreturnende=eig(A);%³/▣ḄᱯÉÊᔣUn=length(A);while1ifisempty(e)return;endd=e(l);f=sum(abs(e-d)<1O*eps);%³ᱯÉÊdḄìᦪëᦪ.g=n-rank(A-d*eye(n));%³A-dEḄaôõḄ2ᓽËᱯÉÊḄéêëᦪ.iff~=gy=0zreturn;ende(find(abs(e-d)<10*eps))=U;%ᑤ◀@ᑨóøḄᱯÉÊend122¢14ᑨ¤/▣ù=:zᑐ=212mᔲ+Úᓄ?Lü|_221.ᙠMatLab#$«¬!ᐭ%a=[01;00]kdjh(a)b=[l22;212;221];kdjh(b)᡻'()%ans=0ans=1()QR/▣A_+Úᓄ/▣B+Úᓄ.(6)ᵨMatLabäl/▣ḄÚᓄ.᪷ç[ᳮ3,l/▣|m+ÚᓄḄý]ᙠÛÜ/▣Q,ginv(Q)AQ3Ú▣Ú▣ḄÚVᐗá3/▣AḄᱯÉÊl/▣ᱯÉÊᑖ8ñᦪeig(A)ÞßḄᱯÉᔣU/▣ÖmÛÜ/▣."011-T¢15³uÛÜḄX¹ᣚ/▣/▣A=11ᓄ3Ú▣.1-101-1110ᙠMatLab#$«¬!ᐭ%a=[0,l,l,-l;l,0,-l,lzl,-1.0,lz-l,1,1,0];[d,v]=eig(a)d'*d%þÿd
▣d,*a*d%▣ᓄ

126᡻:d=-0.50000.28870.78870.21130.5000-0.28870.21130.78870.5000-0.28870.5774-0.5774-0.5000-0.866000V=-3.000000001.000000001.000000001.0000ans=1.00000.0000000.00001.0000-0.00000.00000-0.00001.0000000.000001.0000ans=-3.0000000-0.00001.0000000-0.00001.00000.000000.00000.00001.0000⌕Ḅ
ᣚ▣d,▣V.5.5.2TUV(1)!ᨵn$%xi(x2,…,x”Ḅ-.ᦪf(x,x,---,x„)=axf+aX2+---+ax^+2ax+2a|x^+---+2a.,121122nn}2iX233n:.;!<=⚗Ḅf=4@+஺2/+…+஺,C:Ḅ᪗EF.᝞HIxwO,Lᨵf(x)>0,ᑣ:f
(P::▣AR
Ḅ(᝞HIx*0,Lᨵf(x)<0,ᑣ:fU(P::▣ARUḄ.VᑣVW/=x7Ax,ᐸZA:▣(:fḄ▣.(2)ᓄ᪗EFᳮ1H\/=—Ax,^ᨵ
ᣚx=Py,afᓄ᪗EFf=a\X\+aX2+…+஻,,ᐸZaa2,…,a”RfḄ▣AḄᱯef.2ᳮ2f=
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127ᳮ3:▣A
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(:▣AUḄᐙᑖi⌕ᩩkRAḄ᜻ᦪ▤stuU(Ꮤᦪ▤stu
.(3)ᵨMatLabyzᓄ᪗EF{16|
ᣚᓄf=x+x[+4XM2+4x]}3+4x2X3᪗EFᙠMatLabᐭA=[1,2,2;2,1,2;2,2,1J;[V,D]=eig(A)᡻V=0.60150.55220.57740.1775-0.79700.5774-0.77890.24480.5774D=-1.0000000-1.00000005.0000VRᡠḄ
▣(aV'AV=D,ᡠX=VY,ᓄḄ22?g=-172+53(4)ᵨMatLabyz
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,⊤U,0⊤
Uy=od=eig(a);ifsum(d>0)==size(a)%ᑨᱯefRᔲᐰ
y=i;elsey=-i;fori=l:size(a)b=a(l:i,l:i);if(l”i*det(b)<=0%ᑨ▣Ḅ᜻ᦪ▤stuRᔲU(Ꮤᦪ▤Rᔲ
.y=0returnendendend{17ᑨf=-5x|6|4+42+4ᐗ3Ḅ
ឋ522'fḄ▣A=2-6020-4ᙠMatLabᐭ:a=[-5,2,2;2,-6,0;2,0,-4]zhd(a)

128᡻:ans=-1RU.5.6¡¢yᑁ¤¥¦§1¨a©Ifª(-=«¬(1——2ᐗ2+43=0-2x,+(3-a)x+x=0ᨵ®¯23X]+2+(1-஺)²3=஺᪷´-=«¬ᨵ®(mᦪᑡu®(ᵨMalLab¶W¦§᝞·:ᙠMatLabᐭsymsxA=___________________yy=det(A)gridonezplot(yy)axis([-l,4,-20,20])᡻ᑡuḄfW.ᦪyyḄ¸F(¹º¸(»᪷ᜧ½ᙠ__________▬À,Áᐭ:yf=char(yy);xl=_________________x2=___________________x3=______________________᡻xl=______________x2=______________x3=___________________»aÂê(-=«¬ᨵ®.2ᵨÄÅ=Æ:⌮(◀Æ(ÉÂᣚ(ÊËÌÆᑣ-Íឋ=«¬(6)Ḅ஺6x+4X+ᓃ=3}34x,+2+2X=13X)4-x4-x+x=0234¶W¦§:

129ᙠᐭA=_____________B=______________Xl=inv(A)*BX2=A\BY=rref([A,B])X3=Y(:,5)X4=klm(A,B)=«Ḅ_________________________________________'AB-E0ஹ3ÏAÑ⌮lḄ⌮஺i0¶W¦§ᙠᐭA=ÒB=C=A*B-eye(2);C([3,4],[3,4])=hlsh=det(C)ni=%▣Ḅ⌮᡻C=__________________hlsh=____________ᵫÃ▣CḄᑡuhlsh(ᡠ▣C.X]+2+/3+4+/5=7,3+x?+2Ô+4-3%5=-2,4-Íឋ=«¬22++24+6x5=23,8xj+3%2+4Ô+34|Õ=12.¶W¦§ᙠᐭA=_____________B=______________jfch(A,B)᡻:__________________________=«¬Ḅ________________________________5Ï▣Ö×Ò▣AḄᑡᔣ%¬Ḅ|$ᨬᜧÚᐵ¬,PÜÝÞÃᨬᜧÚᐵ¬Ḅᑡᔣ%¬ᵨᨬᜧÚᐵ¬Íឋ⊤ß.ᙠMatLabᐭA=

130rref(A)᡻:________________________________ᔣ%¬Ḅà(ᑡᔣ%¬ḄᨬᜧÚᐵ¬!$ᔣ%(©▣AḄáᑡWᑡᔣ%¬Ḅ|$ᨬᜧÚᐵ¬(ᐸâᔣ%ᵨᨬᜧÚᐵ¬Íឋ⊤ß6|
ᣚᓄ£=3ä+3/+©/2+8å*3+4}2}3᪗EF(PᑨḄ
ឋ.¶W¦§ᙠMatLabᐭA=__________________________[V,D]=eig(A)zhd(A)᡻ᡠḄ
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