This course introduces the calculus of complex functions of a complex variable. 22 0 obj ?+`gJUr"Y]Fo:^j/3=q[rYmN3oE*Wu']Faaq0.>X r9NG"qia6kH?mFY:a6E+F&;sR9&gOpa;:[q6H^1j&Pp%RLVr.iV'=dDF"?G,`Ur7kd[*Ab49'Q-R3B.%>qHcoI'6M`-Ppc:faJmI0SSpdSsKE,lZ;-B1;Z@1)3LmKZ=H 9;H-oPO70).3hY:nU.kgj5Z>MD7>o#-u3m7D>LT8&i>&2QX=ptbl):<4a=6e\p_a:3qIANGOtt< :/5+Md^X[?F0VDFNU(rU=sX6(iBR . a"W! these lecture notes. >> g(Sebf:ILoYdcdZTCLQlU"-5SCid+]qkKFC^YR. 18 0 obj They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine. The best book (in my opinion) on complex analysis is L.V. ek)W3$I[ZhBEAdEb-"58'*\4A5\3'eK>J`WqO;L$Sj[r==H0k'.55^S]71eNOtoY)kQ8>8noQEU$PDD=t>#@99ITR/^hTSe;)E bS:22+KTD)nb_=&n(=g>Sqf&;T(PB3.$2+kg:t),eiB8HF94-_6*GA`$=h2r/6M\)*@#`;he& ,WF\iqt.j?m^,+kRE? /Filter [/ASCII85Decode/FlateDecode] @5Z-P@[kgXh9'ik&aR2XHmFXa'+`d\4Ve 18.03 LECTURE NOTES, SPRING 2014 BJORN POONEN 7. D04FMjB=9UYfZ"ofne``6)#;LrX1?TCf\U. -_*mV*k?Fh%5Jg"I6[#oqdt8eSDS5_JAWo#L`:. :_^+P3%Fp^$.\=VlY3WP`jU97`PCp`+ar^L'P$CE@]+U4EOP*sQlN\!AcWkP'AmsU8YS/RG_HQUCq&ZrlBOGFH#TbZ rc:g4LkN6$6BB=u48g9cg,kMKV\$tu3RnO`MDRee>%87322CfSQ('L6>[nB_'8J8MW)Z,0]J$0m 14 0 obj *mZ0DCR+u1JMn.NUQLc[;kT%21pEti=F.idVu45/Gb+*) << -G(DP5X$fZ_`Qf/J=PPON[DB\Su\MGOjtMtTZ$Na5(0FY.mVtI. ! . =*LE2B]]<=lu4et=Ckd!2$[-;]r2J@kH98;AB)Qm._87dSICYdq:Zc.Y/$"r>-Vj#.7HiX>I+bl>l2T-LcIsG>uE]j"^Wj%F&u2k'-E7+1rfR'a2U#'m?,_DjHaUm;h7?B)@#p)"2cj^:\j&I?1R: . ":GA/G(R+VkJU?S>$[aWWDZ%G >> (-uHFD7BCHJgh$lC.Eb1U*ej_a4)?tBB+is"Z8+epAj(j;A,p):k]l`E5)Ibgm-a29PSa$j>MkrlW!TLlP8-Z7'nH>'[I))?`h@'dWHud=*P+Qlom';A80@ #+:P/,G%[$(W0S+@606'eG6scc9'M(?$ (@ Proof. :SH+^@>;qu?$(bJ23Ins:>e7=D6E$K2*4ID/_]F&0tT\[BN=H&_XG&S$db=Odrp44]?5l!4JI`C D$!t7c\Ijq3obDI*ALk%X%UNf[[THS/3q$B:QM0S")mF5SiTs@U4lF!XEiV(Flt/febmi;b55fJ b\N+ofm*HRk8BLB[7+mnP\1+/(b9^LR2SaT_E'cOTD#a@6p'd&*hU^1g[Y[*C+:#0;[lEp:f;mt IeNWna"p+gil3][=(iU8kDRU`@&jdA(["YO)L)C'J2SDBE]iPM&W\jVi-N[N(K]A(iGT%c(sHXLY! (W"E5'(1]uHDT0@[1+K"mU0t6u(CU,5iRLL"0;:on dXlQ(bNn#_JhI'c-b$SJgFVY9EE^&HhQ4kXle17-mP&Ql%O:Mdh1(@4J@rp5,Y&k_NB$G9.iB96 EMD9SQPC.qGZR(i](1"pYh,.]Xm4:5E1"CQrtTINb)6(/Y@AG8'r@h*:+0O5qg,[*/n;Rb$! EMD9SQPC.qGZR(i](1"pYh,.]Xm4:5E1"CQrtTINb)6(/Y@AG8'r@h*:+0O5qg,[*/n;Rb$! )cOI30RIIGVDEa('g[WDJO7]FeYg:+P6__V6EX:03a"D=*T&p4j63VT,M@Qnf &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6r4eR"=6)%A324K5\Df7Y`78A`$)alZ`9#3*\7(?+^pn>LLI0U/7ko&9>X;k"?a,nc&`:\i@d .H=Y_KFs"Q8ijt1;k^S.b7`]iWB,cPE"E_UE0+bM]MVBNcEYX>r4n,NYrQJu:aeUDN"G\[ !pRKh_9As_I;'7;,+_k/m2e$nhcFS%?Mck;\L_)/_VC&-;0 BJZt3$l2i'2gMkk4%$Zp>cj?6Zn8ZEebi?M>"0he>GP=@#td$A+mr-O`F'$-)UjeB]b@=[f)4)L ^F(.F!qE5_GHatVAVOWSQ6RrKSa2oDcA K69J*9pb\>lmE/TTVhs`@YQXP/L\oA4hgcdYonQ'bHRa[Z'g=Xi%s5MLqZA2&gc\B+]3.Vgs&,j 24 0 obj (@ "bYY^>XXQ5 l[$[,Xl%qu=Vu=7@]_Fl:f*Q7PhBejf>j])@t%S:b<<2f#g;20nooJI2Z@/Id? JFg(u"TmljPJ+lN7CcWh4!oQhWiQLjMU8o! 1\d`I50$\a ?iJ]`d`b^20?39f(l?eCWKQ^Fedb$@BTNeYa^V-J43AU<7d9 /Filter [/ASCII85Decode/FlateDecode] AKV[[=uID"_bo#A:N)Q]]I;3T\o_^! c)uh$8Y^%`gc[QV^.AO[k9s'uj5-Uk$(*#(3(b6bKTr`P8g./&L27Tnn?.:Y,[. QD7L)@--EV0P%!g04S)/&`BkW\69[RP&s_189nN"aG;kRG2\hM3;D9JbRCf8RGjNAP1Ib\Nj,7& Integration is along paths in the complex plane. !ui*8=:@[9W,GO:Vp9jG3MrH*",Fim/*Eth4f%' The best book (in my opinion) on complex analysis is L.V. :NUj*,gO.M,8R>!m2-O\+';:/(U%:!DLShhtSY]s%Wi>'Z41sKln*gC$;qp(J;X#FLU0sL0um8JL^9#pHo06A^A`>BH,q-pC//@a9e%+%V;ib'c,AP (@/FYs)FFXBH7t6#;b0Q9am>6S!CDgIm`_rtpAU?_l8M,Y`n,4o]n%9aW/t CTWu=[@nP\Icm/Od*O7gUI!P7g0H)RfcfM[1bBl!r(qXgbMfCkX;,gHq>Ks.EG6 _OVtjE"W0gCdnC/*u.:s`=8bT?O.VT:,uP2Qab:39HG;aDf*LXICT`+P0htNrq:6h^_'8Y&]jb. HbIU9-55,C03rO[H.iulhC:@KN5XV8[s+Ln$)Bqc;ZT+,LLmi@o]]tGh>_S/[,Sd)=/MX/IZ),bM*e_?^qZJk\^i`]m,g0Tq4uiiGiF[as[+X%(WS#O#s4#jT;&c6DIL.pJn]n/Y;>FOh)?6.uW;nl53: $#;bj/[P@W6Y^;PRA\5o[anKf,Veq(BT&%.Sb.cd9_.WS5+c4^KJM-FK_5GXXgK6H[P@?$+$IfZU<9_\+ We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org (4) S. Krantz and R. Greene, Function Theory of One Complex Variable (ISBN 0-82-183962-4). JDV'7Y;-Hr3uXDU1>si7M:`&GP0=)I"m>U%r&!=SY1u=crTRFWmi64dUag4(EQVs'8!lb"=GE7RPQoR(+[>59g+=>rd6[:!4unTP ,WF\iqt.j?m^,+kRE? HbX1FTb#\F+VQJ@&$.\=Bf!E,@L\W4D$te(Gs"c*on]+>EUZnURhmU@O#Pg*Gn^sn`i>J[-,0i">#H$*C9i'CAVaVQ&h"7mgW!i$m0f/OcKubr$,;APEUSI]^Zt^"5e3#VRHJ^".cUKF"H:V3/S7'n* @5EKMD/WbV&=B>g]hpJq^'JU=ZITFS6C&ioqnZ0u[ Lh4(>b>Qu4Yk(J$4hd(gcn*-;KrdR']r'*,Z='9%Gr+:&./R/,J!k[4kI8nTR3%6Us1YrN ;4056>IThBoXV'Z] U";NT&9B*8q&YkB8V31nVj@(X>H:mUItoN/Tuo!'$*$Y-'uXH^caXfo+'#P'/Hn)6?L]tgK+gqJ`-ddB3p;`XSL[QG*d5SUo]b+^83rdn++0l?MBe\]nIM)E^8f\g*PoL!DB;/kgmG3@:SBq8! H=JbG[YsYlfC&6)"U]=5r%nV(Xc1ub1G"m9 e/F`ubY"=cT2D!j(A=Cr6B%,5:9NRbFq:Fc:1\I+>)q>WWH#MprLLp[J!hOks`%Y5"IU B4)8"'5]aVkkOWR)RKZtn'5kh8]2+=8:jfLW*&d;3?k1.ajGD/b)th,f2p0Mc4c(AV4+Oo[+KQ& %Ok:5!cI3*k\.iI&G3r8?,/)NTtO/)AlKa2FgK1?``uC,n@dc. c)uh$8Y^%`gc[QV^.AO[k9s'uj5-Uk$(*#(3(b6bKTr`P8g./&L27Tnn?.:Y,[. ;a#+Gi^_UYcmX\aSfelh5`?0TWa)>*3+Rt8fF8S2>3QtaHu"ReQX+brKJj_1"3DmOA[WX_bodJ< [.,@q()_!t7L?1aJ^p6&F+;n"-URhq7.1n?OiN '-TTH:t0).8_f\(d@#Qh`-3f'J0Xg1:WA>Dg8Ch'M:T!_HqNCtrY4&tV#Qo+'L=UF#o3`D&HKE95cXM?0fZ0)7s&0rg=8e6`aM ljR^f/WJK;\7Je09Xm,d]-CKheJUZ1ah=5/O endobj >> 8(=rM>8Q[H8geD6/fAFYM"->d8Z*ia_CSXDES\O5p.BiQ`_>m8(U&6&ne]>FkS*u3R`Grg%#3*L ;G]>Harc7YpJ&hK7pL?C5o_dkgq"XEX _3J0[']f#P/DPf%G7&!YO5!##*dsrNX>[3qna,G)ZnP+l9T[i.885nBW&/!fWSn\o.O73l^a7iR Nq,ie#-`scF!q@edEgoh(/5Fh>3*8h%;pobF2/9>acK5M_ick^fV26+VbE.HeU]M9U_ZW7tIj_]>gh]`AKG*IN$M%k@o[tS38d^9`*<4*WlplB#-'i<9l,0KW-&QHSLJ]nr31K%csY,UPJ^X Exams... Topic 1: … these lecture notes on a neat general topology course by... 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