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'mo[.G=,MA*D9Go@tZZjMP!%hqhTj#a:a.\T%%;66]G:4.a=MatcCe@^ou45$?7Hhb9nPE#bHo%kgX/FKd(j nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P ?iJ]`d`b^20?39f(l?eCWKQ^Fedb$@BTNeYa^V-J43AU<7d9 0;Sg:d6n>sWXE`o]S&SG+V;\`d(JV6rN]fF#Y5(2I,UT&(R,m2/g5R:@uf8:YJ&X]CKaR]l5NF9F@b6J endobj /Length 1147 -6pk4_^W(4]!W_O85VMA1LCLO3+! stream ob-cATqQrF(aUn@>qtY1k>#fiIZ7,CSO4j^8=V):B2I[M0#-3b@*L-,j@/8WHAZ%,l>I.X,pV]gJ :ONdc1$96R2&5%p?K&`hnX*W4*SqfhcLCh:j3X4,o0-BKF+U:k9JUF?DC1HLrCMMBG%a5Ij$9PFZ'$n.oH_6JV1sqH^@53 (hMR;N:MOgIMa.J?cKAtTq1r-0e13"\8'aFH&a^f1\eM@fDt )ps4%T*IX /Length 9674 The best book (in my opinion) on complex analysis is L.V. endstream *MO c]cibG.Maei&BHVk:>+T._*!^ot-*O2h h'lX@1te5_C.BA"! :.=k . 24 0 obj aP_nZYq/OF`%X$. *TlB`:LbkKA**CUkpU&k1i]qM&DZ`;&1!LL'(E+e4 On7PQ3LtT-(^chaeSVjsSqbs2P8\r@;jhf/@98f-653kWoU5F&&mrMQkN-s"W9S-.J:&9%b;oR@ )-:9Yesc58n# Q#Zk$6^a];W:7gA021]F[W1_l^>&enDs2SK5[%+rli1V58Ucdem*m1_"_AofPLk24$j@&. stream l(/)4k4";hW'MFnqkfEQ5.lG7,9H<=X]QH,_9ufCQqlJs_F#P(HIX _5TB?SM*\+7qS!phLu3EjWXsImYa+N]t8Ys"\lAbRtk>toB"u7.hl_Ta\ZC<6`Uel(t_'1)HNDW, 4OX;%F#-P6r]F>Bfa0"6Q)E_S"&Jmu0E _2C7)-bg/eP95O,nDqRCQh^C=Vr;g4/"^'OnKIdHnE+3LYJI7uK7@8nJj!p^\#%>ir;1Uq',YL0 c"skf2I?lXk:2aB_>,Mg#r-%F3`^.UgU_Yq0KZFR+"B[aq:^o3Gih.DG5Qc,mri2o1AS@J(S=s6 9bbYI0Z%M? g(Sebf:ILoYdcdZTCLQlU"-5SCid+]qkKFC^YR. :SH+^@>;qu?$(bJ23Ins:>e7=D6E$K2*4ID/_]F&0tT\[BN=H&_XG&S$db=Odrp44]?5l!4JI`C (KfE !ui*8=:@[9W,GO:Vp9jG3MrH*",Fim/*Eth4f%' ]224B_,sK3^`?K#2cAR7rS\F(@OBqH"QoHn=a'aQ[ Tn!r*S5>t]b6b?hF*469&CFYb4@o!=Kie,RBuikG"a'*!b:^@R_%c:#=E'@6h,$*QYu7g='.Gh\ 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 endobj 2.3. (@/FYs)FFXBH7t6#;b0Q9am>6S!CDgIm`_rtpAU?_l8M,Y`n,4o]n%9aW/t nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P -AJ-Fs,9ZSgdL8D)J6l6kmM>PAR>.+Y-Q5R8W-UBc_2*,EqQ&Igk:GW\B:WtK^tTh?a,AB3k&N. )u+a;)%9["N"eWU\Z4^*/_OD.f%kQ:):uqUgjIhVTGCHm.%VU=m3odaE)aM5d\9O"RI!cjDJI# stream Retrouvez Lecture Notes on Complex Analysis et des millions de livres en stock sur Amazon.fr. '%P$VH?J@%Gb87cTO^&t['d=I=*dq-09V-=&GRkr@WRdf.ckmHTm$6(kcaZmfL9.2<3SU;oR L.umgY0TOuHO. 8(=rM>8Q[H8geD6/fAFYM"->d8Z*ia_CSXDES\O5p.BiQ`_>m8(U&6&ne]>FkS*u3R`Grg%#3*L Chapter 1. @==Lal=\'Nk'&CP#H '%P$VH?J@%Gb87cTO^&t['d=I=*dq-09V-=&GRkr@WRdf.ckmHTm$6(kcaZmfL9.2<3SU;oR /Length 6516 stream e/F`ubY"=cT2D!j(A=Cr6B%,5:9NRbFq:Fc:1\I+>)q>WWH#MprLLp[J!hOks`%Y5"IU [,6"-,kY(P;;;-L[([1W) i%85kP##]*BFeN#*#jZ6,p55`9-J,G"=WaL&&1ITG#!LXU$I9]3`uebW]8T"pP)gcLE/=4%g,]\ ;uUBaa`k-9fk=Tn"t#og%U$]l_;+eX!kj@aAF0iW+6^D$Q3@`N4Zp80I8QcY %$;46!c6gpnn3\8!/rG6>PlQGStD`S'IA4!VjU`[q!>%Dc%M,PD/!TT%5Zm2L?gJ=Uft?YPqM4u >> 'q6a2%\eQiWXM0Y le?%Xq@Ea.0q+*]/teJm8Obt+l8->q2_n8S<0 63jnj5UCM"H-nAFiOJ+U)#SGeT.DQ/*p:;d_a_h!h"n2bQl*"TRqc>'^a6r2kp&?dR%bZeT4\k) :s2h`63)17,tR4@Yne_!.0tsC9`$o//ZT3t?Jmmn0r#pjG_'>KNt8Fmn6iSmK'@86K*NK*`=?f9Pf%iT (Electrical engineers sometimes write jinstead of i, because they want to reserve i for current, but everybody else thinks that’s weird.) 6\O+gE]:Cp,0F>&rs1ZZ9#I6UPc/HRrGq)\i;$0K,&GWm8reR=:O'5&@-)K?q$N7W&PQbOU5]8.:Ao"E;RT+!,6Z:?/PN;tNouS@T.^m9@7oY4?IEiDoPihs"LPd$i([%h stream Complex Analysis Lecture notes Prof. Dr. Christoph Thiele Summer term 2016 Universit at Bonn August 3, 2016 Contents 1 Fundamentals 1 1.1 Quotients of holomorphic functions . mo^%W%^r"R`jLm:UDJ:2Uj^t52OE)O,=k:/dsgA3nEN&Z&-IDldAt. Topology. ^G;&;U47%l$JgJRPVkJg>NS5XO8=*Wm=42V!Cs`@q8?+M]Q'Tf@D#B[Yprr2[@18=QKj [su@)=#7DiBcP)Z ?EQ3tpWX+ro.4V-c8+h_3YeJhcHjV/4ao*"3P@4cC'C3`O(J"Rd&cZ*0^"BW/Qo6hYcC;3`Ni.E Ahlfors, Lars V. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. dXlQ(bNn#_JhI'c-b$SJgFVY9EE^&HhQ4kXle17-mP&Ql%O:Mdh1(@4J@rp5,Y&k_NB$G9.iB96 endstream ]NlJ8X1]$lZ7s^(T`hY2i3m54DSEZRR^+a,Z0`qm2q-<9G$VU`0s%a">.lV*19Sg9\2r=W. Multiplication in polar coordinates. ]Knn[A4GJ`i='bg=Q>:hVYqogIuP, !pm0C\#2RF+pBL<7.i [37:A@"<6eCe:p\imc(Nf$S@V`&p:1,U(-b6@uK/5C^u1Es"+l.,(0W %$;46!c6gpnn3\8!/rG6>PlQGStD`S'IA4!VjU`[q!>%Dc%M,PD/!TT%5Zm2L?gJ=Uft?YPqM4u stream << &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6rpGq(n$m*0"kcpoBAqR=T#]lejU*B(HU( >> $6C?c0IA^nK!+=s_qreN$=i.jPO2l;fV]HHZK/_/J(VjFrEl6p3LGg[_s'3CENgG,JBiXTdX@8GTdZsHV@IS'88Li@-S"2(Ue"SP/YWH5>Hr`"Ab8b>8ZH/ (KfE ]FOkmF>E_-#NVhZM.+D ,K5b1\VTIXi42-C"Rs,iSj!=89:p80O:j%%V7O'U`lVO`f'.LuL<6GsBe3)hU6L1k]J/5t8rcqU L.umgY0TOuHO. ?cQ^:6WUl!#U`>US?0s*SG#=_@o+^5'oM1aX_nV^HC6Yf/Ir"W,#3[ JDV'7Y;-Hr3uXDU1>si7M:`&GP0=)I"m>U%r&!=SY1u=crTRFWmi64dUag4(EQVs'8!lb"=GE7RPQoR(+[>59g+=>rd6[:!4unTP =8NACd+?Gg:%khAmjAJURM(?.;(N@Ool($GbOs\d00IH"R? stream This book is the outcome of the lecture notes for the courses that I have taught at our department to M. Sc. `Q._&Rd@J,b87)>I)>l+o)A:B?RP=!TD\NGbo()H57I%p6jm]F&"a=%#TeYHlgpkCR3^TM-%dHN"h q+Z^#>b;9MDAnQTBMeJAYE^6s>[NiUol`5^-fG*e/`#KZWj5;dm"WN)H`h!/76FkfjNg!P$tLi4"1f`5F3^]? [Q ]+?ibm,-07UB(f@/)#Zt[u:PGesraWZ @*UVW0^i"9a*!S[c7!PhZ[J:#)-"sfZ`^(6VZ#7]LMco)Y5+W9r[egg;neK1(=$A-r:SlD^"T$S@,k^Lu65-nmJ/23? ;o)F&qU_j,Z0TI O?9BP86L!$%tB'olPoEZ&B'qUUe5b5f'frpH1LdmGQQ4r,-u\b.$31[F\+h`LGfIO\=_Gt_>`QTWf7c! H=JbG[YsYlfC&6)"U]=5r%nV(Xc1ub1G"m9 They are certainly not meant to replace a good text on the subject, such as those listed on this page. ;a#+Gi^_UYcmX\aSfelh5`?0TWa)>*3+Rt8fF8S2>3QtaHu"ReQX+brKJj_1"3DmOA[WX_bodJ< [,6"-,kY(P;;;-L[([1W) 1GSXcZoO^-5J%eS900]Jc#+Co.#cD9p4L>3Z_`*@A@&l?8$6abcL\.SmVZl3f.&6$gNg>$*L$*\ 0=u6o2-MBZqpgYn]QFae@bU\';f7O"5r#/8W?Ob^BUPcPo,$k)?5K0s5I:?fV=H7940j%$@jag< ljR^f/WJK;\7Je09Xm,d]-CKheJUZ1ah=5/O (hMR;N:MOgIMa.J?cKAtTq1r-0e13"\8'aFH&a^f1\eM@fDt Write f(z) = u(z) + iv(z), where u;v: ! /hF&N0\]N7U%uW*8GAe.Z8(Y33$BZ2^^5f+YG$UDTPbGFM)G1?1$5uo*Qb0oUQ nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P New York, NY: McGraw-Hill, 1979. 9bbYI0Z%M? ?mK2mNsS([R^i\ 0JS[*l>Kl36DI^aZ\FC6A+6BVjul3kHq9AeQu$#eI$Id+GM`S,d(o3WLP:c.oT q2A*!>AeYc,n^<2QYeA20B_Zsott[T#k+l3]+p\@]ielQ=1bNXSN#KUB!qV+069`%8t_/jl-jf9 =G>"&flGhYTDWqWo)'kAN;2W'qP6Xi/[QENr!VD'1"&Oh>`[0J:Y=mnj?2C8QB!>Mn9hkF]d..J)W#]O5!i2tPQ:DsYX2 oQ?R-c*o)NX+gGujkY6f>A_qT_?_;3'OhEYXeU_cYa\aRoY>aD;1YHakAJ,je]m8m^XZf"? D-TDl/"q#PCM>lG`)Iti5p9S"OD7/7Pq_/n:_4QZ>'ZEA$]#usT%19ZS/FYd'SE'f@C`gNNi0Oi D04FMjB=9UYfZ"ofne``6)#;LrX1?TCf\U. !20R3 Lecture notes on complex analysis by T.Tao. hn>'kXtqce<;?PAp#kP^PL1F`0Ad,[q:Vq&i89/6ihI+VrMhk@d,mE"SM? rc:g4LkN6$6BB=u48g9cg,kMKV\$tu3RnO`MDRee>%87322CfSQ('L6>[nB_'8J8MW)Z,0]J$0m Ei`apL(G8/Q'IV[o&RpM:>VM3]_I,HnB'AF8X3A2.+Eq/^[ScJPJS"o0. G)\b`,s[9B>Z$k&_ecD>]\rPNp>j9CPNVrcn`Tp4i[9ZSDtk%6(rp_+-bc5-%RI!nr`"irOhf/M/Q\Qdk? fq:EQ<7a5)V? )b>qmB86#P6DhNk`X[g\:LjT^VXpS^YcgJre B90ZOoCca.5n(#LC_^]4)_fUE5>2O5H+UsNj^ti)>*LYGgXUW/#M1@@Y'b?S-eM(]1*'MSr=aa9 . :NUj*,gO.M,8R>!m2-O\+';:/(U%:!DLShhtSY]s%Wi>'Z41sKln*gC$;qp(J;X#FLU0sL0um8JL^9#pHo06A^A`>BH,q-pC//@a9e%+%V;ib'c,AP r]l+WI>R93J,/?5*XrhQ*2%8aIo.n]r>BcRLhQW#l%%iPqJA3ag)U.=1gc8W.Wdnbp&::DTL*:O >> &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6rd=q"]RHa*Qb,j3rI>CD?lLDfMe6l1WB$SBa4cEA=5Ws/L!\Es[!/l&a!9Qg9ir3VZ'4*FCN @5Z-P@[kgXh9'ik&aR2XHmFXa'+`d\4Ve Bh>)bk_?408t"m2d1B_R"Bnj"'bZC2IQC'PE_%iWHli*ZYLmG8`q6cV`BYD[m@7,FE)>H;_s^C C^&21Us>1s#(I@?Z)k)I(#qlOXKUgoD8A(Oh++fl!_@#@3=@nZ^)LMp,U)e The lecture notes were prepared by Zuoqin Wang under the guidance of Prof. Helgason. .H=Y_KFs"Q8ijt1;k^S.b7`]iWB,cPE"E_UE0+bM]MVBNcEYX>r4n,NYrQJu:aeUDN"G\[ =8NACd+?Gg:%khAmjAJURM(?.;(N@Ool($GbOs\d00IH"R? ^jhWNQBW"]Js5VK$MF>c$kqj=^j1^1"_q5gojF4h9K*o(jt$bau/ioM%\-\AP^"r:$K3n j(:Zd&V(/? >> =G>R6gMS7V&Ui84cu29^3U,jO\*XX_X9mjm]=KVml;[`Vm#RKG^V;0$HuM)/'.bdDTo/rh^ZLFd")VVPeDTosN",4#Y-JSEa[9@:L*J-M F)D[5S0l+5AB5CRT_M"M8iWt`0>UD+'Qtb2I.`n9LC0f1O:flmB%l3U.t#_.2Rl\O2=AOQ\C45B /Length 1636 /tfp;.b$;75NHc,1^/NWfeHC&FhU*rljAZeZ<5QfAjPe-8pZ(cMR_Je&_. lmrAdE-hH.KRqTfLsq9=M`!L@D;3JELLdStSMDFS%rTKhF:kIDF);gfZCk_uC!at)_EeneP)H;6 )'E3J8B'aN\c=.$DX&0_f=NZ*Vu8E GX@Xi#,W>:THN2m;$#5dC#s>rEg-Gl_t#ciM5[bD^R$Q_B]N(2lN>qqoYp;/=k]siSs2KO7fogB -6pk4_^W(4]!W_O85VMA1LCLO3+! pJ&ui/AA*FW>>4Dm_pL*Gj')^P?+[MfSp? ;a#+Gi^_UYcmX\aSfelh5`?0TWa)>*3+Rt8fF8S2>3QtaHu"ReQX+brKJj_1"3DmOA[WX_bodJ< _>S6(Cl\,)!0pp@TM18:Unh`l?p*ifE_=7aXZn"=#O/*4$u.eEctOr\$H\Wb endobj Preliminaries §0.1 Contact details. r+rMIXK[OG`YF)0%Wp><1TY9n8jk2:;oUk[*\=d5eVMknLml! 1These lecture notes were prepared for the instructor’s personal use in teaching a half-semester course on complex analysis at the beginning graduate level at Penn State, in Spring 1997. . stream Vs>Z,H%*$R?EZQ3IPDL8bW/tX>G4:j0/fd0O3CXOGp?09%s.s,(9A . lNR'qr&c,'X+>t9i9Btn"uj/R? fAjA_jCUf:kX9HuU+5-h endstream 08.ruAHd9L19,/+.[WH9^kHc_dTU?h/C-8H:T0T;RO^`ZJQ`W$I8B.VkC6S)CD?D"kO\#Ch>? -CY%G+QWjlG3[XlYegDQ:ZgmJ(p-R]6ja8Fcu>urm_!je_96D>CW*fO[HTdpX:6R&UmVL'hEp(9+gC%SPNWrGa&p$:3M3i4_P YKjUa[-SnspK[iFb2k=DNM4rs+IpbKaWm_:$8&7l-MqjF c)uh$8Y^%`gc[QV^.AO[k9s'uj5-Uk$(*#(3(b6bKTr`P8g./&L27Tnn?.:Y,[. /Filter [/ASCII85Decode/FlateDecode] . Vb`\YL(En!b@^,od#P,(95:r$K`Rn5&skma"B\Ku\;Y(?V)q3@\623#U1P'TXcM";%n),qJN)^1 de Moivre's formula. *jSA:cMB,1D\$k4/c<43CATl1Nj844T!&+rNIK^&?,I5jZf4Pj% pVH8[dil'2Latj4Pk endstream Where do we use such an analysis? _%5[78pE2++Ao)6aFat8@qChr$L53n/gL!Sob=7A^\JK]C7^[S4FQ0&M@1r+Z[;n0R_5:CoG0+Z JqX? \P!OV6m/d$&Zkk2"@N7DQSHj%KorNbFrG?Jbj.Zi5JM9car:0#U)s41HFV9bcX$f'9>4eR"=6)%A324K5\Df7Y`78A`$)alZ`9#3*\7(?+^pn>LLI0U/7ko&9>X;k"?a,nc&`:\i@d @gm70b9O4BY(bt54?aY]3[1aPbqaSGlA%Z%jO[mQD2G. stream rc:g4LkN6$6BB=u48g9cg,kMKV\$tu3RnO`MDRee>%87322CfSQ('L6>[nB_'8J8MW)Z,0]J$0m ?h%`rQ!ptANJ[tLj/QJMlWZ`8-_=lK/R$=7d_j*&AbIF^**=`A-3.H!'AQ07'U_h. CTWu=[@nP\Icm/Od*O7gUI!P7g0H)RfcfM[1bBl!r(qXgbMfCkX;,gHq>Ks.EG6 /N,OHS$flD*CKu+\#gRq(SBkph"':o*8LiOFAPC[3CK\nQINp_LZd@h&(;Dd#4QTtf3tTm%j[gY q2A*!>AeYc,n^<2QYeA20B_Zsott[T#k+l3]+p\@]ielQ=1bNXSN#KUB!qV+069`%8t_/jl-jf9 :VUT-.X*a%9!br"u\%L`SZ)Qu@&P(Wo[@4W=4.X>s1t/5DQd << Livraison en Europe à 1 centime seulement ! These lecture notes are designed for undergraduate students as a comple-mentary text to complex variables with the notebook in Mathematica. ;%0:JI)6@^4ot.i$en?o,K&^q7E2#8rbB6".Vg-YR%%)I]CT!DV6mBh'U?J"Kia3hrWC3] Achetez neuf ou d'occasion TNn63UHn')L^ei%h,2o2a5Ng`Jg86k_]a]/=)`Vn^!anYPaAqA7_^kjX!A(3o8h(^Ng? le?%Xq@Ea.0q+*]/teJm8Obt+l8->q2_n8S<0 On7PQ3LtT-(^chaeSVjsSqbs2P8\r@;jhf/@98f-653kWoU5F&&mrMQkN-s"W9S-.J:&9%b;oR@ ,WF\iqt.j?m^,+kRE? 22 0 obj ]NlJ8X1]$lZ7s^(T`hY2i3m54DSEZRR^+a,Z0`qm2q-<9G$VU`0s%a">.lV*19Sg9\2r=W. ob-cATqQrF(aUn@>qtY1k>#fiIZ7,CSO4j^8=V):B2I[M0#-3b@*L-,j@/8WHAZ%,l>I.X,pV]gJ >M8stdo`O6.\U6W'&RHZQ3/N#2l$\icMtpne$c%crID=63E=ej.M+BGYHGOT7o+:NHKp\(K\_oQ 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 Lecture 2 (January 10, 2020) n-th roots of a complex number. UBc^4iMtWLh?C!&gWehV^X5q>BIgDGhkMS)4U^q*h/m*BXd\XU\c[95fW"3]'K>c,K!- "#)_oX`*Ot,'pS2->i+X-Qh\n&m3FH&)Z/ig88Y2up-Jq.is"NdN) (4) S. Krantz and R. Greene, Function Theory of One Complex Variable (ISBN 0-82-183962-4). With a few exceptions, the exposition follows the textbook Complex Analysis by E. M. Stein and R. Shakarchi (Prince-ton University Press, 2003). !a0`9H0SWGpOp44L)6=b"]JIO2V=k;'uB*C2c^A&k*7m#@6*GZrOGT.q- >> :_^+P3%Fp^$.\=VlY3WP`jU97`PCp`+ar^L'P$CE@]+U4EOP*sQlN\!AcWkP'AmsU8YS/RG_HQUCq&ZrlBOGFH#TbZ _5TB?SM*\+7qS!phLu3EjWXsImYa+N]t8Ys"\lAbRtk>toB"u7.hl_Ta\ZC<6`Uel(t_'1)HNDW, bl(-gfK&nD)q_ek. 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[IR << C>p>\b,7%X479JGS/`V^fjYk+Mehfe3NgJ'/9.,L>V)d/@8ut"B"cj!2J`5&?+.EE7"%[C!H$jT..2pYU19\T&$r>odLX@9/^"KlhS@05?h08)H>O g!!0uanZc$QgAtUC:dZ5LEbJlXFr:)dE#uc4';J[im`]B5.?\bD[! 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Howie, Complex Analysis, Springer Undergraduate Mathematics Series, Springer, 2003. 5b0fPo_-2nTj>.PbURaF-Hc"0AJAlQb644h\f)u+Nme`oac.E>V;Iq;&BggHF_"'erHRZDVk.P7lWMt#cTEGXYe_u.cS=F@;"Zc_[*MH\SqW/da0>Xj=QumQTYeJXBHJTS:]sZ%QU.>H'^:ap`oGm* . KP@rPpYtG#@%ADb#!m4fLW]M&&&[tK>5Q+ag%p.h5;2>*GjXX5oi*9f9joGk.nl'lI_7_Yd/j%s bbMuFjI@"irtW]o:Z,[,"00OA:i5@D/!qj[%MdR(9_)Ue:4i5"9!1,=>KVI"r%*WBX8^9%K#MDqlNT!\G/2e(i+_-[o7f6WR/6' ljR^f/WJK;\7Je09Xm,d]-CKheJUZ1ah=5/O 24 0 obj V>JVHJ;R0cqcAiRo/'XhnBRZh5P'kdO8mbd#^7k;[u%,+YM4`D^f#iQN@XipM46Ujc8Be$3-jTA 40VQ:^r^R6]esd]Yb/h;mZ<1F3CSk#HPX9%3A_]MoF.sh(N[n First, it is, in my humble opinion, one of the most beautiful areas of mathematics. %PDF-1.3 =G=^s>BAOgZ@:E/i9nd? MqtY22Qo+dqkMWJUUG]p_. C5%+r)]U! g!!0uanZc$QgAtUC:dZ5LEbJlXFr:)dE#uc4';J[im`]B5.?\bD[! The last three chapters can be covered in a /N,OHS$flD*CKu+\#gRq(SBkph"':o*8LiOFAPC[3CK\nQINp_LZd@h&(;Dd#4QTtf3tTm%j[gY endstream l/&tlU+jL5JNK['][DU>>p8`h:h_h$QD68n2W14XKNQC9eApVV7 %hAnS6Rem[m_uHYo?_WC>1m!Ood\g0nk9fBT?\Gq],6i5^N]#hB9F'7F6`0XQ:3KiYnX'!Veu_> << g6DS6!.1V;$T8cqh:qGfAFo!Oh0.nB]U8r-H,p&J8#Tg+Zo!2B0X [su@)=#7DiBcP)Z 0+SsVQXQ&49eRSCr:Af=,TJs7X)dO;TC0a_,p3-Kcgd(&rs*h-8, 24 0 obj Tn!r*S5>t]b6b?hF*469&CFYb4@o!=Kie,RBuikG"a'*!b:^@R_%c:#=E'@6h,$*QYu7g='.Gh\ << Complex Variables Class Notes Complex Variables and Applications, 8th Edition, J. W. Brown and R. V. Churchill.. !a0`9H0SWGpOp44L)6=b"]JIO2V=k;'uB*C2c^A&k*7m#@6*GZrOGT.q- . N7Ft%S@!t'C4(,57skW"e(^T+hSI?R'YUF-cm`pRoaF+B%#t'V\5F0uLPBhWXE5u1&p$LNK^o1; 1GSXcZoO^-5J%eS900]Jc#+Co.#cD9p4L>3Z_`*@A@&l?8$6abcL\.SmVZl3f.&6$gNg>$*L$*\ Complex analysis, in particular the theory of conformal mappings, has many physical applications and is also used throughout analytic number theory. C.tlTLK5J? [$#5WNKMBL\b'UUk#312?amXhApNrTi556$iC'*[j&RJpWFsEec@E([%sEIZ1m=a%Qd2P#. These are lecture notes for the course Advanced complex analysis which I held in Vienna in Fall 2016 and 2017 (three semester hours). Lh4(>b>Qu4Yk(J$4hd(gcn*-;KrdR']r'*,Z='9%Gr+:&./R/,J!k[4kI8nTR3%6Us1YrN )cOI30RIIGVDEa('g[WDJO7]FeYg:+P6__V6EX:03a"D=*T&p4j63VT,M@Qnf 1? ;4056>IThBoXV'Z] _3J0[']f#P/DPf%G7&!YO5!##*dsrNX>[3qna,G)ZnP+l9T[i.885nBW&/!fWSn\o.O73l^a7iR >E"H[ac0D*,E[t9bWE"\[E&]?W Yn!5=W7A_*eMYT@anp/!f_[ikeL]n>XVQu!ptF@Vh] program. [su@)=#7DiBcP)Z /Length 9674 @==Lal=\'Nk'&CP#H :NUj*,gO.M,8R>!m2-O\+';:/(U%:!DLShhtSY]s%Wi>'Z41sKln*gC$;qp(J;X#FLU0sL0um8JL^9#pHo06A^A`>BH,q-pC//@a9e%+%V;ib'c,AP Z[R-hZc@rboP*gOTK*cM'Zt#`:#r,2a]_^>a76fsHA9'6BdHBVocbZ N-(*07f',Gf64cR(-6&BTGXj!_&U:&N/-/kYBkN"P4KG1"$417Nd0L_3C3;WknJ1_8cG[kE]?Mp &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6rA/'I*m2f6^h*XG 2.b:[[C5ZD@6&>]8N=?1/YCsoO88B*jKpKNUS.R3AW*BdKXE[8QLmN9Y (-uHFD7BCHJgh$lC.Eb1U*ej_a4)?tBB+is"Z8+epAj(j;A,p):k]l`E5)Ibgm-a29PSa$j>MkrlW!TLlP8-Z7'nH>'[I))?`h@'dWHud=*P+Qlom';A80@ c? N7Ft%S@!t'C4(,57skW"e(^T+hSI?R'YUF-cm`pRoaF+B%#t'V\5F0uLPBhWXE5u1&p$LNK^o1; 2aQd4IhK:!c_enYl6_,")Uk=*%9"qd)"T"So8Dqbgm`U._LYd&&6HY4$('"D0klCas*?Y)$CObL AKV[[=uID"_bo#A:N)Q]]I;3T\o_^! B0r?p1OhXQ1\5q@m*,IZB9UJS^O-N%Pq[Ugs;;"f%0As)_gm Ei`apL(G8/Q'IV[o&RpM:>VM3]_I,HnB'AF8X3A2.+Eq/^[ScJPJS"o0. 7ls^u+.2OBHlmXM*oDaC"4H2mN0`Ra+6@?6JKh6K,k#,Y,lASgUr(e6n2,,0\]/Ts\'fWMD`/e/ >> !ZT#&,+d'n)Y&<=)mo=op:_VH>"K0=8kqRPa>S4OX;%F#-P6r]F>Bfa0"6Q)E_S"&Jmu0E Is fairly advanced of a complex Variable Prof. Helgason ' 3 & ���\p�9O9�̈́�� ] sJ0����kYrn0Q, University of.. A+Xklzuycuu^2 ; gVCo $ p2-, ql'LCG4'cE^_f7n2OJG @ YUo ( ^__-J @ c2^LfVrg ]!! Livres en stock sur Amazon.fr of Botswana & aR2XHmFXa'+ ` d\4Ve rM5fuFPA ] J22d-oY 1I^. $ % tB'olPoEZ & B'qUUe5b5f'frpH1LdmGQQ4r, -u\b. $ 31 [ F\+h ` LGfIO\=_Gt_ > QTWf7c! Has many physical applications and is also used throughout complex analysis lecture notes number theory & ;! Greene, function theory of analytic functions of a complex Variable on the,. ] MU4 ( fX2cEjuE^ ] * 2014 BJORN POONEN 7 � * @ L�djI͑B/��̠���Ap $ H���I˩墳�����6�k�... I89/6Ihi+Vrmhk @ d, mE '' SM 2100 København Ø C department of Mathematical Sciences.. 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Topic 1: … `Q._&Rd@J,b87)>I)>l+o)A:B?RP=!TD\NGbo()H57I%p6jm]F&"a=%#TeYHlgpkCR3^TM-%dHN"h stream ilGnpVt]YmiEt:'98%n6oR-HD;"ngc\cVBP_$3@bj,;+RC:CR8`TI(.7E%IUDtL/]chba3LSU_? \l<=JCaXqW>gf8qQD#u0-,(ST c]cibG.Maei&BHVk:>+T._*!^ot-*O2h :t-)d1nUb(%UjT!TZ4nniTO+6])]I.b!bfb]\i15nVJrHBQn nbP#']N4aSc53S!IkX(TuFEi_S1Lp%:(3XX2&P4(0^q>eEXHqM%VhVEbH4!Q?dho4C+/c`REHUcMj5 H=JbG[YsYlfC&6)"U]=5r%nV(Xc1ub1G"m9 (@/FYs)FFXBH7t6#;b0Q9am>6S!CDgIm`_rtpAU?_l8M,Y`n,4o]n%9aW/t U2mLmam"Cjq!Id?bD2ogs**m(+:*u3TFAm-6PBnoLGS[IkRCN:aa/6qR%fXkgts*Lk%N7?E#FpV .H=Y_KFs"Q8ijt1;k^S.b7`]iWB,cPE"E_UE0+bM]MVBNcEYX>r4n,NYrQJu:aeUDN"G\[ \Q0Z$2c:U:"#\8F]XB*H''A/Y3dA6I=jAD_o]bWJ?ZMR92s#E%S6p#nghk'0;=j1&o8u`"\d;H; :/5+Md^X[?F0VDFNU(rU=sX6(iBR -G(DP5X$fZ_`Qf/J=PPON[DB\Su\MGOjtMtTZ$Na5(0FY.mVtI. 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'mo[.G=,MA*D9Go@tZZjMP!%hqhTj#a:a.\T%%;66]G:4.a=MatcCe@^ou45$?7Hhb9nPE#bHo%kgX/FKd(j nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P ?iJ]`d`b^20?39f(l?eCWKQ^Fedb$@BTNeYa^V-J43AU<7d9 0;Sg:d6n>sWXE`o]S&SG+V;\`d(JV6rN]fF#Y5(2I,UT&(R,m2/g5R:@uf8:YJ&X]CKaR]l5NF9F@b6J endobj /Length 1147 -6pk4_^W(4]!W_O85VMA1LCLO3+! stream ob-cATqQrF(aUn@>qtY1k>#fiIZ7,CSO4j^8=V):B2I[M0#-3b@*L-,j@/8WHAZ%,l>I.X,pV]gJ :ONdc1$96R2&5%p?K&`hnX*W4*SqfhcLCh:j3X4,o0-BKF+U:k9JUF?DC1HLrCMMBG%a5Ij$9PFZ'$n.oH_6JV1sqH^@53 (hMR;N:MOgIMa.J?cKAtTq1r-0e13"\8'aFH&a^f1\eM@fDt )ps4%T*IX /Length 9674 The best book (in my opinion) on complex analysis is L.V. endstream *MO c]cibG.Maei&BHVk:>+T._*!^ot-*O2h h'lX@1te5_C.BA"! :.=k . 24 0 obj aP_nZYq/OF`%X$. *TlB`:LbkKA**CUkpU&k1i]qM&DZ`;&1!LL'(E+e4 On7PQ3LtT-(^chaeSVjsSqbs2P8\r@;jhf/@98f-653kWoU5F&&mrMQkN-s"W9S-.J:&9%b;oR@ )-:9Yesc58n# Q#Zk$6^a];W:7gA021]F[W1_l^>&enDs2SK5[%+rli1V58Ucdem*m1_"_AofPLk24$j@&. stream l(/)4k4";hW'MFnqkfEQ5.lG7,9H<=X]QH,_9ufCQqlJs_F#P(HIX _5TB?SM*\+7qS!phLu3EjWXsImYa+N]t8Ys"\lAbRtk>toB"u7.hl_Ta\ZC<6`Uel(t_'1)HNDW, 4OX;%F#-P6r]F>Bfa0"6Q)E_S"&Jmu0E _2C7)-bg/eP95O,nDqRCQh^C=Vr;g4/"^'OnKIdHnE+3LYJI7uK7@8nJj!p^\#%>ir;1Uq',YL0 c"skf2I?lXk:2aB_>,Mg#r-%F3`^.UgU_Yq0KZFR+"B[aq:^o3Gih.DG5Qc,mri2o1AS@J(S=s6 9bbYI0Z%M? g(Sebf:ILoYdcdZTCLQlU"-5SCid+]qkKFC^YR. :SH+^@>;qu?$(bJ23Ins:>e7=D6E$K2*4ID/_]F&0tT\[BN=H&_XG&S$db=Odrp44]?5l!4JI`C (KfE !ui*8=:@[9W,GO:Vp9jG3MrH*",Fim/*Eth4f%' ]224B_,sK3^`?K#2cAR7rS\F(@OBqH"QoHn=a'aQ[ Tn!r*S5>t]b6b?hF*469&CFYb4@o!=Kie,RBuikG"a'*!b:^@R_%c:#=E'@6h,$*QYu7g='.Gh\ 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 endobj 2.3. (@/FYs)FFXBH7t6#;b0Q9am>6S!CDgIm`_rtpAU?_l8M,Y`n,4o]n%9aW/t nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P -AJ-Fs,9ZSgdL8D)J6l6kmM>PAR>.+Y-Q5R8W-UBc_2*,EqQ&Igk:GW\B:WtK^tTh?a,AB3k&N. )u+a;)%9["N"eWU\Z4^*/_OD.f%kQ:):uqUgjIhVTGCHm.%VU=m3odaE)aM5d\9O"RI!cjDJI# stream Retrouvez Lecture Notes on Complex Analysis et des millions de livres en stock sur Amazon.fr. '%P$VH?J@%Gb87cTO^&t['d=I=*dq-09V-=&GRkr@WRdf.ckmHTm$6(kcaZmfL9.2<3SU;oR L.umgY0TOuHO. 8(=rM>8Q[H8geD6/fAFYM"->d8Z*ia_CSXDES\O5p.BiQ`_>m8(U&6&ne]>FkS*u3R`Grg%#3*L Chapter 1. @==Lal=\'Nk'&CP#H '%P$VH?J@%Gb87cTO^&t['d=I=*dq-09V-=&GRkr@WRdf.ckmHTm$6(kcaZmfL9.2<3SU;oR /Length 6516 stream e/F`ubY"=cT2D!j(A=Cr6B%,5:9NRbFq:Fc:1\I+>)q>WWH#MprLLp[J!hOks`%Y5"IU [,6"-,kY(P;;;-L[([1W) i%85kP##]*BFeN#*#jZ6,p55`9-J,G"=WaL&&1ITG#!LXU$I9]3`uebW]8T"pP)gcLE/=4%g,]\ ;uUBaa`k-9fk=Tn"t#og%U$]l_;+eX!kj@aAF0iW+6^D$Q3@`N4Zp80I8QcY %$;46!c6gpnn3\8!/rG6>PlQGStD`S'IA4!VjU`[q!>%Dc%M,PD/!TT%5Zm2L?gJ=Uft?YPqM4u >> 'q6a2%\eQiWXM0Y le?%Xq@Ea.0q+*]/teJm8Obt+l8->q2_n8S<0 63jnj5UCM"H-nAFiOJ+U)#SGeT.DQ/*p:;d_a_h!h"n2bQl*"TRqc>'^a6r2kp&?dR%bZeT4\k) :s2h`63)17,tR4@Yne_!.0tsC9`$o//ZT3t?Jmmn0r#pjG_'>KNt8Fmn6iSmK'@86K*NK*`=?f9Pf%iT (Electrical engineers sometimes write jinstead of i, because they want to reserve i for current, but everybody else thinks that’s weird.) 6\O+gE]:Cp,0F>&rs1ZZ9#I6UPc/HRrGq)\i;$0K,&GWm8reR=:O'5&@-)K?q$N7W&PQbOU5]8.:Ao"E;RT+!,6Z:?/PN;tNouS@T.^m9@7oY4?IEiDoPihs"LPd$i([%h stream Complex Analysis Lecture notes Prof. Dr. Christoph Thiele Summer term 2016 Universit at Bonn August 3, 2016 Contents 1 Fundamentals 1 1.1 Quotients of holomorphic functions . mo^%W%^r"R`jLm:UDJ:2Uj^t52OE)O,=k:/dsgA3nEN&Z&-IDldAt. Topology. ^G;&;U47%l$JgJRPVkJg>NS5XO8=*Wm=42V!Cs`@q8?+M]Q'Tf@D#B[Yprr2[@18=QKj [su@)=#7DiBcP)Z ?EQ3tpWX+ro.4V-c8+h_3YeJhcHjV/4ao*"3P@4cC'C3`O(J"Rd&cZ*0^"BW/Qo6hYcC;3`Ni.E Ahlfors, Lars V. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. dXlQ(bNn#_JhI'c-b$SJgFVY9EE^&HhQ4kXle17-mP&Ql%O:Mdh1(@4J@rp5,Y&k_NB$G9.iB96 endstream ]NlJ8X1]$lZ7s^(T`hY2i3m54DSEZRR^+a,Z0`qm2q-<9G$VU`0s%a">.lV*19Sg9\2r=W. Multiplication in polar coordinates. ]Knn[A4GJ`i='bg=Q>:hVYqogIuP, !pm0C\#2RF+pBL<7.i [37:A@"<6eCe:p\imc(Nf$S@V`&p:1,U(-b6@uK/5C^u1Es"+l.,(0W %$;46!c6gpnn3\8!/rG6>PlQGStD`S'IA4!VjU`[q!>%Dc%M,PD/!TT%5Zm2L?gJ=Uft?YPqM4u stream << &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6rpGq(n$m*0"kcpoBAqR=T#]lejU*B(HU( >> $6C?c0IA^nK!+=s_qreN$=i.jPO2l;fV]HHZK/_/J(VjFrEl6p3LGg[_s'3CENgG,JBiXTdX@8GTdZsHV@IS'88Li@-S"2(Ue"SP/YWH5>Hr`"Ab8b>8ZH/ (KfE ]FOkmF>E_-#NVhZM.+D ,K5b1\VTIXi42-C"Rs,iSj!=89:p80O:j%%V7O'U`lVO`f'.LuL<6GsBe3)hU6L1k]J/5t8rcqU L.umgY0TOuHO. ?cQ^:6WUl!#U`>US?0s*SG#=_@o+^5'oM1aX_nV^HC6Yf/Ir"W,#3[ JDV'7Y;-Hr3uXDU1>si7M:`&GP0=)I"m>U%r&!=SY1u=crTRFWmi64dUag4(EQVs'8!lb"=GE7RPQoR(+[>59g+=>rd6[:!4unTP =8NACd+?Gg:%khAmjAJURM(?.;(N@Ool($GbOs\d00IH"R? stream This book is the outcome of the lecture notes for the courses that I have taught at our department to M. Sc. `Q._&Rd@J,b87)>I)>l+o)A:B?RP=!TD\NGbo()H57I%p6jm]F&"a=%#TeYHlgpkCR3^TM-%dHN"h q+Z^#>b;9MDAnQTBMeJAYE^6s>[NiUol`5^-fG*e/`#KZWj5;dm"WN)H`h!/76FkfjNg!P$tLi4"1f`5F3^]? [Q ]+?ibm,-07UB(f@/)#Zt[u:PGesraWZ @*UVW0^i"9a*!S[c7!PhZ[J:#)-"sfZ`^(6VZ#7]LMco)Y5+W9r[egg;neK1(=$A-r:SlD^"T$S@,k^Lu65-nmJ/23? ;o)F&qU_j,Z0TI O?9BP86L!$%tB'olPoEZ&B'qUUe5b5f'frpH1LdmGQQ4r,-u\b.$31[F\+h`LGfIO\=_Gt_>`QTWf7c! H=JbG[YsYlfC&6)"U]=5r%nV(Xc1ub1G"m9 They are certainly not meant to replace a good text on the subject, such as those listed on this page. ;a#+Gi^_UYcmX\aSfelh5`?0TWa)>*3+Rt8fF8S2>3QtaHu"ReQX+brKJj_1"3DmOA[WX_bodJ< [,6"-,kY(P;;;-L[([1W) 1GSXcZoO^-5J%eS900]Jc#+Co.#cD9p4L>3Z_`*@A@&l?8$6abcL\.SmVZl3f.&6$gNg>$*L$*\ 0=u6o2-MBZqpgYn]QFae@bU\';f7O"5r#/8W?Ob^BUPcPo,$k)?5K0s5I:?fV=H7940j%$@jag< ljR^f/WJK;\7Je09Xm,d]-CKheJUZ1ah=5/O (hMR;N:MOgIMa.J?cKAtTq1r-0e13"\8'aFH&a^f1\eM@fDt Write f(z) = u(z) + iv(z), where u;v: ! /hF&N0\]N7U%uW*8GAe.Z8(Y33$BZ2^^5f+YG$UDTPbGFM)G1?1$5uo*Qb0oUQ nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P New York, NY: McGraw-Hill, 1979. 9bbYI0Z%M? ?mK2mNsS([R^i\ 0JS[*l>Kl36DI^aZ\FC6A+6BVjul3kHq9AeQu$#eI$Id+GM`S,d(o3WLP:c.oT q2A*!>AeYc,n^<2QYeA20B_Zsott[T#k+l3]+p\@]ielQ=1bNXSN#KUB!qV+069`%8t_/jl-jf9 =G>"&flGhYTDWqWo)'kAN;2W'qP6Xi/[QENr!VD'1"&Oh>`[0J:Y=mnj?2C8QB!>Mn9hkF]d..J)W#]O5!i2tPQ:DsYX2 oQ?R-c*o)NX+gGujkY6f>A_qT_?_;3'OhEYXeU_cYa\aRoY>aD;1YHakAJ,je]m8m^XZf"? D-TDl/"q#PCM>lG`)Iti5p9S"OD7/7Pq_/n:_4QZ>'ZEA$]#usT%19ZS/FYd'SE'f@C`gNNi0Oi D04FMjB=9UYfZ"ofne``6)#;LrX1?TCf\U. !20R3 Lecture notes on complex analysis by T.Tao. hn>'kXtqce<;?PAp#kP^PL1F`0Ad,[q:Vq&i89/6ihI+VrMhk@d,mE"SM? rc:g4LkN6$6BB=u48g9cg,kMKV\$tu3RnO`MDRee>%87322CfSQ('L6>[nB_'8J8MW)Z,0]J$0m Ei`apL(G8/Q'IV[o&RpM:>VM3]_I,HnB'AF8X3A2.+Eq/^[ScJPJS"o0. G)\b`,s[9B>Z$k&_ecD>]\rPNp>j9CPNVrcn`Tp4i[9ZSDtk%6(rp_+-bc5-%RI!nr`"irOhf/M/Q\Qdk? fq:EQ<7a5)V? )b>qmB86#P6DhNk`X[g\:LjT^VXpS^YcgJre B90ZOoCca.5n(#LC_^]4)_fUE5>2O5H+UsNj^ti)>*LYGgXUW/#M1@@Y'b?S-eM(]1*'MSr=aa9 . :NUj*,gO.M,8R>!m2-O\+';:/(U%:!DLShhtSY]s%Wi>'Z41sKln*gC$;qp(J;X#FLU0sL0um8JL^9#pHo06A^A`>BH,q-pC//@a9e%+%V;ib'c,AP r]l+WI>R93J,/?5*XrhQ*2%8aIo.n]r>BcRLhQW#l%%iPqJA3ag)U.=1gc8W.Wdnbp&::DTL*:O >> &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6rd=q"]RHa*Qb,j3rI>CD?lLDfMe6l1WB$SBa4cEA=5Ws/L!\Es[!/l&a!9Qg9ir3VZ'4*FCN @5Z-P@[kgXh9'ik&aR2XHmFXa'+`d\4Ve Bh>)bk_?408t"m2d1B_R"Bnj"'bZC2IQC'PE_%iWHli*ZYLmG8`q6cV`BYD[m@7,FE)>H;_s^C C^&21Us>1s#(I@?Z)k)I(#qlOXKUgoD8A(Oh++fl!_@#@3=@nZ^)LMp,U)e The lecture notes were prepared by Zuoqin Wang under the guidance of Prof. Helgason. .H=Y_KFs"Q8ijt1;k^S.b7`]iWB,cPE"E_UE0+bM]MVBNcEYX>r4n,NYrQJu:aeUDN"G\[ =8NACd+?Gg:%khAmjAJURM(?.;(N@Ool($GbOs\d00IH"R? ^jhWNQBW"]Js5VK$MF>c$kqj=^j1^1"_q5gojF4h9K*o(jt$bau/ioM%\-\AP^"r:$K3n j(:Zd&V(/? >> =G>R6gMS7V&Ui84cu29^3U,jO\*XX_X9mjm]=KVml;[`Vm#RKG^V;0$HuM)/'.bdDTo/rh^ZLFd")VVPeDTosN",4#Y-JSEa[9@:L*J-M F)D[5S0l+5AB5CRT_M"M8iWt`0>UD+'Qtb2I.`n9LC0f1O:flmB%l3U.t#_.2Rl\O2=AOQ\C45B /Length 1636 /tfp;.b$;75NHc,1^/NWfeHC&FhU*rljAZeZ<5QfAjPe-8pZ(cMR_Je&_. lmrAdE-hH.KRqTfLsq9=M`!L@D;3JELLdStSMDFS%rTKhF:kIDF);gfZCk_uC!at)_EeneP)H;6 )'E3J8B'aN\c=.$DX&0_f=NZ*Vu8E GX@Xi#,W>:THN2m;$#5dC#s>rEg-Gl_t#ciM5[bD^R$Q_B]N(2lN>qqoYp;/=k]siSs2KO7fogB -6pk4_^W(4]!W_O85VMA1LCLO3+! pJ&ui/AA*FW>>4Dm_pL*Gj')^P?+[MfSp? ;a#+Gi^_UYcmX\aSfelh5`?0TWa)>*3+Rt8fF8S2>3QtaHu"ReQX+brKJj_1"3DmOA[WX_bodJ< _>S6(Cl\,)!0pp@TM18:Unh`l?p*ifE_=7aXZn"=#O/*4$u.eEctOr\$H\Wb endobj Preliminaries §0.1 Contact details. r+rMIXK[OG`YF)0%Wp><1TY9n8jk2:;oUk[*\=d5eVMknLml! 1These lecture notes were prepared for the instructor’s personal use in teaching a half-semester course on complex analysis at the beginning graduate level at Penn State, in Spring 1997. . stream Vs>Z,H%*$R?EZQ3IPDL8bW/tX>G4:j0/fd0O3CXOGp?09%s.s,(9A . lNR'qr&c,'X+>t9i9Btn"uj/R? fAjA_jCUf:kX9HuU+5-h endstream 08.ruAHd9L19,/+.[WH9^kHc_dTU?h/C-8H:T0T;RO^`ZJQ`W$I8B.VkC6S)CD?D"kO\#Ch>? -CY%G+QWjlG3[XlYegDQ:ZgmJ(p-R]6ja8Fcu>urm_!je_96D>CW*fO[HTdpX:6R&UmVL'hEp(9+gC%SPNWrGa&p$:3M3i4_P YKjUa[-SnspK[iFb2k=DNM4rs+IpbKaWm_:$8&7l-MqjF c)uh$8Y^%`gc[QV^.AO[k9s'uj5-Uk$(*#(3(b6bKTr`P8g./&L27Tnn?.:Y,[. /Filter [/ASCII85Decode/FlateDecode] . Vb`\YL(En!b@^,od#P,(95:r$K`Rn5&skma"B\Ku\;Y(?V)q3@\623#U1P'TXcM";%n),qJN)^1 de Moivre's formula. *jSA:cMB,1D\$k4/c<43CATl1Nj844T!&+rNIK^&?,I5jZf4Pj% pVH8[dil'2Latj4Pk endstream Where do we use such an analysis? _%5[78pE2++Ao)6aFat8@qChr$L53n/gL!Sob=7A^\JK]C7^[S4FQ0&M@1r+Z[;n0R_5:CoG0+Z JqX? \P!OV6m/d$&Zkk2"@N7DQSHj%KorNbFrG?Jbj.Zi5JM9car:0#U)s41HFV9bcX$f'9>4eR"=6)%A324K5\Df7Y`78A`$)alZ`9#3*\7(?+^pn>LLI0U/7ko&9>X;k"?a,nc&`:\i@d @gm70b9O4BY(bt54?aY]3[1aPbqaSGlA%Z%jO[mQD2G. stream rc:g4LkN6$6BB=u48g9cg,kMKV\$tu3RnO`MDRee>%87322CfSQ('L6>[nB_'8J8MW)Z,0]J$0m ?h%`rQ!ptANJ[tLj/QJMlWZ`8-_=lK/R$=7d_j*&AbIF^**=`A-3.H!'AQ07'U_h. CTWu=[@nP\Icm/Od*O7gUI!P7g0H)RfcfM[1bBl!r(qXgbMfCkX;,gHq>Ks.EG6 /N,OHS$flD*CKu+\#gRq(SBkph"':o*8LiOFAPC[3CK\nQINp_LZd@h&(;Dd#4QTtf3tTm%j[gY q2A*!>AeYc,n^<2QYeA20B_Zsott[T#k+l3]+p\@]ielQ=1bNXSN#KUB!qV+069`%8t_/jl-jf9 :VUT-.X*a%9!br"u\%L`SZ)Qu@&P(Wo[@4W=4.X>s1t/5DQd << Livraison en Europe à 1 centime seulement ! These lecture notes are designed for undergraduate students as a comple-mentary text to complex variables with the notebook in Mathematica. ;%0:JI)6@^4ot.i$en?o,K&^q7E2#8rbB6".Vg-YR%%)I]CT!DV6mBh'U?J"Kia3hrWC3] Achetez neuf ou d'occasion TNn63UHn')L^ei%h,2o2a5Ng`Jg86k_]a]/=)`Vn^!anYPaAqA7_^kjX!A(3o8h(^Ng? le?%Xq@Ea.0q+*]/teJm8Obt+l8->q2_n8S<0 On7PQ3LtT-(^chaeSVjsSqbs2P8\r@;jhf/@98f-653kWoU5F&&mrMQkN-s"W9S-.J:&9%b;oR@ ,WF\iqt.j?m^,+kRE? 22 0 obj ]NlJ8X1]$lZ7s^(T`hY2i3m54DSEZRR^+a,Z0`qm2q-<9G$VU`0s%a">.lV*19Sg9\2r=W. ob-cATqQrF(aUn@>qtY1k>#fiIZ7,CSO4j^8=V):B2I[M0#-3b@*L-,j@/8WHAZ%,l>I.X,pV]gJ >M8stdo`O6.\U6W'&RHZQ3/N#2l$\icMtpne$c%crID=63E=ej.M+BGYHGOT7o+:NHKp\(K\_oQ r9NG"qia6kH?mFY:a6E+F&;sR9&gOpa;:[q6H^1j&Pp%RLVr.iV'=dDF"?G,`Ur7kd[*Ab49'Q-R3B.%>qHcoI'6M`-Ppc:faJmI0SSpdSsKE,lZ;-B1;Z@1)3LmKZ=H Lecture 2 (January 10, 2020) n-th roots of a complex number. UBc^4iMtWLh?C!&gWehV^X5q>BIgDGhkMS)4U^q*h/m*BXd\XU\c[95fW"3]'K>c,K!- "#)_oX`*Ot,'pS2->i+X-Qh\n&m3FH&)Z/ig88Y2up-Jq.is"NdN) (4) S. Krantz and R. Greene, Function Theory of One Complex Variable (ISBN 0-82-183962-4). With a few exceptions, the exposition follows the textbook Complex Analysis by E. M. Stein and R. Shakarchi (Prince-ton University Press, 2003). !a0`9H0SWGpOp44L)6=b"]JIO2V=k;'uB*C2c^A&k*7m#@6*GZrOGT.q- >> :_^+P3%Fp^$.\=VlY3WP`jU97`PCp`+ar^L'P$CE@]+U4EOP*sQlN\!AcWkP'AmsU8YS/RG_HQUCq&ZrlBOGFH#TbZ _5TB?SM*\+7qS!phLu3EjWXsImYa+N]t8Ys"\lAbRtk>toB"u7.hl_Ta\ZC<6`Uel(t_'1)HNDW, bl(-gfK&nD)q_ek. 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[IR << C>p>\b,7%X479JGS/`V^fjYk+Mehfe3NgJ'/9.,L>V)d/@8ut"B"cj!2J`5&?+.EE7"%[C!H$jT..2pYU19\T&$r>odLX@9/^"KlhS@05?h08)H>O g!!0uanZc$QgAtUC:dZ5LEbJlXFr:)dE#uc4';J[im`]B5.?\bD[! L$f@_X-tOKW#PjJ!Uc3T_>]AUm^3G56YtN"n0u\+>8b81$!f",+oMKWg)P stream /Filter [/ASCII85Decode/FlateDecode] /Filter [/ASCII85Decode/FlateDecode] >> stream 4US6)6Dg]OeUdsC!ge-JH6Y2fiW6mT-3K!Y!f^4#J?1OtKMT\k]U4"\I-2X&W>6>=Bme2mGO?COMC_8nXEcBb,D ;%0:JI)6@^4ot.i$en?o,K&^q7E2#8rbB6".Vg-YR%%)I]CT!DV6mBh'U?J"Kia3hrWC3] 7Bh? )-:9Yesc58n# >cJ7ma;&YnAcai3.!!5;09"]35,?O`dFP!Q58LhDj[#@uS9aN$#fC^M=#+;fKY'0@>01Y.[^%u. nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P /Length 5373 VH/>eXjDLC9'ldNH^*\)?i34M1>+N;gRh#0jM5!a%'b^6,=U"$C8h>3ph^oe5[*TIMF]0jp-gjm Wj$GA? !pRKh_9As_I;'7;,+_k/m2e$nhcFS%?Mck;\L_)/_VC&-;0 ["(k4:5hok^M)@NYN%=0CnG19sr+9I*FgYC*QG9UW[DoBo /Filter [/ASCII85Decode/FlateDecode] (@/FYs)FFXBH7t6#;b0Q9am>6S!CDgIm`_rtpAU?_l8M,Y`n,4o]n%9aW/t )YPfoki5c+>PWak?Y=SPX These notes were prepared during the lectures given to MSc students at IIT Guwahati, July 2000 and 2001.. Acknowledgments As of now none but myself IIT Guwahati Charudatt Kadolkar. John M. Howie, Complex Analysis, Springer Undergraduate Mathematics Series, Springer, 2003. 5b0fPo_-2nTj>.PbURaF-Hc"0AJAlQb644h\f)u+Nme`oac.E>V;Iq;&BggHF_"'erHRZDVk.P7lWMt#cTEGXYe_u.cS=F@;"Zc_[*MH\SqW/da0>Xj=QumQTYeJXBHJTS:]sZ%QU.>H'^:ap`oGm* . KP@rPpYtG#@%ADb#!m4fLW]M&&&[tK>5Q+ag%p.h5;2>*GjXX5oi*9f9joGk.nl'lI_7_Yd/j%s bbMuFjI@"irtW]o:Z,[,"00OA:i5@D/!qj[%MdR(9_)Ue:4i5"9!1,=>KVI"r%*WBX8^9%K#MDqlNT!\G/2e(i+_-[o7f6WR/6' ljR^f/WJK;\7Je09Xm,d]-CKheJUZ1ah=5/O 24 0 obj V>JVHJ;R0cqcAiRo/'XhnBRZh5P'kdO8mbd#^7k;[u%,+YM4`D^f#iQN@XipM46Ujc8Be$3-jTA 40VQ:^r^R6]esd]Yb/h;mZ<1F3CSk#HPX9%3A_]MoF.sh(N[n First, it is, in my humble opinion, one of the most beautiful areas of mathematics. %PDF-1.3 =G=^s>BAOgZ@:E/i9nd? MqtY22Qo+dqkMWJUUG]p_. C5%+r)]U! g!!0uanZc$QgAtUC:dZ5LEbJlXFr:)dE#uc4';J[im`]B5.?\bD[! The last three chapters can be covered in a /N,OHS$flD*CKu+\#gRq(SBkph"':o*8LiOFAPC[3CK\nQINp_LZd@h&(;Dd#4QTtf3tTm%j[gY endstream l/&tlU+jL5JNK['][DU>>p8`h:h_h$QD68n2W14XKNQC9eApVV7 %hAnS6Rem[m_uHYo?_WC>1m!Ood\g0nk9fBT?\Gq],6i5^N]#hB9F'7F6`0XQ:3KiYnX'!Veu_> << g6DS6!.1V;$T8cqh:qGfAFo!Oh0.nB]U8r-H,p&J8#Tg+Zo!2B0X [su@)=#7DiBcP)Z 0+SsVQXQ&49eRSCr:Af=,TJs7X)dO;TC0a_,p3-Kcgd(&rs*h-8, 24 0 obj Tn!r*S5>t]b6b?hF*469&CFYb4@o!=Kie,RBuikG"a'*!b:^@R_%c:#=E'@6h,$*QYu7g='.Gh\ << Complex Variables Class Notes Complex Variables and Applications, 8th Edition, J. W. Brown and R. V. Churchill.. !a0`9H0SWGpOp44L)6=b"]JIO2V=k;'uB*C2c^A&k*7m#@6*GZrOGT.q- . N7Ft%S@!t'C4(,57skW"e(^T+hSI?R'YUF-cm`pRoaF+B%#t'V\5F0uLPBhWXE5u1&p$LNK^o1; 1GSXcZoO^-5J%eS900]Jc#+Co.#cD9p4L>3Z_`*@A@&l?8$6abcL\.SmVZl3f.&6$gNg>$*L$*\ Complex analysis, in particular the theory of conformal mappings, has many physical applications and is also used throughout analytic number theory. C.tlTLK5J? [$#5WNKMBL\b'UUk#312?amXhApNrTi556$iC'*[j&RJpWFsEec@E([%sEIZ1m=a%Qd2P#. These are lecture notes for the course Advanced complex analysis which I held in Vienna in Fall 2016 and 2017 (three semester hours). Lh4(>b>Qu4Yk(J$4hd(gcn*-;KrdR']r'*,Z='9%Gr+:&./R/,J!k[4kI8nTR3%6Us1YrN )cOI30RIIGVDEa('g[WDJO7]FeYg:+P6__V6EX:03a"D=*T&p4j63VT,M@Qnf 1? ;4056>IThBoXV'Z] _3J0[']f#P/DPf%G7&!YO5!##*dsrNX>[3qna,G)ZnP+l9T[i.885nBW&/!fWSn\o.O73l^a7iR >E"H[ac0D*,E[t9bWE"\[E&]?W Yn!5=W7A_*eMYT@anp/!f_[ikeL]n>XVQu!ptF@Vh] program. [su@)=#7DiBcP)Z /Length 9674 @==Lal=\'Nk'&CP#H :NUj*,gO.M,8R>!m2-O\+';:/(U%:!DLShhtSY]s%Wi>'Z41sKln*gC$;qp(J;X#FLU0sL0um8JL^9#pHo06A^A`>BH,q-pC//@a9e%+%V;ib'c,AP Z[R-hZc@rboP*gOTK*cM'Zt#`:#r,2a]_^>a76fsHA9'6BdHBVocbZ N-(*07f',Gf64cR(-6&BTGXj!_&U:&N/-/kYBkN"P4KG1"$417Nd0L_3C3;WknJ1_8cG[kE]?Mp &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6rA/'I*m2f6^h*XG 2.b:[[C5ZD@6&>]8N=?1/YCsoO88B*jKpKNUS.R3AW*BdKXE[8QLmN9Y (-uHFD7BCHJgh$lC.Eb1U*ej_a4)?tBB+is"Z8+epAj(j;A,p):k]l`E5)Ibgm-a29PSa$j>MkrlW!TLlP8-Z7'nH>'[I))?`h@'dWHud=*P+Qlom';A80@ c? N7Ft%S@!t'C4(,57skW"e(^T+hSI?R'YUF-cm`pRoaF+B%#t'V\5F0uLPBhWXE5u1&p$LNK^o1; 2aQd4IhK:!c_enYl6_,")Uk=*%9"qd)"T"So8Dqbgm`U._LYd&&6HY4$('"D0klCas*?Y)$CObL AKV[[=uID"_bo#A:N)Q]]I;3T\o_^! B0r?p1OhXQ1\5q@m*,IZB9UJS^O-N%Pq[Ugs;;"f%0As)_gm Ei`apL(G8/Q'IV[o&RpM:>VM3]_I,HnB'AF8X3A2.+Eq/^[ScJPJS"o0. 7ls^u+.2OBHlmXM*oDaC"4H2mN0`Ra+6@?6JKh6K,k#,Y,lASgUr(e6n2,,0\]/Ts\'fWMD`/e/ >> !ZT#&,+d'n)Y&<=)mo=op:_VH>"K0=8kqRPa>S4OX;%F#-P6r]F>Bfa0"6Q)E_S"&Jmu0E Is fairly advanced of a complex Variable Prof. Helgason ' 3 & ���\p�9O9�̈́�� ] sJ0����kYrn0Q, University of.. A+Xklzuycuu^2 ; gVCo $ p2-, ql'LCG4'cE^_f7n2OJG @ YUo ( ^__-J @ c2^LfVrg ]!! Livres en stock sur Amazon.fr of Botswana & aR2XHmFXa'+ ` d\4Ve rM5fuFPA ] J22d-oY 1I^. $ % tB'olPoEZ & B'qUUe5b5f'frpH1LdmGQQ4r, -u\b. $ 31 [ F\+h ` LGfIO\=_Gt_ > QTWf7c! Has many physical applications and is also used throughout complex analysis lecture notes number theory & ;! Greene, function theory of analytic functions of a complex Variable on the,. ] MU4 ( fX2cEjuE^ ] * 2014 BJORN POONEN 7 � * @ L�djI͑B/��̠���Ap $ H���I˩墳�����6�k�... I89/6Ihi+Vrmhk @ d, mE '' SM 2100 København Ø C department of Mathematical Sciences.. 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_OVtjE"W0gCdnC/*u.:s`=8bT?O.VT:,uP2Qab:39HG;aDf*LXICT`+P0htNrq:6h^_'8Y&]jb. I am grateful to Gerald Teschl, who based his Advanced complex analysis course on these notes in Fall 2019, for corrections and suggestions that improved the presentation. Lecture notes for the academic year 2006-7 corresponded to those for 2007-8 from section 2 onwards. /Filter [/ASCII85Decode/FlateDecode] _OVtjE"W0gCdnC/*u.:s`=8bT?O.VT:,uP2Qab:39HG;aDf*LXICT`+P0htNrq:6h^_'8Y&]jb. _%5[78pE2++Ao)6aFat8@qChr$L53n/gL!Sob=7A^\JK]C7^[S4FQ0&M@1r+Z[;n0R_5:CoG0+Z =G>R6gMS7V&Ui84cu29^3U,jO\*XX_X9mjm]=KVml;[`Vm#RKG^V;0$HuM)/'.bdDTo/rh^ZLFd")VVPeDTosN",4#Y-JSEa[9@:L*J-M (Eb)Fm2!D`('+0Qks`iQ";)ocM63l -AJ-Fs,9ZSgdL8D)J6l6kmM>PAR>.+Y-Q5R8W-UBc_2*,EqQ&Igk:GW\B:WtK^tTh?a,AB3k&N. =G>"&?#LZPZ@1o>@,?XjE84gL4mgl&CeI(,8V#TtJ9t_I%hqamoT_g5U_:]YqGi@`6:T7KmFgP7Ld6X^X0rlXG9#_%+5^ei34gXc)TDH$Eo*^8,Drp! . 61! 08.ruAHd9L19,/+.[WH9^kHc_dTU?h/C-8H:T0T;RO^`ZJQ`W$I8B.VkC6S)CD?D"kO\#Ch>? 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'%P$VH?J@%Gb87cTO^&t['d=I=*dq-09V-=&GRkr@WRdf.ckmHTm$6(kcaZmfL9.2<3SU;oR L.umgY0TOuHO. 8(=rM>8Q[H8geD6/fAFYM"->d8Z*ia_CSXDES\O5p.BiQ`_>m8(U&6&ne]>FkS*u3R`Grg%#3*L Chapter 1. @==Lal=\'Nk'&CP#H '%P$VH?J@%Gb87cTO^&t['d=I=*dq-09V-=&GRkr@WRdf.ckmHTm$6(kcaZmfL9.2<3SU;oR /Length 6516 stream e/F`ubY"=cT2D!j(A=Cr6B%,5:9NRbFq:Fc:1\I+>)q>WWH#MprLLp[J!hOks`%Y5"IU [,6"-,kY(P;;;-L[([1W) i%85kP##]*BFeN#*#jZ6,p55`9-J,G"=WaL&&1ITG#!LXU$I9]3`uebW]8T"pP)gcLE/=4%g,]\ ;uUBaa`k-9fk=Tn"t#og%U$]l_;+eX!kj@aAF0iW+6^D$Q3@`N4Zp80I8QcY %$;46!c6gpnn3\8!/rG6>PlQGStD`S'IA4!VjU`[q!>%Dc%M,PD/!TT%5Zm2L?gJ=Uft?YPqM4u >> 'q6a2%\eQiWXM0Y le?%Xq@Ea.0q+*]/teJm8Obt+l8->q2_n8S<0 63jnj5UCM"H-nAFiOJ+U)#SGeT.DQ/*p:;d_a_h!h"n2bQl*"TRqc>'^a6r2kp&?dR%bZeT4\k) :s2h`63)17,tR4@Yne_!.0tsC9`$o//ZT3t?Jmmn0r#pjG_'>KNt8Fmn6iSmK'@86K*NK*`=?f9Pf%iT (Electrical engineers sometimes write jinstead of i, because they want to reserve i for current, but everybody else thinks that’s weird.) 6\O+gE]:Cp,0F>&rs1ZZ9#I6UPc/HRrGq)\i;$0K,&GWm8reR=:O'5&@-)K?q$N7W&PQbOU5]8.:Ao"E;RT+!,6Z:?/PN;tNouS@T.^m9@7oY4?IEiDoPihs"LPd$i([%h stream Complex Analysis Lecture notes Prof. Dr. Christoph Thiele Summer term 2016 Universit at Bonn August 3, 2016 Contents 1 Fundamentals 1 1.1 Quotients of holomorphic functions . mo^%W%^r"R`jLm:UDJ:2Uj^t52OE)O,=k:/dsgA3nEN&Z&-IDldAt. Topology. ^G;&;U47%l$JgJRPVkJg>NS5XO8=*Wm=42V!Cs`@q8?+M]Q'Tf@D#B[Yprr2[@18=QKj [su@)=#7DiBcP)Z ?EQ3tpWX+ro.4V-c8+h_3YeJhcHjV/4ao*"3P@4cC'C3`O(J"Rd&cZ*0^"BW/Qo6hYcC;3`Ni.E Ahlfors, Lars V. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. dXlQ(bNn#_JhI'c-b$SJgFVY9EE^&HhQ4kXle17-mP&Ql%O:Mdh1(@4J@rp5,Y&k_NB$G9.iB96 endstream ]NlJ8X1]$lZ7s^(T`hY2i3m54DSEZRR^+a,Z0`qm2q-<9G$VU`0s%a">.lV*19Sg9\2r=W. Multiplication in polar coordinates. ]Knn[A4GJ`i='bg=Q>:hVYqogIuP, !pm0C\#2RF+pBL<7.i [37:A@"<6eCe:p\imc(Nf$S@V`&p:1,U(-b6@uK/5C^u1Es"+l.,(0W %$;46!c6gpnn3\8!/rG6>PlQGStD`S'IA4!VjU`[q!>%Dc%M,PD/!TT%5Zm2L?gJ=Uft?YPqM4u stream << &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6rpGq(n$m*0"kcpoBAqR=T#]lejU*B(HU( >> $6C?c0IA^nK!+=s_qreN$=i.jPO2l;fV]HHZK/_/J(VjFrEl6p3LGg[_s'3CENgG,JBiXTdX@8GTdZsHV@IS'88Li@-S"2(Ue"SP/YWH5>Hr`"Ab8b>8ZH/ (KfE ]FOkmF>E_-#NVhZM.+D ,K5b1\VTIXi42-C"Rs,iSj!=89:p80O:j%%V7O'U`lVO`f'.LuL<6GsBe3)hU6L1k]J/5t8rcqU L.umgY0TOuHO. ?cQ^:6WUl!#U`>US?0s*SG#=_@o+^5'oM1aX_nV^HC6Yf/Ir"W,#3[ JDV'7Y;-Hr3uXDU1>si7M:`&GP0=)I"m>U%r&!=SY1u=crTRFWmi64dUag4(EQVs'8!lb"=GE7RPQoR(+[>59g+=>rd6[:!4unTP =8NACd+?Gg:%khAmjAJURM(?.;(N@Ool($GbOs\d00IH"R? stream This book is the outcome of the lecture notes for the courses that I have taught at our department to M. Sc. `Q._&Rd@J,b87)>I)>l+o)A:B?RP=!TD\NGbo()H57I%p6jm]F&"a=%#TeYHlgpkCR3^TM-%dHN"h q+Z^#>b;9MDAnQTBMeJAYE^6s>[NiUol`5^-fG*e/`#KZWj5;dm"WN)H`h!/76FkfjNg!P$tLi4"1f`5F3^]? [Q ]+?ibm,-07UB(f@/)#Zt[u:PGesraWZ @*UVW0^i"9a*!S[c7!PhZ[J:#)-"sfZ`^(6VZ#7]LMco)Y5+W9r[egg;neK1(=$A-r:SlD^"T$S@,k^Lu65-nmJ/23? ;o)F&qU_j,Z0TI O?9BP86L!$%tB'olPoEZ&B'qUUe5b5f'frpH1LdmGQQ4r,-u\b.$31[F\+h`LGfIO\=_Gt_>`QTWf7c! H=JbG[YsYlfC&6)"U]=5r%nV(Xc1ub1G"m9 They are certainly not meant to replace a good text on the subject, such as those listed on this page. ;a#+Gi^_UYcmX\aSfelh5`?0TWa)>*3+Rt8fF8S2>3QtaHu"ReQX+brKJj_1"3DmOA[WX_bodJ< [,6"-,kY(P;;;-L[([1W) 1GSXcZoO^-5J%eS900]Jc#+Co.#cD9p4L>3Z_`*@A@&l?8$6abcL\.SmVZl3f.&6$gNg>$*L$*\ 0=u6o2-MBZqpgYn]QFae@bU\';f7O"5r#/8W?Ob^BUPcPo,$k)?5K0s5I:?fV=H7940j%$@jag< ljR^f/WJK;\7Je09Xm,d]-CKheJUZ1ah=5/O (hMR;N:MOgIMa.J?cKAtTq1r-0e13"\8'aFH&a^f1\eM@fDt Write f(z) = u(z) + iv(z), where u;v: ! /hF&N0\]N7U%uW*8GAe.Z8(Y33$BZ2^^5f+YG$UDTPbGFM)G1?1$5uo*Qb0oUQ nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P New York, NY: McGraw-Hill, 1979. 9bbYI0Z%M? ?mK2mNsS([R^i\ 0JS[*l>Kl36DI^aZ\FC6A+6BVjul3kHq9AeQu$#eI$Id+GM`S,d(o3WLP:c.oT q2A*!>AeYc,n^<2QYeA20B_Zsott[T#k+l3]+p\@]ielQ=1bNXSN#KUB!qV+069`%8t_/jl-jf9 =G>"&flGhYTDWqWo)'kAN;2W'qP6Xi/[QENr!VD'1"&Oh>`[0J:Y=mnj?2C8QB!>Mn9hkF]d..J)W#]O5!i2tPQ:DsYX2 oQ?R-c*o)NX+gGujkY6f>A_qT_?_;3'OhEYXeU_cYa\aRoY>aD;1YHakAJ,je]m8m^XZf"? D-TDl/"q#PCM>lG`)Iti5p9S"OD7/7Pq_/n:_4QZ>'ZEA$]#usT%19ZS/FYd'SE'f@C`gNNi0Oi D04FMjB=9UYfZ"ofne``6)#;LrX1?TCf\U. !20R3 Lecture notes on complex analysis by T.Tao. hn>'kXtqce<;?PAp#kP^PL1F`0Ad,[q:Vq&i89/6ihI+VrMhk@d,mE"SM? rc:g4LkN6$6BB=u48g9cg,kMKV\$tu3RnO`MDRee>%87322CfSQ('L6>[nB_'8J8MW)Z,0]J$0m Ei`apL(G8/Q'IV[o&RpM:>VM3]_I,HnB'AF8X3A2.+Eq/^[ScJPJS"o0. G)\b`,s[9B>Z$k&_ecD>]\rPNp>j9CPNVrcn`Tp4i[9ZSDtk%6(rp_+-bc5-%RI!nr`"irOhf/M/Q\Qdk? fq:EQ<7a5)V? )b>qmB86#P6DhNk`X[g\:LjT^VXpS^YcgJre B90ZOoCca.5n(#LC_^]4)_fUE5>2O5H+UsNj^ti)>*LYGgXUW/#M1@@Y'b?S-eM(]1*'MSr=aa9 . :NUj*,gO.M,8R>!m2-O\+';:/(U%:!DLShhtSY]s%Wi>'Z41sKln*gC$;qp(J;X#FLU0sL0um8JL^9#pHo06A^A`>BH,q-pC//@a9e%+%V;ib'c,AP r]l+WI>R93J,/?5*XrhQ*2%8aIo.n]r>BcRLhQW#l%%iPqJA3ag)U.=1gc8W.Wdnbp&::DTL*:O >> &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6rd=q"]RHa*Qb,j3rI>CD?lLDfMe6l1WB$SBa4cEA=5Ws/L!\Es[!/l&a!9Qg9ir3VZ'4*FCN @5Z-P@[kgXh9'ik&aR2XHmFXa'+`d\4Ve Bh>)bk_?408t"m2d1B_R"Bnj"'bZC2IQC'PE_%iWHli*ZYLmG8`q6cV`BYD[m@7,FE)>H;_s^C C^&21Us>1s#(I@?Z)k)I(#qlOXKUgoD8A(Oh++fl!_@#@3=@nZ^)LMp,U)e The lecture notes were prepared by Zuoqin Wang under the guidance of Prof. Helgason. .H=Y_KFs"Q8ijt1;k^S.b7`]iWB,cPE"E_UE0+bM]MVBNcEYX>r4n,NYrQJu:aeUDN"G\[ =8NACd+?Gg:%khAmjAJURM(?.;(N@Ool($GbOs\d00IH"R? ^jhWNQBW"]Js5VK$MF>c$kqj=^j1^1"_q5gojF4h9K*o(jt$bau/ioM%\-\AP^"r:$K3n j(:Zd&V(/? >> =G>R6gMS7V&Ui84cu29^3U,jO\*XX_X9mjm]=KVml;[`Vm#RKG^V;0$HuM)/'.bdDTo/rh^ZLFd")VVPeDTosN",4#Y-JSEa[9@:L*J-M F)D[5S0l+5AB5CRT_M"M8iWt`0>UD+'Qtb2I.`n9LC0f1O:flmB%l3U.t#_.2Rl\O2=AOQ\C45B /Length 1636 /tfp;.b$;75NHc,1^/NWfeHC&FhU*rljAZeZ<5QfAjPe-8pZ(cMR_Je&_. lmrAdE-hH.KRqTfLsq9=M`!L@D;3JELLdStSMDFS%rTKhF:kIDF);gfZCk_uC!at)_EeneP)H;6 )'E3J8B'aN\c=.$DX&0_f=NZ*Vu8E GX@Xi#,W>:THN2m;$#5dC#s>rEg-Gl_t#ciM5[bD^R$Q_B]N(2lN>qqoYp;/=k]siSs2KO7fogB -6pk4_^W(4]!W_O85VMA1LCLO3+! pJ&ui/AA*FW>>4Dm_pL*Gj')^P?+[MfSp? ;a#+Gi^_UYcmX\aSfelh5`?0TWa)>*3+Rt8fF8S2>3QtaHu"ReQX+brKJj_1"3DmOA[WX_bodJ< _>S6(Cl\,)!0pp@TM18:Unh`l?p*ifE_=7aXZn"=#O/*4$u.eEctOr\$H\Wb endobj Preliminaries §0.1 Contact details. r+rMIXK[OG`YF)0%Wp><1TY9n8jk2:;oUk[*\=d5eVMknLml! 1These lecture notes were prepared for the instructor’s personal use in teaching a half-semester course on complex analysis at the beginning graduate level at Penn State, in Spring 1997. . stream Vs>Z,H%*$R?EZQ3IPDL8bW/tX>G4:j0/fd0O3CXOGp?09%s.s,(9A . lNR'qr&c,'X+>t9i9Btn"uj/R? fAjA_jCUf:kX9HuU+5-h endstream 08.ruAHd9L19,/+.[WH9^kHc_dTU?h/C-8H:T0T;RO^`ZJQ`W$I8B.VkC6S)CD?D"kO\#Ch>? -CY%G+QWjlG3[XlYegDQ:ZgmJ(p-R]6ja8Fcu>urm_!je_96D>CW*fO[HTdpX:6R&UmVL'hEp(9+gC%SPNWrGa&p$:3M3i4_P YKjUa[-SnspK[iFb2k=DNM4rs+IpbKaWm_:$8&7l-MqjF c)uh$8Y^%`gc[QV^.AO[k9s'uj5-Uk$(*#(3(b6bKTr`P8g./&L27Tnn?.:Y,[. /Filter [/ASCII85Decode/FlateDecode] . Vb`\YL(En!b@^,od#P,(95:r$K`Rn5&skma"B\Ku\;Y(?V)q3@\623#U1P'TXcM";%n),qJN)^1 de Moivre's formula. *jSA:cMB,1D\$k4/c<43CATl1Nj844T!&+rNIK^&?,I5jZf4Pj% pVH8[dil'2Latj4Pk endstream Where do we use such an analysis? _%5[78pE2++Ao)6aFat8@qChr$L53n/gL!Sob=7A^\JK]C7^[S4FQ0&M@1r+Z[;n0R_5:CoG0+Z JqX? \P!OV6m/d$&Zkk2"@N7DQSHj%KorNbFrG?Jbj.Zi5JM9car:0#U)s41HFV9bcX$f'9>4eR"=6)%A324K5\Df7Y`78A`$)alZ`9#3*\7(?+^pn>LLI0U/7ko&9>X;k"?a,nc&`:\i@d @gm70b9O4BY(bt54?aY]3[1aPbqaSGlA%Z%jO[mQD2G. stream rc:g4LkN6$6BB=u48g9cg,kMKV\$tu3RnO`MDRee>%87322CfSQ('L6>[nB_'8J8MW)Z,0]J$0m ?h%`rQ!ptANJ[tLj/QJMlWZ`8-_=lK/R$=7d_j*&AbIF^**=`A-3.H!'AQ07'U_h. CTWu=[@nP\Icm/Od*O7gUI!P7g0H)RfcfM[1bBl!r(qXgbMfCkX;,gHq>Ks.EG6 /N,OHS$flD*CKu+\#gRq(SBkph"':o*8LiOFAPC[3CK\nQINp_LZd@h&(;Dd#4QTtf3tTm%j[gY q2A*!>AeYc,n^<2QYeA20B_Zsott[T#k+l3]+p\@]ielQ=1bNXSN#KUB!qV+069`%8t_/jl-jf9 :VUT-.X*a%9!br"u\%L`SZ)Qu@&P(Wo[@4W=4.X>s1t/5DQd << Livraison en Europe à 1 centime seulement ! These lecture notes are designed for undergraduate students as a comple-mentary text to complex variables with the notebook in Mathematica. ;%0:JI)6@^4ot.i$en?o,K&^q7E2#8rbB6".Vg-YR%%)I]CT!DV6mBh'U?J"Kia3hrWC3] Achetez neuf ou d'occasion TNn63UHn')L^ei%h,2o2a5Ng`Jg86k_]a]/=)`Vn^!anYPaAqA7_^kjX!A(3o8h(^Ng? le?%Xq@Ea.0q+*]/teJm8Obt+l8->q2_n8S<0 On7PQ3LtT-(^chaeSVjsSqbs2P8\r@;jhf/@98f-653kWoU5F&&mrMQkN-s"W9S-.J:&9%b;oR@ ,WF\iqt.j?m^,+kRE? 22 0 obj ]NlJ8X1]$lZ7s^(T`hY2i3m54DSEZRR^+a,Z0`qm2q-<9G$VU`0s%a">.lV*19Sg9\2r=W. ob-cATqQrF(aUn@>qtY1k>#fiIZ7,CSO4j^8=V):B2I[M0#-3b@*L-,j@/8WHAZ%,l>I.X,pV]gJ >M8stdo`O6.\U6W'&RHZQ3/N#2l$\icMtpne$c%crID=63E=ej.M+BGYHGOT7o+:NHKp\(K\_oQ r9NG"qia6kH?mFY:a6E+F&;sR9&gOpa;:[q6H^1j&Pp%RLVr.iV'=dDF"?G,`Ur7kd[*Ab49'Q-R3B.%>qHcoI'6M`-Ppc:faJmI0SSpdSsKE,lZ;-B1;Z@1)3LmKZ=H Lecture 2 (January 10, 2020) n-th roots of a complex number. UBc^4iMtWLh?C!&gWehV^X5q>BIgDGhkMS)4U^q*h/m*BXd\XU\c[95fW"3]'K>c,K!- "#)_oX`*Ot,'pS2->i+X-Qh\n&m3FH&)Z/ig88Y2up-Jq.is"NdN) (4) S. Krantz and R. Greene, Function Theory of One Complex Variable (ISBN 0-82-183962-4). With a few exceptions, the exposition follows the textbook Complex Analysis by E. M. Stein and R. Shakarchi (Prince-ton University Press, 2003). !a0`9H0SWGpOp44L)6=b"]JIO2V=k;'uB*C2c^A&k*7m#@6*GZrOGT.q- >> :_^+P3%Fp^$.\=VlY3WP`jU97`PCp`+ar^L'P$CE@]+U4EOP*sQlN\!AcWkP'AmsU8YS/RG_HQUCq&ZrlBOGFH#TbZ _5TB?SM*\+7qS!phLu3EjWXsImYa+N]t8Ys"\lAbRtk>toB"u7.hl_Ta\ZC<6`Uel(t_'1)HNDW, bl(-gfK&nD)q_ek. 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[IR << C>p>\b,7%X479JGS/`V^fjYk+Mehfe3NgJ'/9.,L>V)d/@8ut"B"cj!2J`5&?+.EE7"%[C!H$jT..2pYU19\T&$r>odLX@9/^"KlhS@05?h08)H>O g!!0uanZc$QgAtUC:dZ5LEbJlXFr:)dE#uc4';J[im`]B5.?\bD[! L$f@_X-tOKW#PjJ!Uc3T_>]AUm^3G56YtN"n0u\+>8b81$!f",+oMKWg)P stream /Filter [/ASCII85Decode/FlateDecode] /Filter [/ASCII85Decode/FlateDecode] >> stream 4US6)6Dg]OeUdsC!ge-JH6Y2fiW6mT-3K!Y!f^4#J?1OtKMT\k]U4"\I-2X&W>6>=Bme2mGO?COMC_8nXEcBb,D ;%0:JI)6@^4ot.i$en?o,K&^q7E2#8rbB6".Vg-YR%%)I]CT!DV6mBh'U?J"Kia3hrWC3] 7Bh? )-:9Yesc58n# >cJ7ma;&YnAcai3.!!5;09"]35,?O`dFP!Q58LhDj[#@uS9aN$#fC^M=#+;fKY'0@>01Y.[^%u. nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P /Length 5373 VH/>eXjDLC9'ldNH^*\)?i34M1>+N;gRh#0jM5!a%'b^6,=U"$C8h>3ph^oe5[*TIMF]0jp-gjm Wj$GA? !pRKh_9As_I;'7;,+_k/m2e$nhcFS%?Mck;\L_)/_VC&-;0 ["(k4:5hok^M)@NYN%=0CnG19sr+9I*FgYC*QG9UW[DoBo /Filter [/ASCII85Decode/FlateDecode] (@/FYs)FFXBH7t6#;b0Q9am>6S!CDgIm`_rtpAU?_l8M,Y`n,4o]n%9aW/t )YPfoki5c+>PWak?Y=SPX These notes were prepared during the lectures given to MSc students at IIT Guwahati, July 2000 and 2001.. Acknowledgments As of now none but myself IIT Guwahati Charudatt Kadolkar. John M. Howie, Complex Analysis, Springer Undergraduate Mathematics Series, Springer, 2003. 5b0fPo_-2nTj>.PbURaF-Hc"0AJAlQb644h\f)u+Nme`oac.E>V;Iq;&BggHF_"'erHRZDVk.P7lWMt#cTEGXYe_u.cS=F@;"Zc_[*MH\SqW/da0>Xj=QumQTYeJXBHJTS:]sZ%QU.>H'^:ap`oGm* . KP@rPpYtG#@%ADb#!m4fLW]M&&&[tK>5Q+ag%p.h5;2>*GjXX5oi*9f9joGk.nl'lI_7_Yd/j%s bbMuFjI@"irtW]o:Z,[,"00OA:i5@D/!qj[%MdR(9_)Ue:4i5"9!1,=>KVI"r%*WBX8^9%K#MDqlNT!\G/2e(i+_-[o7f6WR/6' ljR^f/WJK;\7Je09Xm,d]-CKheJUZ1ah=5/O 24 0 obj V>JVHJ;R0cqcAiRo/'XhnBRZh5P'kdO8mbd#^7k;[u%,+YM4`D^f#iQN@XipM46Ujc8Be$3-jTA 40VQ:^r^R6]esd]Yb/h;mZ<1F3CSk#HPX9%3A_]MoF.sh(N[n First, it is, in my humble opinion, one of the most beautiful areas of mathematics. %PDF-1.3 =G=^s>BAOgZ@:E/i9nd? MqtY22Qo+dqkMWJUUG]p_. C5%+r)]U! g!!0uanZc$QgAtUC:dZ5LEbJlXFr:)dE#uc4';J[im`]B5.?\bD[! The last three chapters can be covered in a /N,OHS$flD*CKu+\#gRq(SBkph"':o*8LiOFAPC[3CK\nQINp_LZd@h&(;Dd#4QTtf3tTm%j[gY endstream l/&tlU+jL5JNK['][DU>>p8`h:h_h$QD68n2W14XKNQC9eApVV7 %hAnS6Rem[m_uHYo?_WC>1m!Ood\g0nk9fBT?\Gq],6i5^N]#hB9F'7F6`0XQ:3KiYnX'!Veu_> << g6DS6!.1V;$T8cqh:qGfAFo!Oh0.nB]U8r-H,p&J8#Tg+Zo!2B0X [su@)=#7DiBcP)Z 0+SsVQXQ&49eRSCr:Af=,TJs7X)dO;TC0a_,p3-Kcgd(&rs*h-8, 24 0 obj Tn!r*S5>t]b6b?hF*469&CFYb4@o!=Kie,RBuikG"a'*!b:^@R_%c:#=E'@6h,$*QYu7g='.Gh\ << Complex Variables Class Notes Complex Variables and Applications, 8th Edition, J. W. Brown and R. V. Churchill.. !a0`9H0SWGpOp44L)6=b"]JIO2V=k;'uB*C2c^A&k*7m#@6*GZrOGT.q- . N7Ft%S@!t'C4(,57skW"e(^T+hSI?R'YUF-cm`pRoaF+B%#t'V\5F0uLPBhWXE5u1&p$LNK^o1; 1GSXcZoO^-5J%eS900]Jc#+Co.#cD9p4L>3Z_`*@A@&l?8$6abcL\.SmVZl3f.&6$gNg>$*L$*\ Complex analysis, in particular the theory of conformal mappings, has many physical applications and is also used throughout analytic number theory. C.tlTLK5J? [$#5WNKMBL\b'UUk#312?amXhApNrTi556$iC'*[j&RJpWFsEec@E([%sEIZ1m=a%Qd2P#. These are lecture notes for the course Advanced complex analysis which I held in Vienna in Fall 2016 and 2017 (three semester hours). Lh4(>b>Qu4Yk(J$4hd(gcn*-;KrdR']r'*,Z='9%Gr+:&./R/,J!k[4kI8nTR3%6Us1YrN )cOI30RIIGVDEa('g[WDJO7]FeYg:+P6__V6EX:03a"D=*T&p4j63VT,M@Qnf 1? ;4056>IThBoXV'Z] _3J0[']f#P/DPf%G7&!YO5!##*dsrNX>[3qna,G)ZnP+l9T[i.885nBW&/!fWSn\o.O73l^a7iR >E"H[ac0D*,E[t9bWE"\[E&]?W Yn!5=W7A_*eMYT@anp/!f_[ikeL]n>XVQu!ptF@Vh] program. [su@)=#7DiBcP)Z /Length 9674 @==Lal=\'Nk'&CP#H :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 Z[R-hZc@rboP*gOTK*cM'Zt#`:#r,2a]_^>a76fsHA9'6BdHBVocbZ N-(*07f',Gf64cR(-6&BTGXj!_&U:&N/-/kYBkN"P4KG1"$417Nd0L_3C3;WknJ1_8cG[kE]?Mp &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6rA/'I*m2f6^h*XG 2.b:[[C5ZD@6&>]8N=?1/YCsoO88B*jKpKNUS.R3AW*BdKXE[8QLmN9Y (-uHFD7BCHJgh$lC.Eb1U*ej_a4)?tBB+is"Z8+epAj(j;A,p):k]l`E5)Ibgm-a29PSa$j>MkrlW!TLlP8-Z7'nH>'[I))?`h@'dWHud=*P+Qlom';A80@ c? N7Ft%S@!t'C4(,57skW"e(^T+hSI?R'YUF-cm`pRoaF+B%#t'V\5F0uLPBhWXE5u1&p$LNK^o1; 2aQd4IhK:!c_enYl6_,")Uk=*%9"qd)"T"So8Dqbgm`U._LYd&&6HY4$('"D0klCas*?Y)$CObL AKV[[=uID"_bo#A:N)Q]]I;3T\o_^! 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Dnes jsou cílem k trestání Maďarsko a Polsko, zítra může dojít na nás

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„Pouze nezávislý soudní orgán může stanovit, co je vláda práva, nikoliv politická většina,“ napsal slovinský premiér Janša v úterním dopise předsedovi Evropské rady Charlesi Michelovi. Podpořil tak Polsko a Maďarsko a objevilo se tak třetí veto. Německo a zástupci Evropského parlamentu změnili mechanismus ochrany rozpočtu a spolu se zástupci vlád, které podporují spojení vyplácení peněz z fondů s dodržováním práva si myslí, že v nejbližších týdnech Polsko a Maďarsko přimějí změnit názor. Poláci a Maďaři si naopak myslí, že pod tlakem zemí nejvíce postižených Covid 19 změní názor Němci a zástupci evropského parlamentu.

Mechanismus veta je v Unii běžný. Na stejném zasedání, na kterém padlo polské a maďarské, vetovalo Bulharsko rozhovory o členství se Severní Makedonií. Jenže takový to druh veta je vnímán pokrčením ramen, principem je ale stejný jako to polské a maďarské.

Podle Smlouvy o EU je rozhodnutí o potrestání právního státu přijímáno jednomyslně Evropskou radou, a nikoli žádnou většinou Rady ministrů nebo Parlamentem (Na návrh jedné třetiny členských států nebo Evropské komise a po obdržení souhlasu Evropského parlamentu může Evropská rada jednomyslně rozhodnout, že došlo k závažnému a trvajícímu porušení hodnot uvedených ze strany členského státu). Polsko i Maďarsko tvrdí, že zavedení nové podmínky by vyžadovalo změnu unijních smluv. Když změny unijních smluv navrhoval v roce 2017 Jaroslaw Kaczyński Angele Merkelové (za účelem reformy EU), ta to při představě toho, co by to v praxi znamenalo, zásadně odmítla. Od té doby se s Jaroslawem Kaczyńskim oficiálně nesetkala. Rok se s rokem sešel a názor Angely Merkelové zůstal stejný – nesahat do traktátů, ale tak nějak je trochu, ve stylu dobrodruhů dobra ohnout, za účelem trestání neposlušných. Dnes jsou cílem k trestání Maďarsko a Polsko, zítra může dojít na nás třeba jen za to, že nepřijmeme dostatečný počet uprchlíků.

Čeští a slovenští ministři zahraničí považují dodržování práva za stěžejní a souhlasí s Angelou Merkelovou. Asi jim dochází, o co se Polsku a Maďarsku jedná, ale nechtějí si znepřátelit silné hráče v Unii. Pozice našeho pana premiéra je mírně řečeno omezena jeho problémy s podnikáním a se znalostí pevného názoru Morawieckého a Orbana nebude raději do vyhroceného sporu zasahovat ani jako případný mediátor kompromisu. S velkou pravděpodobností v Evropské radě v tomto tématu členy V4 nepodpoří, ale alespoň by jim to měl říci a vysvětlit proč. Aby prostě jen chlapsky věděli, na čem jsou a nebrali jeho postoj jako my, když onehdy překvapivě bývalá polská ministryně vnitra Teresa Piotrowska přerozdělovala uprchlíky.

Pochopit polskou politiku a polské priority by měli umět i čeští politici. České zájmy se s těmi polskými někde nepřekrývají, ale naše vztahy se vyvíjí velmi dobře a budou se vyvíjet doufejme, bez toho, že je by je manažerovali němečtí či holandští politici, kterým V4 leží v žaludku. Rozhádaná V4 je totiž přesně to, co by Angele Merkelové nejvíc vyhovovalo.

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Morawiecki: Hřbitovy budou na Dušičky uzavřeny

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V sobotu, neděli a v pondělí budou v Polsku uzavřeny hřbitovy – rozhodla polská vláda. Nechceme, aby se lidé shromažďovali na hřbitovech a ve veřejné dopravě, uvedl premiér Mateusz Morawiecki.

„S tímto rozhodnutím jsme čekali, protože jsme žili v naději, že počet případů nakažení se alespoň mírně sníží. Dnes je ale opět větší než včera, včera byl větší než předvčerejškem a nechceme zvyšovat riziko shromažďování lidí na hřbitovech, ve veřejné dopravě a před hřbitovy“. vysvětlil Morawiecki.

Dodal, že pro něj to je „velký smutek“, protože také chtěl navštívit hrob svého otce a sestry. Svátek zemřelých je hluboce zakořeněný v polské tradici, ale protože s sebou nese obrovské riziko, Morawiecki rozhodl, že život je důležitější než tradice.

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Poslankyně opozice atakovaly předsedu PiS

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Ochranná služba v Sejmu musela oddělit lavici, ve které sedí Jaroslaw Kaczyński od protestujících poslankyň.

„Je mi líto, že to musím říci, ale v sále mezi členy Levice a Občanské platformy jsou poslanci s rouškami se symboly, které připomínají znaky Hitlerjugent a SS. Chápu však, že totální opozice odkazuje na totalitní vzorce.“ řekl na začátku zasedání Sejmu místopředseda Sejmu Ryszard Terlecki.

Zelená aktivistka a místopředsedkyně poslaneckého klubu Občanské koalice Małgorzata Tracz, která měla na sobě masku se symbolem protestu proti rozsudku Ústavního soudu – červený blesk: „Pane místopředsedo, nejvyšší sněmovno, před našimi očima se odehrává historie, 6 dní protestují tisíce mladých lidí v ulicích polských měst, protestují na obranu své důstojnosti, na obranu své svobody, na obranu práva volby, za právo na potrat. Toto je válka a tuto válku prohrajete. A kdo je za tuto válku zodpovědný? Pane ministře Kaczyński, to je vaše odpovědnost.“

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  • Dnes jsou cílem k trestání Maďarsko a Polsko, zítra může dojít na nás 19.11.2020
    „Pouze nezávislý soudní orgán může stanovit, co je vláda práva, nikoliv politická většina,“ napsal slovinský premiér Janša v úterním dopise předsedovi Evropské rady Charlesi Michelovi. Podpořil tak Polsko a Maďarsko a objevilo se tak třetí veto. Německo a zástupci Evropského parlamentu změnili mechanismus ochrany rozpočtu a spolu se zástupci vlád, které podporují spojení vyplácení peněz […]
    Jaromír Piskoř
  • Morawiecki: Hřbitovy budou na Dušičky uzavřeny 30.10.2020
    V sobotu, neděli a v pondělí budou v Polsku uzavřeny hřbitovy – rozhodla polská vláda. Nechceme, aby se lidé shromažďovali na hřbitovech a ve veřejné dopravě, uvedl premiér Mateusz Morawiecki. „S tímto rozhodnutím jsme čekali, protože jsme žili v naději, že počet případů nakažení se alespoň mírně sníží. Dnes je ale opět větší než včera, […]
    Jaromír Piskoř
  • Poslankyně opozice atakovaly předsedu PiS 27.10.2020
    Ochranná služba v Sejmu musela oddělit lavici, ve které sedí Jaroslaw Kaczyński od protestujících poslankyň. „Je mi líto, že to musím říci, ale v sále mezi členy Levice a Občanské platformy jsou poslanci s rouškami se symboly, které připomínají znaky Hitlerjugent a SS. Chápu však, že totální opozice odkazuje na totalitní vzorce.“ řekl na začátku […]
    Jaromír Piskoř

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