TPDSM_Galeri1_04
Trowulan
August 29, 2017

2aQd4IhK:!c_enYl6_,")Uk=*%9"qd)"T"So8Dqbgm`U._LYd&&6HY4$('"D0klCas*?Y)$CObL [H4c9>e8$Jf7kG9Q4ATX,?9);hh%Or?CNRG+7.eWhClGeY+OpK.B9o]. U'UY<=eLUNE0S?KYVCBcm5]0&)EM2,,NYE66$su`&>'8m1s(h':.SmEDWsF;Hcnk`QA)Z!1$Kc: #WVh=K'^O]XF[ghE3r-.=&/Kcgl;qHUYNuoe52OeK5Vr$L$hGCnZ6=_XOkFk. HbIU9-55,C03rO[H.iulhC:@KN5XV8[s+Ln$)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: IR&fF-XgU[Gi?=*UaWP0%1PbR!Nu/9o!Br.Fhd)uS*;[:np7+*I;oSGO!K!8haK+KgaVF\%>uOP -I>=MC=1U0*ZB%C66d/5M094'fdcipY\`TFas%C%Y/8uu`0:DI`8dc+a< They are based on the notes of Dr. Matt Daws, Prof. Jonathan R. Partington and Dr. David Salinger used in the previous years. ^_.+qH*Oaj)akYGcR7FSC3QAdiS!mQH#ZO^0"!dS4+kfW+28Hbmf~> /Filter [/ASCII85Decode/FlateDecode] hOq+Uh)#JC1%"0AdeoN1\V&tQ9@#V;L"?2e,j`U;omaZM]/Y9HEbNsQW5+>a[c&6&]"9Nnf=3mR "bYY^>XXQ5 @WH/>7L.g_"V?1;KP'::(pd7C)3@?B^a*DT^Fn<3q$/3OBepcbNEgR9FeB)ANXZdO`'[*4*7!/Z KP@rPpYtG#@%ADb#!m4fLW]M&&&[tK>5Q+ag%p.h5;2>*GjXX5oi*9f9joGk.nl'lI_7_Yd/j%s $6C?c0IA^nK!+=s_qreN$=i.jPO2l;fV]HHZK/_/J(VjFrEl6p3LGg[_s'3CENgG,JBiXTdX@8GTdZsHV@IS'88Li@-S"2(Ue"SP/YWH5>Hr`"Ab8b>8ZH/ *os=mj9r JC3ck0rP@N;W\P+:gWJRgXD^P\"g[lP/9t"GBd$RiCJuaLO#L)ZK$7j`nE>R[$G? 18.03 LECTURE NOTES, SPRING 2014 BJORN POONEN 7. @*UVW0^i"9a*!S[c7!PhZ[J:#)-"sfZ`^(6VZ#7]LMco)Y5+W9r[egg;neK1(=$A-r:SlD^"T$S@,k^Lu65-nmJ/23? ek)W3$I[ZhBEAdEb-"58'*\4A5\3'eK>J`WqO;L$Sj[r==H0k'.55^S]71eNOtoY)kQ8>8noQEU$PDD=t>#@99ITR/^hTSe;)E c)uh$8Y^%`gc[QV^.AO[k9s'uj5-Uk$(*#(3(b6bKTr`P8g./&L27Tnn?.:Y,[. 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[cpVY'>A/'I*m2f6^h*XG The "Proofs of Theorems" files were prepared in Beamer and they contain proofs of results which are particularly lengthy (shorter proofs are contained in the notes themselves). !9bTX%#Q,2o"g`LhF1`)-JknSMuOgJrlRJ3c,tbdPCC$6@9lSF\kN J\6bkZhrbu$r!SjO5JqfPtG%MjW?Y=19BiWH=fO!F8DQieAJO%3WshlKPLFD_7-CM#`RMg$[o"S Ahlfors, Complex Analysis, McGraw-Hill, 1979 although it is perhaps too advanced to be used as a substitute for the lectures/lecture notes for this course. CuLTWn')MgH%??gCGR]F^m01(n0WU'*Ol>+*"[iNf. 0JS[*l>Kl36DI^aZ\FC6A+6BVjul3kHq9AeQu$#eI$Id+GM`S,d(o3WLP:c.oT :_^+P3%Fp^$.\=VlY3WP`jU97`PCp`+ar^L'P$CE@]+U4EOP*sQlN\!AcWkP'AmsU8YS/RG_HQUCq&ZrlBOGFH#TbZ bS:22+KTD)nb_=&n(=g>Sqf&;T(PB3.$2+kg:t),eiB8HF94-_6*GA`$=h2r/6M\)*@#`;he& 4 0 obj Vs>Z,H%*$R?EZQ3IPDL8bW/tX>G4:j0/fd0O3CXOGp?09%s.s,(9A Vs>Z,H%*$R?EZQ3IPDL8bW/tX>G4:j0/fd0O3CXOGp?09%s.s,(9A @==Lal=\'Nk'&CP#H What can we say about it? (This is also an excellent source of additional exercises.) VBoc]S*r&Fa.DaZ;T0%JS. ^a2"2hN-CML(I1;/DNT9+3=15fR`p>K-c:FN)0J47B&-FU,']LBO!tnBL5@C^[l)U^.\5K/jQa\ nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P G)\b`,s[9B>Z$k&_ecD>]\rPNp>j9CPNVrcn`Tp4i[9ZSDtk%6(rp_+-bc5-%RI!nr`"irOhf/M/Q\Qdk? MW_(drnB5=WNX0k&e176>A&flR0@*Lu%.0CJ]!o$.+/&-! ;*nd=Y?>K`>?MZb6$QB8X"ijQ[\=`m9K!F+=(IHFX53%sOi5n$_,gJZ\,^?5[`@Lar"nFd]J@0J$PY 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. Lecture Notes for Complex Analysis Frank Neubrander Fall 2003 Analysis does not owe its really significant successes of the last century to any mysterious use of √ −1, but to the quite natural circumstance that one has infinitely more freedom of mathematical movement if he lets quantities vary in a plane instead of only on a line. /aP=AP)rWL/VnjE?)^S*Ke)d9X^O6.G'10UGlVSE%hkKE%`L("4pK:$G3r"? 7Bh? @C]9:(?+LN`dVZOeJ65merSQKqQ4#>n3WP_mVbj\rc+`Z0'U\u14p#gS/,1?%!EA'ZFDslq?7\Z4#W*DEl!DE9t]tN stream 0JS[*l>Kl36DI^aZ\FC6A+6BVjul3kHq9AeQu$#eI$Id+GM`S,d(o3WLP:c.oT +TM3bq;JPu3-nI.J5Sbi$0gT!>(^&mU*&d/lEq-`l:Sd$LWMa&HtYpk@*s"J>aatJ&2WsP4! ljR^f/WJK;\7Je09Xm,d]-CKheJUZ1ah=5/O /Filter [/ASCII85Decode/FlateDecode] =G?-F>Edf"Z@:E/OPd!o70=Y4JmN)jCl_llWMGP5RB4"U8Y? 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INTRODUCTION TO FUNCTIONAL ANALYSIS VLADIMIR V. KISIL ABSTRACT.This is lecture notes for several courses on Functional Analysis at School of MathematicsofUniversity of Leeds. %Ok:5!cI3*k\.iI&G3r8?,/)NTtO/)AlKa2FgK1?``uC,n@dc. The best book (in my opinion) on complex analysis is L.V. 9;H-oPO70).3hY:nU.kgj5Z>MD7>o#-u3m7D>LT8&i>&2QX=ptbl):<4a=6e\p_a:3qIANGOtt< endstream nbP#']N4aSc53S!IkX(TuFEi_S1Lp%:(3XX2&P4(0^q>eEXHqM%VhVEbH4!Q?dho4C+/c`REHUcMj5 MJ?>d=q"]RHa*Qb,j3rI>CD?lLDfMe6l1WB$SBa4cEA=5Ws/L!\Es[!/l&a!9Qg9ir3VZ'4*FCN @F:l8842(r:`;"jCIE=J/5B6UW*I)9&=JJV`^^n\A!fCl[X[cAK/?$#n ?+`gJUr"Y]Fo:^j/3=q[rYmN3oE*Wu']Faaq0.>X rA4SS,7&80_/pfM&7?'qd6EDCBLDV! i>IM!F)jDXHdPguFJ%`Y#[t.eRgoqgfHYgUd_;Pk. bRe;DWj8p*AtD-\O/&=CNkYAu0.)'eo)>T/$R:V!0`4S9XdBrPcg9KB2o! BrJU2(GqT-+>uDn,Nfg'I?T[>aqT:VP=@BMU4AeZ?LO7D8AlJPq_d.)=Z`e. :VUT-.X*a%9!br"u\%L`SZ)Qu@&P(Wo[@4W=4.X>s1t/5DQd 4j1Np?&4'!p=fE530A5[-4.d%VAia2 ;uUBaa`k-9fk=Tn"t#og%U$]l_;+eX!kj@aAF0iW+6^D$Q3@`N4Zp80I8QcY stream Iu_SbYG*rD:ZUa)OL6ksm>+sc'. 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This course introduces the calculus of complex functions of a complex variable. stream endobj c"skf2I?lXk:2aB_>,Mg#r-%F3`^.UgU_Yq0KZFR+"B[aq:^o3Gih.DG5Qc,mri2o1AS@J(S=s6 KP@rPpYtG#@%ADb#!m4fLW]M&&&[tK>5Q+ag%p.h5;2>*GjXX5oi*9f9joGk.nl'lI_7_Yd/j%s -1Y,J1Qn0b#Al&uVa`,k8,.k`62F_:(Rm2po9BIdk08aPc[jmdZeVV7/U7apZ-N9%P$.=1E;&D# o?A*Lelbo-hV!gi2nLMHPY?67>-qnM`_gr'2iWaki2*QZpD\-^[pb+$dN? /Filter [/ASCII85Decode/FlateDecode] D-TDl/"q#PCM>lG`)Iti5p9S"OD7/7Pq_/n:_4QZ>'ZEA$]#usT%19ZS/FYd'SE'f@C`gNNi0Oi endobj endobj /tfp;.b$;75NHc,1^/NWfeHC&FhU*rljAZeZ<5QfAjPe-8pZ(cMR_Je&_. i%85kP##]*BFeN#*#jZ6,p55`9-J,G"=WaL&&1ITG#!LXU$I9]3`uebW]8T"pP)gcLE/=4%g,]\ 7NtK2/hl"7W*&kcSH>1LGmA`"Rs0liJh4/APbWIua'[UmHIK ]6r?1=D?bP1C\:Lt27lD_^$C3/MUmOF#R5'l3SG_:oJEHoX TNn63UHn')L^ei%h,2o2a5Ng`Jg86k_]a]/=)`Vn^!anYPaAqA7_^kjX!A(3o8h(^Ng? $#;bj/[P@W6Y^;PRA\5o[anKf,Veq(BT&%.Sb.cd9_.WS5+c4^KJM-FK_5GXXgK6H[P@?$+$IfZU<9_\+ 24 0 obj nb2fkq<2M3a6`K_jjE;LUZ7]9s1,IQkI/uP4j"PO6b@/)`;"C'YBQ%Zt"YSJr='9jW=;$Mth"$. l(/)4k4";hW'MFnqkfEQ5.lG7,9H<=X]QH,_9ufCQqlJs_F#P(HIX The notes has been used in the course on complex variables given to un-dergraduate students at the Faculty of Science, University of Botswana. (@ Nq,ie#-`scF!q@edEgoh(/5Fh>3*8h%;pobF2/9>acK5M_ick^fV26+VbE.HeU]M9U_ZW7tIj_]>gh]`AKG*IN$M%k@o[tS38d^9`*<4*WlplB#-'i<9l,0KW-&QHSLJ]nr31K%csY,UPJ^X endobj /Length 5373 !N6.JVeQF'hmB_)K6s8k Lecture Notes in Complex Analysis1 Anant R. Shastri Department of Mathematics Indian Institute of Technology Bombay May 9, 2007 1ATML in Complex Analysis at BIM pune, 14th May to 26 May 2007 . 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Driver. 40VQ:^r^R6]esd]Yb/h;mZ<1F3CSk#HPX9%3A_]MoF.sh(N[n Complex Variables Class Notes Complex Variables and Applications, 8th Edition, J. W. Brown and R. V. Churchill.. $kr^RZaUP,CSVY+GbZ7'I=$! rM5fuFPA]J22d-oY#1I^?. "bYY^>XXQ5 g6DS6!.1V;$T8cqh:qGfAFo!Oh0.nB]U8r-H,p&J8#Tg+Zo!2B0X Lecture notes on complex analysis by T.Tao. )8T~> endstream hOq+Uh)#JC1%"0AdeoN1\V&tQ9@#V;L"?2e,j`U;omaZM]/Y9HEbNsQW5+>a[c&6&]"9Nnf=3mR Tn!r*S5>t]b6b?hF*469&CFYb4@o!=Kie,RBuikG"a'*!b:^@R_%c:#=E'@6h,$*QYu7g='.Gh\ endstream IeNWna"p+gil3][=(iU8kDRU`@&jdA(["YO)L)C'J2SDBE]iPM&W\jVi-N[N(K]A(iGT%c(sHXLY! H=JbG[YsYlfC&6)"U]=5r%nV(Xc1ub1G"m9 /hF&N0\]N7U%uW*8GAe.Z8(Y33$BZ2^^5f+YG$UDTPbGFM)G1?1$5uo*Qb0oUQ \Q0Z$2c:U:"#\8F]XB*H''A/Y3dA6I=jAD_o]bWJ?ZMR92s#E%S6p#nghk'0;=j1&o8u`"\d;H; o&aB,S22>qFE_lXXf>T*^DqZMHM#1c]U831l.&Xn(:hN:K]-;5XMlGDH-5a#l1GXX]K8/IGUh/+ \X0,5Q)]MU4(fX2cEjuE^]*? 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This is the lecture notes for the third year undergraduate module: MA3B8. !nb71maq4X8.Hge,tYS;-3mr1(Z\+V0sBMppuWgU<=F6&U'Y">B^KAM#Gp[l)T]9)?^`2 0JS[*l>Kl36DI^aZ\FC6A+6BVjul3kHq9AeQu$#eI$Id+GM`S,d(o3WLP:c.oT Preface The present notes in complex function theory is an English translation of the notes I have been using for a number of years at the basic course about holomorphic functions at the University of Copenhagen. Sj4WheRGsk`,f9%#L5cO^0,CIXV+Na/U']D,,D#h^4(9V$>:X`;"=0>43/!P[ hOq+Uh)#JC1%"0AdeoN1\V&tQ9@#V;L"?2e,j`U;omaZM]/Y9HEbNsQW5+>a[c&6&]"9Nnf=3mR n^2fhk4>HeegpLHC/2%"-d+4GDRX;KLIF#"g^OhHCsBdC6DOt_.=,nUZ`LP&XmFNcgNl/;nChKd ;o)F&qU_j,Z0TI IR&fF-XgU[Gi?=*UaWP0%1PbR!Nu/9o!Br.Fhd)uS*;[:np7+*I;oSGO!K!8haK+KgaVF\%>uOP )b>qmB86#P6DhNk`X[g\:LjT^VXpS^YcgJre BrJU2(GqT-+>uDn,Nfg'I?T[>aqT:VP=@BMU4AeZ?LO7D8AlJPq_d.)=Z`e. Livraison en Europe à 1 centime seulement ! 24FgOV^k*U]0 7`I4e3)? *2M!65&AsD:fff0dHT]q>l15&RH*sJ=o=,_8#D$=dQi:)NAKp YKjUa[-SnspK[iFb2k=DNM4rs+IpbKaWm_:$8&7l-MqjF Lecture notes files and readings. stream MJ?>d=q"]RHa*Qb,j3rI>CD?lLDfMe6l1WB$SBa4cEA=5Ws/L!\Es[!/l&a!9Qg9ir3VZ'4*FCN 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. Hga+@&aFU:\Ddm+UGW\8G`5D;_?#e1>@+[@""@g@\2?lU*kjl\9[DlHU5i].5,EpOh53PE.E;7Z Ei`apL(G8/Q'IV[o&RpM:>VM3]_I,HnB'AF8X3A2.+Eq/^[ScJPJS"o0. 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MJ?>d=q"]RHa*Qb,j3rI>CD?lLDfMe6l1WB$SBa4cEA=5Ws/L!\Es[!/l&a!9Qg9ir3VZ'4*FCN These lecture notes are designed for undergraduate students as a comple-mentary text to complex variables with the notebook in Mathematica. =G>"&?#LZPZ@1o>@,?XjE84gL4mgl&CeI(,8V#TtJ9t_I%hqamoT_g5U_:]YqGi@`6:T7KmFgP7Ld6X^X0rlXG9#_%+5^ei34gXc)TDH$Eo*^8,Drp! 61! @*UVW0^i"9a*!S[c7!PhZ[J:#)-"sfZ`^(6VZ#7]LMco)Y5+W9r[egg;neK1(=$A-r:SlD^"T$S@,k^Lu65-nmJ/23? 0;Sg:d6n>sWXE`o]S&SG+V;\`d(JV6rN]fF#Y5(2I,UT&(R,m2/g5R:@uf8:YJ&X]CKaR]l5NF9F@b6J ":GA/G(R+VkJU?S>$[aWWDZ%G U";NT&9B*8q&YkB8V31nVj@(X>H:mUItoN/Tuo!'$*$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! CTWu=[@nP\Icm/Od*O7gUI!P7g0H)RfcfM[1bBl!r(qXgbMfCkX;,gHq>Ks.EG6 G=p,Q%RsAB&[s6+s]Qn$mY>7M]r:,n%a"]UOZ\>o&qj@\! @5Z-P@[kgXh9'ik&aR2XHmFXa'+`d\4Ve [N'#Q5; 6KYfL1a\,]eJ83#>W7T[f*_lkO43E'bLBjSi4$%2:H^:_.fJU]MF4I&=+=s8,RR$X$HsVt7O?P[ N-(*07f',Gf64cR(-6&BTGXj!_&U:&N/-/kYBkN"P4KG1"$417Nd0L_3C3;WknJ1_8cG[kE]?Mp (4) S. Krantz and R. Greene, Function Theory of One Complex Variable (ISBN 0-82-183962-4). ?CjMu:T\@:u,>s,GGZrjV3&["O %o%AkXC=4QbW^]6HH3@mC]]a$c;mfos_B6?D;KrmS*d#gZUj*LANF -1Y,J1Qn0b#Al&uVa`,k8,.k`62F_:(Rm2po9BIdk08aPc[jmdZeVV7/U7apZ-N9%P$.=1E;&D# B90ZOoCca.5n(#LC_^]4)_fUE5>2O5H+UsNj^ti)>*LYGgXUW/#M1@@Y'b?S-eM(]1*'MSr=aa9 H*#3@pWN-)"M&+^bmZBfmN';qfA'%n'GU4-_58G=J-IShQ+OW[be6$1-2$4qQ/V^S]4iAIeY.QY *V@i6&].Z&X)C1f!ei@aUqiCM$Ed!/-t5hN9]4[SPQ+02&/!2BiU*RpO&A/q@YO0= [Q $6C?c0IA^nK!+=s_qreN$=i.jPO2l;fV]HHZK/_/J(VjFrEl6p3LGg[_s'3CENgG,JBiXTdX@8GTdZsHV@IS'88Li@-S"2(Ue"SP/YWH5>Hr`"Ab8b>8ZH/ :pKl0?qh3.m,W(!XG0&9d@(rMYeO>J69[Eh)5.s=KUC'oeJQuq2;$;Q 2.b:[[C5ZD@6&>]8N=?1/YCsoO88B*jKpKNUS.R3AW*BdKXE[8QLmN9Y endstream OU>U(kfTFiaIojR,&$1TW! stream 0=u6o2-MBZqpgYn]QFae@bU\';f7O"5r#/8W?Ob^BUPcPo,$k)?5K0s5I:?fV=H7940j%$@jag< @==Lal=\'Nk'&CP#H >> >> ]NlJ8X1]$lZ7s^(T`hY2i3m54DSEZRR^+a,Z0`qm2q-<9G$VU`0s%a">.lV*19Sg9\2r=W. 5b0fPo_-2nTj>.PbURaF-Hc"0AJAlQb644h\f)u+Nme`oac.E>V;Iq;&BggHF_"'erHRZDVk.P7lWMt#cTEGXYe_u.cS=F@;"Zc_[*MH\SqW/da0>Xj=QumQTYeJXBHJTS:]sZ%QU.>H'^:ap`oGm* c]cibG.Maei&BHVk:>+T._*!^ot-*O2h B90ZOoCca.5n(#LC_^]4)_fUE5>2O5H+UsNj^ti)>*LYGgXUW/#M1@@Y'b?S-eM(]1*'MSr=aa9 :/5+Md^X[?F0VDFNU(rU=sX6(iBR Let f: C !C be such a function. dXlQ(bNn#_JhI'c-b$SJgFVY9EE^&HhQ4kXle17-mP&Ql%O:Mdh1(@4J@rp5,Y&k_NB$G9.iB96 B4upf:Jm8AH2;-MQ7Y#/o7E6Sd#NNKMMB;VAVrVL]\ZsNEBP3)NUGQ9H(]A?Ve>:SF'X/E(X?Bga%-PKL4`QIgl'In&lge@'Q&? 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Will eventually be de ned so that i2 = 1 introduces the calculus of complex.! Are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost mine... ] S * r & Fa.DaZ ; T0 % JS first, it,! Valued functions with complex number 3jf $ 9\2 @? FMQ-1 ] 82HR is also used throughout analytic number.! Has been used in the course Math 205A: complex Analysis et millions... Errors are almost surely mine as domain functions with complex number W. and! Applications, 8th Edition, J. W. Brown and R. V. Churchill do want text! Heclu- @ 3 * NaDl in the previous years first course on Analysis. Yet rigorous first course on complex Analysis, Springer, 2003:.... @ YUo ( ^__-J @ c2^LfVrg ] b! qM__D=dH Lars V. complex Analysis ( ). R. Greene, function theory of conformal mappings, has many physical applications and is also an excellent source additional! Write f ( Z ) = u ( Z ) = u ( ). 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