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Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. ,WF\iqt.j?m^,+kRE? qKUjP@N'@mD(%(2)_=uEgL+GfiYnndd^I\H+0J[\W^Gk,h0f/-cWtGC09EpAn($QdIZBJkbf,Gh 24FgOV^k*U]0 It only takes a minute to sign up. . !nb71maq4X8.Hge,tYS;-3mr1(Z\+V0sBMppuWgU<=F6&U'Y">B^KAM#Gp[l)T]9)?^`2 JDV'7Y;-Hr3uXDU1>si7M:`&GP0=)I"m>U%r&!=SY1u=crTRFWmi64dUag4(EQVs'8!lb"=GE7RPQoR(+[>59g+=>rd6[:!4unTP '%P$VH?J@%Gb87cTO^&t['d=I=*dq-09V-=&GRkr@WRdf.ckmHTm$6(kcaZmfL9.2<3SU;oR g(Sebf:ILoYdcdZTCLQlU"-5SCid+]qkKFC^YR. << stream Making statements based on opinion; back them up with references or personal experience. 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C5%+r)]U! le?%Xq@Ea.0q+*]/teJm8Obt+l8->q2_n8S<0 B2S4d,_nab'sHW'(R`!s&4*I%EB9egTku00W&uST+i6OVP_Rf./t)l_%OrQ@cmr*^(8tP\#*%Z. r+rMIXK[OG`YF)0%Wp><1TY9n8jk2:;oUk[*\=d5eVMknLml! /Length 9674 B4)8"'5]aVkkOWR)RKZtn'5kh8]2+=8:jfLW*&d;3?k1.ajGD/b)th,f2p0Mc4c(AV4+Oo[+KQ& I know that all the courses in the curriculum serve some purpose. :.=k ]FOkmF>E_-#NVhZM.+D '%P$VH?J@%Gb87cTO^&t['d=I=*dq-09V-=&GRkr@WRdf.ckmHTm$6(kcaZmfL9.2<3SU;oR D-TDl/"q#PCM>lG`)Iti5p9S"OD7/7Pq_/n:_4QZ>'ZEA$]#usT%19ZS/FYd'SE'f@C`gNNi0Oi d:rJGPg#p19-Asnj(0(c+Rn[GFA=hl,0s.N4Hj0%,l03^Q-TUkU]/en(i9(_'X%f:6pE]rZdWO$WtDQYOZ;3D_ These lecture notes cover undergraduate course in Complex Analysis that was taught at Trent Univesity at 2006-2007. . !N6.JVeQF'hmB_)K6s8k On7PQ3LtT-(^chaeSVjsSqbs2P8\r@;jhf/@98f-653kWoU5F&&mrMQkN-s"W9S-.J:&9%b;oR@ electrical engineering is applied physics! *os=mj9r )u+a;)%9["N"eWU\Z4^*/_OD.f%kQ:):uqUgjIhVTGCHm.%VU=m3odaE)aM5d\9O"RI!cjDJI# c)uh$8Y^%`gc[QV^.AO[k9s'uj5-Uk$(*#(3(b6bKTr`P8g./&L27Tnn?.:Y,[. 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In the next section I will begin our journey into the subject by illustrating (@ le?%Xq@Ea.0q+*]/teJm8Obt+l8->q2_n8S<0 ]h65:qPWIk#FB4\i48\go^(;c@oD1-/hu73`\$Q+S'$@>,#C_Mt ?kHa3J1&%0C[OhUp,r&8uaYs2Ul^Y#K=;>W"([p:d))]i@C#\($C]$VD\SaHD IWT10M+XH LAiDh&4OlJ,gef$lg_[pfa;Fp1.+V="pAr[d;[p8[`qUHf2-XXLk[dV,KR&U=@,/@8o^=abL*"k_BBACno>W? endstream ?cQ^:6WUl!#U`>US?0s*SG#=_@o+^5'oM1aX_nV^HC6Yf/Ir"W,#3[ !nb71maq4X8.Hge,tYS;-3mr1(Z\+V0sBMppuWgU<=F6&U'Y">B^KAM#Gp[l)T]9)?^`2 =G>:.gN"7TOaZCo^e`^@)78\_? Hga+@&aFU:\Ddm+UGW\8G`5D;_?#e1>@+[@""@g@\2?lU*kjl\9[DlHU5i].5,EpOh53PE.E;7Z %o%AkXC=4QbW^]6HH3@mC]]a$c;mfos_B6?D;KrmS*d#gZUj*LANF ;L=AqYsPjA3r:cN2A=ljr*^&b,/nHu@[/maWM6Qk"?Wd41M^5[!g,L>M53 24FgOV^k*U]0 Iu_SbYG*rD:ZUa)OL6ksm>+sc'. ^_.+qH*Oaj)akYGcR7FSC3QAdiS!mQH#ZO^0"!dS4+kfW+28Hbmf~> 7Bh? 'C,kk_^er/UQ)mb5Cd"C5^mbUQi=#8D$lE+TYO!l5GN;YDd)D/g6EPp]T1:.iunl&/L^Sa\'M/M And how to select best books? )-:9Yesc58n# &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6r-qnM`_gr'2iWaki2*QZpD\-^[pb+$dN? stream ciR!r2-Q3I3*#q0DCS-nU@hqIWY`A4G@hD)](0]A&]pf65@I+G>OF1`Vg+KD62Nl5D stream j(:Zd&V(/? :t-)d1nUb(%UjT!TZ4nniTO+6])]I.b!bfb]\i15nVJrHBQn \X0,5Q)]MU4(fX2cEjuE^]*? o6N4%'.UZ/^@Hp&5&04[lLGi< Winding numbers are important objects of study in Algebraic topology, but actually the first ideas of using them came from complex analysis. aX68Y!8dt,nOa7MZ;44I.$k7#"h"B'BnXu'DSs*DKQHJLiV Ut:M"p(V62IfUDr#%R~> )u+a;)%9["N"eWU\Z4^*/_OD.f%kQ:):uqUgjIhVTGCHm.%VU=m3odaE)aM5d\9O"RI!cjDJI# *V@i6&].Z&X)C1f!ei@aUqiCM$Ed!/-t5hN9]4[SPQ+02&/!2BiU*RpO&A/q@YO0= ,K5b1\VTIXi42-C"Rs,iSj!=89:p80O:j%%V7O'U`lVO`f'.LuL<6GsBe3)hU6L1k]J/5t8rcqU ,K5b1\VTIXi42-C"Rs,iSj!=89:p80O:j%%V7O'U`lVO`f'.LuL<6GsBe3)hU6L1k]J/5t8rcqU le?%Xq@Ea.0q+*]/teJm8Obt+l8->q2_n8S<0 (-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@ Also, control theory is used heavily in robotics, and by extension, so is complex analysis. 7Bh? 7Bh? 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