2016年广播电视大学《复变函数》作业答案参考小抄

电大复变函数作业答案参考小抄第1章复数与复变函数一、单项选择题1、C2、D3、D4、C二、填空题1、2XY23、连通的开集ZZ,RE4、。0,YX三、计算题1、解令1IM,1RE,1ZZIZ则45ARG22Z2、解23SINCO23SINCO1,1ARG,ZZI令3、解I则11IIZ。232I4、解,27,7ZZKARGZZ则令233,3,1052302IEEKEIIIIK四、证明题1、证明22222YXBYXAXYIIIZ令则1222B2、证明_21211_2_121221ZZZZZZ左边第2章解析函数一、单项选择题1、D2、D3、C4、C二、填空题1、不解析2、及其领域内可导3、2Z4、三、计算题1、解ZZFFZZRE0LIMLI00REZ2、解SINCOZFYEIVUFXXX3、见课本79页例28。4、解依CR条件RE_212112120,11222,222XYIXZFCIIIZFFCIIVUZXYVXYDUVUXYX时，有即当又222ZIZIZIYI四、证明题1、证明XIYIZFIYXZ,则令在复平面内处处解析。条件满足且在复平面内处处可微，,01,0ZFVURCVUYXYXX2、证明00内为常数在常数常数，内解析，在GZFVUVUUIFZYXYXYX第3章初等函数一、单项选择题1、A2、D3、B4、A二、填空题1、2、3、E1SINCOI24、,4LNZKI三、计算题1、解。2222,YXZXYIZEE2、解21IIIZCOSRESIN2221222YXZYXYXYXYXIZ3、解,LN,LNIZI2SICO2EZI4、解,31IZ,23LN23LN1ZKIKIARGIL四、证明题1、证明IEEIEZIZIZIZIZI22SIN左边右边ZIIZIZICOSN所以命题得证。2、证明NXXASI2SIN令NXXBCOS2CSO12SINI1SIN2SINSICOI21SNI21SNINS1212112XXXAXXEXEEEIBIXINIXINIIXNXII则命题得证。第4章解析函数的积分理论一、单项选择题1、D2、A3、B4、A二、填空题1、2、ML3、74、CCDZGZFE1三、计算题1、解积分路径的参数方程为102TITTZ21IM10IIDTITZDC2、解DZZEF132SIN0,1,ZFF根据柯西积分定理内解析在和其奇点为3、解IIF21321，的奇点为4、解、内处在处不解析，但内在函数CEZCZEZ055124420510IEIDZEDZFNFZCCNN处解析。根据公式0,441ZFZZ由柯西积分定理知内解析在区域内，且均不在四、证明题1、证明1221内解析在，的奇点为ZFZF20020222020110COS451COS451COSINSICOSNIS,0DDIDIDEIDZDIEZZIZ为偶函数，又令由柯西积分定理知2证设由圆周围成的区域为，易知，为有界闭区域RZGRZG因函数在内不是常数，在内解析，且在有界闭区域上连续，所以，FCS由最大模原理有ZMZF,COS这表明在内取不到最大值，故它只能在的边界上取到最大值GGRZ，即在圆周上必存在一点，使得，且有MRZ0ZMZF010FZF故结论得证第5章解析函数的幂级数表示一、单项选择题1、B2、B3、D4、C二填空题1、2、一3、04、一Z三、计算题四、证明题第6章解析函数的罗朗级数表示一、单项选择题1、D2、C3、D4、B二、填空题1、2、3、一NNAZC内解析去心邻域RAZ04、本性三、计算题NNNNZZZZF01002321311解1,11,020120ZZZZFNN上式两边逐项求导的幂级数可展成内处处解析，且在上有一奇点在解31,313132300ZZZFNNN解1,1,20,4001ZENZEZNEEZNZZ收敛圆域为在复平面内处处解析又因为解由泰勒定理知SIN2SI2IZIZIZIIZIEZEE左边SINCOS135,INCO222222得证成立即在复平面上成立推得定理由解析函数惟一性定理轴上有在并且都在复平面内解析与设证明ZZFFXXFFCOSF2121120,100NNNZZZZZFF解析的圆域为使的有限奇点为21121,22ZZZFF解析的圆域为使的有限奇点为四、证明题第七章残数及其应用一、单项选择题1、B2、A3、A4、C二、填空题1、23、44、0LIMZFAZAGF三、计算题是可去奇点。为其奇点且0,1SINLMLI033ZZZFZ1,0461,03,42的一级极点是知由定理个零点有显然令ZFZZZZZGFG0,2002的本性奇点是所以主要部分有无穷多项可展成罗朗级数在其去心邻域内的有限奇点只有ZFZNZEFZFFNZ6046,6101250,3881,2663级极点的为可知定理由级零点的为知根据定理且解析在点其中的有限奇点为ZFZFZZEZFZF231LIM2LI,RE,21LIMLI0,RE,0120ZZFZFSZFZFSZ的一级极点，都是1COSSIN1,REI为奇数为偶数的一级零点是的一级零点，是NZZFSZFZN四、证明题第8章一、单项选择题1、C2、D3、D4、D二、填空题1、单叶、保角2、解析、不为零3、4、,32123241ZZZ1平面上的圆周三、计算题02,RE2,E,RE,E201LIM2LI,RE1M2,04LILI,E,1,R2413222ZFSZFSZFSIZFSDZFSZZFZFIIISZZFZFICZZZIIZ则，有四个奇点12241,RE21121OS1C4222202AAZFSIDZAZAZIZDACCCCI，于是时，可得变到由，当，则令,LIM2LM,RE,02等式得证等式右边等式左边的一级极点为，且一个在上半平面的奇点只有则令AAIZZAIZIZEFFSDXFA013,3,RE,E41LIM,3LI,233,01,24244等式得证等式右边等式左边计算其次一级极点的均为且易知与即个只有在上半平面的全部奇点解方程便得令在上半平面的全部奇点首先求出ZQPSZPSIDXXIZZQPIZQPIIZZQPZ2ARG01,012,1,RE,1平面实轴剪开的为从原点出发沿正平面上的角形区域为因确定由最后得中代入与将其次首先令解为确定KKNNIIGFNKKZNZGRRZR20,20,200XXXIEGEYXZYEZEIYX为圆周由对应规律得平面上的线段为因确定由最后得对应规律中代入与将其次首先令解为确定12121101,33232ZIIIZIIZZ则有解令0,432132ZIZIZIIZI则有解令四、证明题,0IM,0,1得证即复平面的上半平面为由此可知的取值范围是与的的取值范围可得与中的由确定由最后得对应规律中代入与将其次首先令解为确定GYXGYEEZEIZXIRE0,RE0RE,IIEE,2得证即的取值范围为中取值范围可得中的由得对应规律中代入与将其次首先令解为确定ABGZGZABYABXUZABZIVUIZ请您删除一下内容，O_O谢谢2016年中央电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄BASKETBALLCANMAKEATRUECLAIMTOBEINGTHEONLYMAJORSPORTTHATISANAMERICANINVENTIONFROMHIGHSCHOOLTOTHEPROFESSIONALLEVEL,BASKETBALLATTRACTSALARGEFOLLOWINGFORLIVEGAMESASWELLASTELEVISIONCOVERAGEOFEVENTSLIKETHENATIONALCOLLEGIATEATHLETICASSOCIATIONNCAAANNUALTOURNAMENTANDTHENATIONALBASKETBALLASSOCIATIONNBAANDWOMENSNATIONALBASKETBALLASSOCIATIONWNBAPLAYOFFSANDITHASALSOMADEAMERICANHEROESOUTOFITSPLAYERANDCOACHLEGENDSLIKEMICHAELJORDAN,LARRYBIRD,EARVIN“MAGIC“JOHNSON,SHERYLSWOOPES,ANDOTHERGREATPLAYERSATTHEHEARTOFTHEGAMEISTHEPLAYINGSPACEANDTHEEQUIPMENTTHESPACEISARECTANGULAR,INDOORCOURTTHEPRINCIPALPIECESOFEQUIPMENTARETHETWOELEVATEDBASKETS,ONEATEACHENDINTHELONGDIRECTIONOFTHECOURT,ANDTHEBASKETBALLITSELFTHEBALLISSPHERICALINSHAPEANDISINFLATEDBASKETBALLSRANGEINSIZEFROM28530IN7276CMINCIRCUMFERENCE,ANDINWEIGHTFROM1822OZ510624GFORPLAYERSBELOWTHEHIGHSCHOOLLEVEL,ASMALLERBALLISUSED,BUTTHEBALLINMENSGAMESMEASURES29530IN7576CMINCIRCUMFERENCE,ANDAWOMENSBALLIS28529IN7274CMINCIRCUMFERENCETHECOVERINGOFTHEBALLISLEATHER,RUBBER,COMPOSITION,ORSYNTHETIC,ALTHOUGHLEATHERCOVERSONLYAREDICTATEDBYRULESFORCOLLEGEPLAY,UNLESSTHETEAMSAGREEOTHERWISEORANGEISTHEREGULATIONCOLORATALLLEVELSOFPLAY,THEHOMETEAMPROVIDESTHEBALLINFLATIONOFTHEBALLISBASEDONTHEHEIGHTOFTHEBALLSBOUNCEINSIDETHECOVERINGORCASING,ARUBBERBLADDERHOLDSAIRTHEBALLMUSTBEINFLATEDTOAPRESSURESUFFICIENTTOMAKEITREBOUNDTOAHEIGHTMEASUREDTOTHETOPOFTHEBALLOF4954IN1214MWHENITISDROPPEDONASOLIDWOODENFLOORFROMASTARTINGHEIGHTOF6FT180MMEASUREDFROMTHEBOTTOMOFTHEBALLTHEFACTORYMUSTTESTTHEBALLS,ANDTHEAIRPRESSURETHATMAKESTHEBALLLEGALINKEEPINGWITHTHEBOUNCETESTISSTAMPEDONTHEBALLDURINGTHEINTENSITYOFHIGHSCHOOLANDCOLLEGETOURNEYSANDTHEPROFESSIONALPLAYOFFS,THISINFLATEDSPHERECOMMANDSCONSIDERABLEATTENTIONBASKETBALLISONEOFFEWSPORTSWITHAKNOWNDATEOFBIRTHONDECEMBER1,1891,INSPRINGFIELD,MASSACHUSETTS,JAMESNAISMITHHUNGTWOHALFBUSHELPEACHBASKETSATTHEOPPOSITEENDSOFAGYMNASIUMANDOUTLINED13RULESBASEDONFIVEPRINCIPLESTOHISSTUDENTSATTHEINTERNATIONALTRAININGSCHOOLOFTHEYOUNGMENSCHRISTIANASSOCIATIONYMCA,WHICHLATERBECAMESPRINGFIELDCOLLEGENAISMITH18611939WASAPHYSICALEDUCATIONTEACHERWHOWASSE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