2016年电大数学与应用数学复变函数练习试题

一、单项选择题1设，则可用表示为（）YXZIZABCD22I2ZI2Z2若，则上半平面可表示为（）ZIABCD0IM0IZ0IMZ0IMZ3（）2D1AZABCDI2I24函数在复平面上可表示为（）ZFEABCD2N0N1NZ2NZ5设，则为的（）ZFSI,2,KFA一级零点B二级零点C三级零点D四级零点二、填空题1设为实数，称形如的为复数YX,YX2设，则称为指数函数，其中“”为自然对数的底ZIZEE3若存在某个，使得，则称点为函数的解析点,ANAZF4函数在点展成罗朗级数，即在内展成罗朗级数ZF115若映射在区域内是，则称此映射为区域内的保形映射WGG三、计算题1设，试求解析函数，使得，且满足23XYUVUZFI23XYU0IF2设，试将在点展成幂级数1ZFZF13计算积分CYXXC2,D22四、证明题试证XNNXX2SII1SISIN一、单项选择题1B2C3D4B5A二、填空题1有序数对23在内处处可导SINCOEYXZF,AN45单叶且保角的10Z三、计算题1解由CR条件有，所以YXVU23XV又因为，得，所以XYVU0C所以CYXV32由此得I32YXZF由得，故0IF1C1I32YXF经验证或I3YXZFI3ZF即为所求2解在内可展成幂级数，有ZF132Z113Z0NNZ，1331Z5解积分路径即为，而被积函数共有两个奇点1与位于内部，所以C2IZICCZD2I,1RES1,RESI22ZZ而,4I,1ES2Z故2IDCZ四、证明题证令NXXACOSCSO1NXXBSI2SIN于是XXBI2IIEEIXI12SINE121IXXN2SINSICON故请您删除一下内容，O_O谢XX2ISISIN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,WHICHLATERBECAMESPRINGFIELDCOLLEGENAISMITH18611939WASAPHYSICALEDUCATIONTEACHERWHOWASSEEKINGATEAMSPORTWITHLIMITEDPHYSICALCONTACTBUTALOTOFRUNNING,JUMPING,SHOOTING,ANDTHEHANDEYECOORDINATIONREQUIREDINHANDLINGABALLTHEPEACHBASKETSHEHUNGASGOALSGAVETHESPORTTHENAMEOFBASKETBALLHISSTUDENTSWEREEXCITEDABOUTTHEGAME,ANDCHRISTMASVACATIONGAVETHEMTHECHANCETOTELLTHEIRFRIENDSANDPEOPLEATTHEIRLOCALYMCASABOUTTHEGAMETHEASSOCIATIONLEADERSWROTETONAISMITHASKINGFORCOPIESOFTHERULES,ANDTHEYWEREPUBLISHEDINTHETRIANGLE,THESCHOOLNEWSPAPER,ONJANUARY15,1892NAISMITHSFIVEBASICPRINCIPLESCENTERONTHEBALL,WHICHWASDESCRIBEDAS“LARGE,LIGHT,ANDHANDLEDWITHTHEHANDS“PLAYERSCOULDNOTMOVETHEBALLBYRUNNINGALONE,ANDNONEOFTHEPLAYERSWASRESTRICTEDAGAINSTHANDLINGTHEBALLTHEPLAYINGAREAWASALSOOPENTOALLPLAYERS,BUTTHEREWASTOBENOPHYSICALCONTACTBETWEENPLAYERSTHEBALLWASTHEOBJECTIVETOSCORE,THEBALLHADTOBESHOTTHROUGHAHORIZONTAL,ELEVATEDGOALTHETEAMWITHTHEMOSTPOINTSATTHEENDOFANALLOTTEDTIMEPERIODWINSEARLYINTHEHISTORYOFBASKETBALL,THELOCALYMCASPROVIDEDTHEGYMNASIUMS,ANDMEMBERSHIPINTHEORGANIZATIONGREWRAPIDLYTHESIZEOFTHELOCALGYMDICTATEDTHENUMBEROFPLAYERSSMALLERGYMSUSEDFIVEPLAYERSONASIDE,ANDTHELARGERGYMSALLOWEDSEVENTONINETHETEAMSIZEBECAMEGENERALLYESTABLISHEDASFIVEIN1895,AND,IN1897,THISWASMADEFORMALINTHERULESTHEYMCALOSTINTERESTINSUPPORTINGTHEGAMEBECAUSE1020BASKETBALLPLAYERSMONOPOLIZEDAGYMNASIUMPREVIOUSLYUSEDBYMANYMOREINAVARIETYOFACTIVITIESYMCAMEMBERSHIPDROPPED,ANDBASKETBALLENTHUSIASTSPLAYEDINLOCALHALLSTHISLEDTOTHEBUILDINGOFBASKETBALLGYMNASIUMSATSCHOOLSANDCOLLEGESANDALSOTOTHEFORMATIONOFPROFESSIONALLEAGUESALTHOUGHBASKETBALLWASBORNINTHEUNITEDSTATES,FIVEOFNAISMITHSORIGINALPLAYERSWERECANADIANS,ANDTHEGAMESPREADTOCANADAIMMEDIATELYITWASPLAYEDINFRANCEBY1893ENGLANDIN1894AUSTRALIA,CHINA,ANDINDIABETWEEN1895AND1900ANDJAPANIN1900FROM1891THROUGH1893,ASOCCERBALLWASUSEDTOPLAYBASKETBALLTHEFIRSTBASKETBALLWASMANUFACTUREDIN1894ITWAS32IN81CMINCIRCUMFERENCE,ORABOUT4IN10CMLARGERTHANASOCCERBALLTHEDEDICATEDBASKETBALLWASMADEOFLACEDLEATHERANDWEIGHEDLESSTHAN20OZ567GTHEFIRSTMOLDEDBALLTHATELIMINATEDTHENEEDFORLACESWASINTRODUCEDIN1948ITSCONSTRUCTIONANDSIZEOF30IN76CMWERERULEDOFFICIALIN1949THERULESETTERSCAMEFROMSEVERALGROUPSEARLYINTHE1900SCOLLEGESANDUNIVERSITIESESTABLISHEDTHEIRRULESCOMMITTEESIN1905,THEYMCAANDTHEAMATEURATHLETI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