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1、AnIntroductiontoComplexAnalysisforEngineersMichaelD.AlderJune3,19971PrefaceThesenotesareintendedtobeofusetoThirdyearElectricalandElec-tronicEngineersattheUniversityofWesternAustraliacomingtogripswithComplexFunctionTheory.Therearemanytextbooksforjustthispurpose,andIhavein
2、sucienttimetowriteatextbook,sothisisnotasubstitutefor,say,MatthewsandHow-ell'sComplexAnalysisforMathematicsandEngineering,[1],butperhapsacomplementtoit.Atthesametime,knowinghowreluctantstudentsaretouseatextbook(exceptasatalismantowardo evil)Ihavetriedtomakethesenotessu
3、cient,inthatastudentwhoreadsthem,understandsthem,anddoestheexercisesinthem,willbeabletousetheconceptsandtech-niquesinlateryears.Itwillalsogetthestudentcomfortablythroughtheexamination.Theshortnessofthecourse,20lectures,forcoveringComplexAnalysis,eitherpresupposesgenius(9
4、0%perspiration)onthepartofthestudentsormaterialskipped.Thesenotesareintendedto llinsomeofthegapsthatwillinevitablyoccurinlectures.Itisasourceofsomedisappoint-menttomethatIcancoversolittleofwhatisabeautifulsubject,richinapplicationsandconnectionswithotherareasofmathematic
5、s.Thisis,then,asortofsampler,andonlytouchestheelements.StylesofMathematicalpresentationchangeovertheyears,andwhatwasdeemedacceptablerigourbyEulerandGaussfailstokeepmodernpuristscontent.McLachlan,[2],clearlysmartedunderthecriticismsofhispresen-tation,andhegoestosometroubl
6、etoexplaininlatereditionsthatthebookisintendedforadi erentaudiencefromthepuristswhodamnedhim.Myexperienceleadsmetofeelthattheneedforrigourhasbeendevelopedtothepointwheretheintuitiveandgeometrichasbeenstunted.Bothhaveapartinmathematics,whichgrowsoutofthecon
ictbetweenthem
7、.Butitseemstomemoreimportanttopenetratetotheideasinasloppy,scru ybutserviceableway,thantoreduceasubjecttopredicatecalculusandomitthewholereasonforstudyingit.Thereisnoknownmeansofpersuadingahardheadedengineerthatasubjectmeritshistimeandenergywhenithasbeenturnedintoanelabo
8、rategame.He,orincreasinglyshe,wantstoseetwoelementsatanearlystage:proceduresforsolvingproblemswhichmake
