Complex_Analysis

《Complex_Analysis》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、FaculteitWiskundeenInformaticaLecturenotesforthecourseComplexAnalysis(2Y480)M.L.J.Hautus,S.W.RienstraSeptember2012Contents1HolomorphicFunctions11.1Complexnumbers..................................11.2Openandclosedsets................................31.3Limitsandcontinuity........................

2、........51.4Differentiablefunctions...............................81.5TheEquationsofCauchy-Riemann.........................111.6Powerseries.....................................142Complexintegration212.1Arcsandcurves...................................212.2Thedefinitionoftheintegral...............

3、.............232.3Cauchy'sIntegralTheorem.............................262.4Theresidue.....................................302.5Cauchy'sIntegralFormula,Taylorseries......................322.6Zeros,entirefunctions,Liouville'sTheorem....................372.7Laurentseries,singularpoints............

4、...............402.8TheLaurentseriesasaFourierseries........................432.9Logarithmsandfractionalpowers.........................442.9.1Definitionofthelogarithm.........................442.9.2Thelogarithmasinverseoftheexponential................462.9.3Thelogarithmofafunction...............

5、.........462.9.4Properties..................................47√2.9.5Thecomplexsquarerootz−a.....................48√2.9.6Thecomplexsquareroota2−z2....................503Residuecalculus513.1Calculationofresidues...............................513.1.1UseoftheLaurentseries..........................5

6、13.1.2Poleoffirstorder..............................523.1.3Typel'Hôpital...............................523.1.4Poleofhigherorder............................533.2Integralsoverafiniteinterval............................533.3Integralsovertherealaxis.............................563.4Integralsofthetype

7、“Fouriertransform”......................583.5Integralsofthetype“Laplacetransform”.....................623.6Integralswithlogarithmsandfractionalpowers..................643.6.1Integralsofthetype“Mellintransform”..................64R