Modulecode
SM-2207
ModuleTitle
ComplexAnalysis
Degree/Diploma
BachelorofScience(Mathematics)
TypeofModule
MajorCore
ModularCredits
4
TotalstudentWorkload
10
hours/week
Contacthours
4
hours/week
Prerequisite
SM-2202MultivariateCalculus
Anti-requisite
None
Aims
Tolearnmainprinciplesofcomplexanalysisanditsapplicationsinotherfieldsofmathematics
LearningOutcomes
Onsuccessfulcompletionofthismodule,astudentwillbeexpectedtobeableto:
Lowerorder: 30% -workwithcomplexnumbers,describevarioussetsinthecomplexplaneand
actionsofelementaryfunctionsonthecharacteristicsets.
Middleorder: 60% -knowtheanalyticityconditionsandpropertiesofanalyticfunctions.
Differentiateandintegratecomplexvaluedfunctions.
Higherorder: 10% -Befamiliarwithresiduesofanalyticfunctionsandtheirapplicationsfor
evaluationofrealandcomplexintegrals.
ModuleContents
-Representationofcomplexnumbersinalgebraicandpolarform.Complexconjugationandmain
propertiesofcomplexnumbers.Rootsofcomplexnumbers.
-Topologyofcomplexplane.Openandclosedsubsets.Compactsets.Continuousarcs.Connected
sets.Multi-valuedandsingle-valuedfunctions.Branchesofmulti-valuedfunctions.Limittheorems.
Continuousfunctions.
-Differentiability.Propertiesofdifferentiablefunctions.Differentiationrules.Cauchy-Riemann
equations.Analyticfunctions.Conformalmappings.Harmonicfunctions.Elementarycomplex
functions
-Lineandcontourintegrals.Cauchytheoremanditsconsequences.Cauchyintegralformulaand
propertiesofanalyticfunctions.Seriesrepresentationofanalyticfunctions.
-Singularpoints.Laurentseriesandclassificationofsingularities.Propertiesofanalyticfunctions
aroundsingularpoints..
-Calculusofresidues.Cauchytheorem.Applications.Evaluationofrealintegralsandsummationof
series.
Assessment
Formative
assessment
Tutorialandfeedback.
Summative
assessment
Examination:60%
Coursework:40%
-1classtest(20%)
-1assignment(20%)

Cauchy Functions and Taylor`s Formula for Time Scales T

Exam 2 Study Guide 2.4 -‐ 3.1 2.4

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