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MATH-505: Complex Analysis

MMAF13E101 = 65
MMAF13E102 = 65
MMAF13E103 = 58
MMAF13E104 = 58
MMAF13E105 = 78
MMAF13E106 = 62
MMAF13E107 = 50
MMAF13E108 = 75
MMAF13E109 = 61
MMAF13E110 = 50
MMAF13E111 = 50
MMAF13E112 = 85
MMAF13E113 = 59
MMAF13E114 = 0
MMAF13E115 = 50
MMAF13E116 = 78
MMAF13E117 = 50
MMAF13E118 = 38
MMAF13E119 = 37
MMAF13E120 = 62

MMAF13E121 = 61
MMAF13E122 = 77
MMAF13E123 = 28
MMAF13E124 = 50
MMAF13E125 = 58
MMAF13E126 = 50
MMAF13E127 = 65
MMAF13E128 = 37
MMAF13E129 = 50
MMAF13E130 = 39
MMAF13E131 = 71
MMAF13E132 = 62
MMAF13E133 = 50
MMAF13E134 = 56
MMAF13E135 = 58
MMAF13E136 = 50
MMAF13E137 = 50
MMAF13E138 = 0
MMAF13E139 = 33
MMAF13E140 = 50

MMAF13E141 = 76
MMAF13E142 = 55
MMAF13E143 = 65
MMAF13E144 = 43
MMAF13E145 = 71
MMAF13E146 = 50
MMAF13E147 = 75
MMAF13E148 = 23
MMAF13E149 = 62
MMAF13E150 = 11
MMAF13E151 = 50
MMAF13E152 = 17
MMAF13E153 = 56
MMAF13E154 = 50
MMAF13E155 = 36
MMAF13E156 = 58
MMAF13E157 = 55
MMAF13E158 = 50
MMAF13E159 = 40
MMAF13E160 = 30
MMAF12E117 = 58
MMAF12E119 = 78
MMAF12E131 = 55
MMAF12E135 = 10
MMAF12E146 = 50


MMAF13M001 20
MMAF13M002 76
MMAF13M003 67
MMAF13M004 76
MMAF13M005 61
MMAF13M006 61
MMAF13M007 65
MMAF13M008 75
MMAF13M009 70
MMAF13M010 70
MMAF13M011 53
MMAF13M012 50
MMAF13M013 41
MMAF13M014 61
MMAF13M015 88
MMAF13M016 50
MMAF13M017 78
MMAF13M018 77
MMAF13M019 51
MMAF13M020 66
MMAF13M021 65
MMAF13M022 32
MMAF13M023 67
MMAF13M024 36
MMAF13M025 0
MMAF13M026 62
MMAF13M027 63
MMAF13M028 9
MMAF13M029 50
MMAF13M030 41
MMAF13M031 85
MMAF13M032 5
MMAF13M033 65
MMAF13M034 67
MMAF13M035 50
MMAF13M036 72
MMAF13M037 50
MMAF13M038 94

This is an introductory course in complex analysis, giving the basics of the theory along with applications, with an emphasis on applications of complex analysis and especially conformal mappings. Students should have a background in real analysis (as in the course Real Analysis I), including the ability to write a simple proof in an analysis context.

  • The Concept of Analytic Functions: The complex numbers and the complex plane<, Functions of a complex variable, General properties of analytic functions, Linear transformations, Basic properties of linear transformation, mapping for problems, stereographic projections, Basic concepts of conformal mapping, The exponential and the logarithmic functions, the trigonometric functions, Taylor’s series, Laurent’s series, infinite series with complex terms, power series, infinite products.
  • Integration in the Complex Domain: Cauchy’s theorem, Cauchy’s integral formula and its applications, Laurent’s expansion, isolated singularities of analytic functions, the residue theorem and its applications.
  • Contour Integration: Definite integrals, partial fraction, expansion of $\cot 2z$,
  • The arguments principle theorem and its applications: Rouche’s theorem,
  • Analytic Continuation: The principle of Analytic Continuation.
  1. J.W Brown and R.V Churchill, Complex Variables and Applications, 8th Edition, McGraw-Hill, 2009.
  2. Dennis Zill, A first course in complex analysis with applications, Jones and Bartlett Publishers, Inc., 2008.
  3. J.H. Mathews and R.W. Howell, Complex analysis for mathematical engineering, Norosa Publishing House Dehli, 2006.
Assignment 1 Download PDF (150KB)
Assignment 2 Download PDF (151KB)
Assignment 3 Download PDF (143KB)


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