# MATH-505: Complex Analysis

## Provisional Results

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

## Objectives of the course

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.

## Course contents

- 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.

## Recommended books

- J.W Brown and R.V Churchill,
*Complex Variables and Applications*, 8th Edition, McGraw-Hill, 2009. - Dennis Zill,
*A first course in complex analysis with applications*, Jones and Bartlett Publishers, Inc., 2008. - J.H. Mathews and R.W. Howell,
*Complex analysis for mathematical engineering*, Norosa Publishing House Dehli, 2006.

## Assignments

Assignment 1 | Download PDF (150KB) |
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Assignment 2 | Download PDF (151KB) |

Assignment 3 | Download PDF (143KB) |

## External links

- Computational Knowledge Engine: http://www.wolframalpha.com