~~NOTOC~~ ====== 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** | [[https://dl.dropboxusercontent.com/u/64787761/MSc_Assignment_01.pdf|Download PDF]] (150KB) | ^**Assignment 2** | [[https://dl.dropboxusercontent.com/u/64787761/MSc_Assignment_02.pdf|Download PDF]] (151KB) | ^**Assignment 3** | [[https://dl.dropboxusercontent.com/u/64787761/MSc_Assignment_03.pdf|Download PDF]] (143KB) | ===== External links===== * http://en.wikipedia.org/wiki/Complex_number * SPDFICON http://math.furman.edu/~dcs/courses/math39/lectures/lecture-5.pdf * SPDFICON http://www.math.wisc.edu/~angenent/Free-Lecture-Notes/freecomplexnumbers.pdf * Computational Knowledge Engine: http://www.wolframalpha.com * http://en.wikipedia.org/wiki/Stereographic_projection * http://mathworld.wolfram.com/StereographicProjection.html * http://www.sosmath.com/trig/Trig2/trig2/trig2.html * http://www.sosmath.com/algebra/logs/log4/log4.html