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MAM149 Complex Analysis 6.0 ECTS credits | |
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TIMEPERIOD: LANGUAGE:English EXAMINER L Maligranda Prof PREREQUISITES The course will be given in english and together with MAM024. COURSE AIM The aim of this course is to give a good understanding of some basic concepts in complex analysis. CONTENTS Complex numbers, complex functions, complex differentiation of functions developing theorems on that such as Cauchy-Riemann equations, analytic functions, reflection principle, harmonic functions and Cauchy-type theorems. Elementary functions of complex variable such as exponential, trigonometric and logarithmic functions. Contour integrals with the nice Cauchy-Goursat theorem which implies all beautifull theory containing Cauchy integral formula. Liouville's theorem, Laurent series, residues and residue theorems. Residue theorems are applied to evaluation of improper real integrals, definite integrals with sines and cosines, argument principle and Rouché theorem. Conformal mappings are studied in the final of the course. TEACHING EXAMINATION The examination consists of a written examination at the end of the course. COURSE GRADE SCALE: ITEMS/CREDITS | |
| Written exam | 6.00ECTS |
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COURSE LITERATURE J.W. Brown and R.V. Churchill, Complex Variables and Applications, Sixth Edition, McGraw-Hill, Inc., New York 1996 (Chapters 1-9) Course information from the department: http://www.sm.luth.se/math/education/ |
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