HNGU M.SC. MATHEMATICS SEMESTER - 3
MSM1302 β COMPLEX ANALYSIS
Unit 1:
- [Revision: Complex numbers and its polar and exponential forms,Powers and roots]
- Regions in the complex plane,
- Continuity and differentiability of complex functions,
- Analytic functions,
- Cauchy-Riemann equations,
- Harmonic Functions of two variables,
- Infinite series of complex numbers,
- Power series functions.
Unit 2:
- The elementary Functions: exponential,
- Trigonometric,
- Hyperbolic functions,
- Logarithmic functions and its branches,
- Rectifiable arcs,
- Complex line integral,
- Complex contour integral,
- Cauchy β Goursat Theorem.
Unit 3:
- Cauchyβs integral formula,
- Derivative of analytic functions,
- Moreraβs theorem,
- Liouvilleβs theorem,
- Fundamental theorem of algebra,
- Taylor expansions,
- Laurent expansions.
Unit 4:
- Singularities,
- Zeros of analytic functions,
- Poles,
- Residues,
- Residue Theorem,
- Residue at poles and examples.
Download Reference Books:
Note : The course is covered by the book: Complex Variables and Applications (Fourth edition) by Rule V Churchill and James W Brown, McGraw Hill, International Editions.
1. The Elements of Complex Analysis - John Duncan, John Wiley & Sons Ltd, London. (1968)
2. Complex Analysis 3rd edition - L V Ahlfors, McGraw Hill, 1966.
3. Functions of one complex variables 2nd edition - J B Conway, Springer Verlag, New York (1973)
4. Complex Analysis - Serge Lang, Addison- Wesley, Publishing Co. (1997)
5. The Elements of Complex Analysis 2nd edition - B Choudary, New Age International Ltd Publishers, New Delhi. (1992)
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| Nov/Dec - 2019 | Download |
| Nov/Dec - 2020 (MCQ) | Download |
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