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Utkal University, Odisha
Mathematics
COMPLEX ANALYSIS
Utkal University, Odisha, Mathematics Semester 6, COMPLEX ANALYSIS Syllabus
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Unit  1 Complex Numbers And Complex Plane
Unit 1
Complex Numbers and Complex plane
1.1 Complex Numbers and Complex plane Basic properties convergence Sets in the Complex plane
1.2 Functions on the Complex plane Continuous functions holomorphic functions
1.3 Power series Integration along curves
Unit  2 Cauchy’s Theorem And Its Applications
Unit 2
Cauchy’s Theorem and Its Applications
2.1 Cauchy’s Theorem and Its Applications Goursat’s theorem
2.2 Local existence of primitives and Cauchy’s theorem in a disc
2.3 Evaluation of some integrals
2.4 Cauchy’s integral formulas
Unit  3 Morera’s Theorem
Unit 3
Morera’s theorem
3.1 Morera’s theorem
3.2 Sequences of holomorphic functions Holomorphic functions defined in terms of integrals
3.3 Schwarz reflection principle
3.4 Zeros and poles
Unit  4 Meromorphic Functions And The Logarithm
Unit 4
Meromorphic Functions and the Logarithm
4.1 Meromorphic Functions and the Logarithm The residue formula Examples
4.2 Singularities and meromorphic functions
4.3 The argument principle and applications
4.4 The complex logarithm
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Other Subjects of Semester6
Number theory
Group theory ii
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