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 Semester-6
Number theory
Group theory ii
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