COURSE SUMMARY
Course Title:
Complex Analysis
Course Code:
18MAT321
Year Taught:
2019
Semester:
6
Degree:
Integrated Degree
School:
School of Arts and Sciences
Campus:
Mysuru

'Complex Analysis' is a course offered in Sixth Semester of B. Sc. - B. Ed. in Physics, Mathematics, Computer Science program at the School of Arts and Sciences, Amrita Vishwa Vidyapeetham, Mysuru campus.

#### Scope and Objectives

On completion of the course, the student teacher will;

To enable students to obtain knowledge of theory of complex functions of a complex variable and get acquainted with different methods and techniques of series and bilinear transformations.

#### Syllabus

Unit I:

Definition, Algebra of complex numbers, polar forms, regions, Limits, continuity, differentiability Analyticity, CR equations, Harmonic Functions.
Chapters 1 & 2.

Unit II:

Conformal mappings, bilinear transformations, Special bilinear transformations, fixed points.
Chapter-9 (Sections: 9.1-9.3).

Unit III:

Contour integral, Cauchy-Goursat theorem, Cauchy’s integral formula, winding number, Primitives
Chapter-4 (Sections: 4.1-4.4, 4.7).

Unit IV:

Sequences, series, power series, uniform convergence of power series, Taylor’s series, Laurent’s series, Integration and differentiation of Power series.
Chapters- 5 & 6 (Sections: 5.1-5.2, 6.1, 6.3-6.5).

Unit V:

Zeros and singularities of analytic functions, types of singularities, poles, residue theorem.
Chapter-7 (Sections: 7.1-7.3).

#### Textbook

1. H S Kasana, Complex variables and Theory and Applications, second edition, Prentice Hall India.

#### References

1. S. Ponnusamy, Foundations of Complex Analysis, 2nd Edition, Narosa Publishing House, 2005.
2. J.W. Brown and R.V. Churchil, Complex Variable and Applications, McGraw Hill, 2008.
3. R. Roopkumar, Complex Analysis, Pearson Education, 2014, Chennai.