'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.
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.
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).
- H S Kasana, Complex variables and Theory and Applications, second edition, Prentice Hall India.
- S. Ponnusamy, Foundations of Complex Analysis, 2nd Edition, Narosa Publishing House, 2005.
- J.W. Brown and R.V. Churchil, Complex Variable and Applications, McGraw Hill, 2008.
- R. Roopkumar, Complex Analysis, Pearson Education, 2014, Chennai.
Related Academic Courses
