Venue: Online and H-303 Office space
Class Timings: Tuesdays and Thursdays 10:00 AM - 11:30AM (Flexible Timings)
First Meeting: 14 August 2025
Syllabus:
Holomorphic functions and their basic properties: Power series expansions; exponential and logarithmic functions; Möbius transformations; Cauchy-Riemann equations; conformality; elementary conformal mappings.
Contour integration: Cauchy’s theorem, Cauchy integral formula, and the calculus of residues.
Meromorphic functions: Laurent expansions, zeros and poles, removable singularities, essential singularities, and the principle of analytic continuation.
Open mapping theorem and maximum modulus principle.
Harmonic functions and connections to harmonic analysis: Poisson integral formula and Jensen’s formula.
Course Outcomes:
Develop proficiency in the theory of holomorphic functions and contour integration.
Apply residue calculus and the open mapping theorem to solve problems.
Apply techniques from harmonic analysis to problems in complex analysis
Text books : J. B. Conway's book: Functions of one Complex Variable
Course evaluation : TBA
- Teacher: Rukmini Dey