Complex Analysis Online Course
The NPTEL is offering free online course for undergraduate/ postgraduate student in Complex Analysis.
About the course:
Enrollment Ends: July 27, 2020
End Date: October 18, 2020
For more details, please visit: https://swayam.gov.in/nd1_noc20_ma50/preview
- This is a first course in Complex Analysis focusing on holomorphic functions and its basic properties like Cauchy’s theorem and residue theorems, the classification of singularities, and the maximum principle.
- We shall study the singularities of holomorphic functions.
- If time permits, we shall also study Branches of the complex logarithm through covering spaces and attempt proving Picard’s theorem.
- Week 1: Construction and algebra of the complex numbers
- Week 2: Geometry of the complex numbers
- Week 3: Complex differentiation and power series, Convergence of power series
- Week 4: Differentiability and the Cauchy-Riemann equations, Maximum principle
- Week 5: Integration along a contour, Integration in rectifiable curves
- Week 6: The fundamental theorem of calculus, Integration by parts
- Week 7: Homotopy, Cauchy’s theorem
- Week 8: Cauchy integral formula, Analytic continuation,
- Week 9: Cauchy’s inequalities, Uniform limit of holomorphic functions
- Week 10: Winding number, General Cauchy integral formula
- Week 11: Singularities of a holomorphic function, Laurent series
- Week 12: The residue theorem, Argument principle, Rouche’s theorem
Enrollment Ends: July 27, 2020
End Date: October 18, 2020
For more details, please visit: https://swayam.gov.in/nd1_noc20_ma50/preview
