Math 2.0

Resources / course

Complex Analysis SDTCZHR9FQ

URIm2://res/SDTCZHR9FQ
Kindcourse
CreatorsPranav Haridas (instructor)
Date2020-12-22
Scopein

Expressions

e1: edition

Languageen
Date2020-12-22
Contents
  • part 1: Week 1
  • session 1: Field of Complex Numbers
  • session 2: Conjugation and Absolute value
  • session 3: Topology on Complex plane
  • session 4: Topology on Complex Plane (Contd)
  • part 2: Week 2
  • session 5: Problem Session
  • session 6: Isometries on the Complex Plane
  • session 7: Functions on the Complex Plane
  • session 8: Complex differentiability
  • part 3: Week 3
  • session 9: Power Series
  • session 10: Differentiation of power series
  • session 11: Problem Session
  • session 12: Cauchy-Riemann equations
  • part 4: Week 4
  • session 13: Harmonic functions
  • session 14: Möbius transformations
  • session 15: Problem session
  • session 16: Curves in the complex plane
  • part 5: Week 5
  • session 17: Complex Integration over curves
  • session 18: First Fundamental theorem of Calculus
  • session 19: Second Fundamental theorem of Calculus
  • session 20: Problem session
  • part 6: Week 6
  • session 21: Homotopy of curves
  • session 22: Cauchy-Goursat theorem
  • session 23: Cauchy's theorem
  • session 24: Problem Session
  • part 7: Week 7
  • session 25: Cauchy Integral Formula
  • session 26: Principle of analytic continuation and Cauchy estimates
  • session 27: Further consequences of Cauchy Integral Formula
  • session 28: Problem session
  • part 8: Week 8
  • session 29: Winding number
  • session 30: Open mapping theorem
  • session 31: Schwarz reflection principle
  • session 32: Problem session
  • part 9: Week 9
  • session 33: Singularities of a holomorphic function
  • session 34: Pole of a function
  • session 35: Laurent Series
  • session 36: Casorati Weierstrass theorem
  • part 10: Week 10
  • session 37: Problem Session
  • session 38: Residue theorem
  • session 39: Argument principle
  • session 40: Problem Session
  • part 11: Week 11
  • session 41: Branch of the Complex logarithm
  • session 42: Automorphisms of the Unit disk
  • session 43: Phragmen Lindelof method
  • session 44: Problem Session
  • part 12: Week 12
  • session 45: Lifting of maps
  • session 46: Covering spaces
  • session 47: Bloch's theorem
  • session 48: Little Picard's theorem

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