Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Pranav Haridas
NPTEL Co-ordinating Institute : IIT Madras
NPTEL Lecture Count : 48
NPTEL Course Size : 5.9 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Field of Complex Numbers
Lecture 2 - Conjugation and Absolute value
Lecture 3 - Topology on Complex plane
Lecture 4 - Topology on Complex Plane (Continued...)
Lecture 5 - Problem Session
Lecture 6 - Isometries on the Complex Plane
Lecture 7 - Functions on the Complex Plane
Lecture 8 - Complex differentiability
Lecture 9 - Power Series
Lecture 10 - Differentiation of power series
Lecture 11 - Problem Session
Lecture 12 - Cauchy-Riemann equations
Lecture 13 - Harmonic functions
Lecture 14 - Möbius transformations
Lecture 15 - Problem session
Lecture 16 - Curves in the complex plane
Lecture 17 - Complex Integration over curves
Lecture 18 - First Fundamental theorem of Calculus
Lecture 19 - Second Fundamental theorem of Calculus
Lecture 20 - Problem session
Lecture 21 - Homotopy of curves
Lecture 22 - Cauchy-Goursat theorem
Lecture 23 - Cauchy's theorem
Lecture 24 - Problem Session
Lecture 25 - Cauchy Integral Formula
Lecture 26 - Principle of analytic continuation and Cauchy estimates
Lecture 27 - Further consequences of Cauchy Integral Formula
Lecture 28 - Problem session
Lecture 29 - Winding number
Lecture 30 - Open mapping theorem
Lecture 31 - Schwarz reflection principle
Lecture 32 - Problem session
Lecture 33 - Singularities of a holomorphic function
Lecture 34 - Pole of a function
Lecture 35 - Laurent Series
Lecture 36 - Casorati Weierstrass theorem
Lecture 37 - Problem Session
Lecture 38 - Residue theorem
Lecture 39 - Argument principle
Lecture 40 - Problem Session
Lecture 41 - Branch of the Complex logarithm
Lecture 42 - Automorphisms of the Unit disk
Lecture 43 - Phragmen Lindelof method
Lecture 44 - Problem Session
Lecture 45 - Lifting of maps
Lecture 46 - Covering spaces
Lecture 47 - Bloch's theorem
Lecture 48 - Little Picard's theorem