PMA207: Complex Analysis (January-May, 2020)
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Amrik's lecture notes:
Each set has one or more lectures and covers a
"set" of closely related topics.
Set 0: A brief introduction to complex numbers (here)
Set 1: (pdf) "geometry of complex plane"
Set 2: (pdf) "basic calculus on complex plane"
Set 3: (pdf) "Cauchy Riemann eqs., analyticity"
(pdf) "more examples on CR eqs."
(pdf) "flow around a cylinder"
Set 4: (pdf) "multi-valuedness & branch cuts"
(pdf) "analyticity of log z on cut plane"
(pdf) "Riemann surface & univalence"
Set 5: (pdf) "introduction to complex integration"
(pdf) "Cauchy-Goursat theorem & proof"
(pdf) "deformation of contour"
(pdf) "maximum principle"
(pdf) "Cauchy integral formula, Liouville
theorem & DBAR derivative"
Set 6: (pdf) "introduction to Laurent series"
(pdf) "proof of Laurent series theorem"
(pdf) "singularities in C"
(pdf) "analytic continuation"
Set 7: (pdf) "introduction to residue calculus"
(pdf) "principal value integrals
& their applications"
(pdf) "application of residue calculus"
(pdf) "Roche's theorem & the argument
principle"
Set 8: (pdf) "introduction to conformal maps"
Tutorial cum HW assignments
HW 1: (pdf) "geometry of complex plane C"
HW 2: (pdf) "calculus on C, CR equations,
multivaluedness"
HW 3: (pdf) "complex integration & Cauchy’s
theorems"
HW 4: (pdf) "series, singularities & analytic
continuation"
HW 5: (pdf) "residue calculus, principal value
integrals & conformal maps"
Solutions to HW assignments
HW 1 solutions: (pdf) "most of it"
HW 2 solutions: (pdf) "all of it"
HW 3 solutions: (pdf) "almost all of it"
Exams & Solutions
MST: (pdf)
MST solutions: (pdf)
News & Resources:
Plan for online learning & evaluation is posted here.
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Video lectures are now posted alongside the lecture notes in green color.
Doubt session archives:
Recordings from doubt sessions are here:
April 25, 2020 (download)
Online evaluation problems:
Problem set 1 (click here), due by 9 pm of 19-4-20.
Feedback & solutions to evaluation problems set 1 is here.
Problem set 2 (click here), due by 9 pm of 26-4-20.
Feedback & solutions to evaluation problems set 2 is here.
Problem set 3 (click here), due by 9 pm of 3-5-20.
Problem set 4 (click here), due by 9 pm of 10-5-20.
Problem set 5 (click here), due by 9 pm of 27-5-20.
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