PMA207: Complex Analysis (January-May, 2020)
Course Instructor: Amrik Sen (email: amriksen@thapar.edu)
Discussion Forum: enter here (password required, hint: <course code><first name of our university> all lower case and without space).
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.
All students are requested to register in the discussion forum (link: see above).
Rules of engagement to participate in the discussion forum will be posted here soon.
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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