PMA207: Complex Analysis (January-May, 2020)

Course Instructor: Amrik Sen (email: amriksen@thapar.edu)

Course Documents: syllabus, lecture plan. 

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"

               (video lecture: Lec10_1)

        (pdf) "maximum principle"

        (pdf) "Cauchy integral formula, Liouville

                theorem & DBAR derivative"

               (video lecture: Lec10_2, Lec11)

Set 6: (pdf) "introduction to Laurent series"

                     (video lecture: Lec12_1)

        (pdf) "proof of Laurent series theorem"

        (pdf) "singularities in C"

               (video lecture: Lec13)

        (pdf) "analytic continuation"

Set 7: (pdf) "introduction to residue calculus"

               (video lecture: Lec16 part 1)

                     (video lecture: Lec16 part 2)

        (pdf) "principal value integrals

                & their applications"

               (video lecture: Lec17_1)

                     (video lecture: Lec17_2)

        (pdf) "application of residue calculus"

               (video lecture: Lec18)

        (pdf) "Roche's theorem & the argument

                 principle"

               (video lecture: Lec19)

Set 8: (pdf) "introduction to conformal maps"

               (video lecture: Lec20)

 

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)

May 2, 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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