Amrik's lecture notes: 

 

Each set has one or more lectures and covers a

"set" of closely related topics.

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Set 0: A brief introduction to complex numbers (here)

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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)

 

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Tutorial cum HW assignments

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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"

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Solutions to HW assignments   

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HW 1 solutions: (pdf) "most of it"  

HW 2 solutions: (pdf) "all of it"

HW 3 solutions: (pdf) "almost all of it"   

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Exams & Solutions  

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MST: (pdf)

MST solutions: (pdf) 

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