Complex Variables II — 2022.2

Instructor · IGCE-UNESP

Problem sheets (in portuguese) I prepared as an instructor for the class of Complex Variables II in the last semester of B.Sc. in Mathematics.

Sheet Topics Posted
Problem Sheet 1 — Initial concepts Harmonic functions and power series 4 Sep 2022
Problem Sheet 2 — Complex path integral I Initial properties and a version of the Fundamental Theorem of Calculus 24 Sep 2022
Problem Sheet 3 — Complex path integral II Connectivity, Cauchy-Goursat Theorem and Cauchy Integral Formula 2 Oct 2022
Problem Sheet 4 — Complex path integral III Modules Maximum Modulus Principle and Liouville’s Theorem 8 Oct 2022
Exam 1 - Review Sheet   16 Oct 2022
Exam 1   26 Oct 2022
Problem Sheet 5 — Laurent Series Singularities and Laurent Series 5 Nov 2022
Problem Sheet 6 — Poles and residues I Residues, poles and Cauchy residue theorem 13 Nov 2022
Problem Sheet 7 — Poles and residues II Argument principle 20 Nov 2022
Problem Sheet 8 — Integral via residues Rouche’s theorem 26 Nov 2022
Problem Sheet 9 — Integral via residues II Improper integrals 2 Dec 2022
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