MATH3401 — Complex Analysis

Lectured by Joe Grotowski in Semester 1 of 2020. Notes typed by Kenton Lam.

Useful links: full lecture notes on one page, summary of topics.

All Pages

/All Notes/
/Lecture 1 — The Complex Field/
/Lecture 2 — Complex Numbers/
/Lecture 3 — Functions of Complex Numbers/
/Lecture 4 — Functions as Mappings/
/Lecture 5 — Mappings 2/
/Lecture 6 — Möbius Transformations 2 & The Extended Complex Plane/
/Lecture 7 — Exponential Maps/
/Lecture 8 — Logarithm/
/Lecture 9 — Branch Cuts & Trigonometric Functions/
/Lecture 10 — Bounded Functions/
/Lecture 11 — Topology Definitions/
/Lecture 12 — Path Connected/
/Lecture 13 — Limits, Continuity and Differentiability/
/Lecture 14 — Derivatives and Cauchy-Riemann/
/Lecture 15 — Wirtinger Operators and Analytic Functions/
/Lecture 16 - Examples of Derivatives and Taylor Series/
/Lecture 17 - Integrations, FToC, Contours/
/Lecture 18 - Jordan Curves, Simple Closed Contours/
/Lecture 19 - Contour Integrals/
/Lecture 20 - Cauchy-Goursat/
/Lecture 21 - Cauchy Integral Formula/
/Lecture 22 - Morera, Liouville Theorem/
/Lecture 23 - Conformal Maps, Harmonic Functions/
/Lecture 24 - Harmonic Conjugates/
/Lecture 25 - Transformations of Harmonic Functions/
/Lecture 26 - Bubbles, Boundary Transformations/
/Lecture 27 - Heat, Transformation/
/Lecture 28 - Scale Factor, Poisson Integral Formula/
/Lecture 29 - Sequences and Series/
/Lecture 30 - Taylor Series and Taylor's Theorem/
/Lecture 31 - Laurent Series, Residues at Poles/
/Lecture 32 - Cauchy Residue, Singularities/
/Lecture 33 - Picard's Theorem, More Singularities/
/Lecture 34 - Zeros, Poles and Cauchy Principal Value/
/Lecture 35 - Cauchy Principal Value Examples/
/Lecture 36 - Jordan's Lemma and Rouche's Theorem/
/Lecture 37 - Additional/
/MATH3401 Summary/
/Revision/
/Tutorial 2 — Assignment 2/