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/