Trent University

Mathematics 3770H

*Complex Analysis*

Archive Page

**Winter 2022**

- MATH 3770H Course Outline
- The texbook: A First Course in Complex Analysis (Version 1.54), by M. Beck, G. Marchesi, D. Pixton, & L. Sabalka.

Licensing terms are given in the book's frontmatter. - Assignment # 1,
2,
3,
4,
5,
2
*e*, 6, 7, 8, 9, 10, 11 - Take-Home Final Examination
*Lectures and Notes*(webm and pdf formats)*The Basics of the Complex Numbers*- video and notes*Absolute Values and Limits in the Complex Numbers*- video and notes*(A Little) Topology in the Complex Plane*- video and notes*Some Properties of Complex Derivatives*- video and notes*Transformations of the Complex Plane*- video and notes*The Extended Complex Plane*- video and notes*The Complex Exponential, Trigonometric, and Hyperbolic Functions*- video and notes*The Complex Logarithm Functions*- video and notes*A Quick Review of Integration in the Cartesian Plane*- video and notes*Complex Integration*- video and notes*Complex Integration II*- video and notes*Cauchy's Theorem*- video and notes*Cauchy's Integral Formula*- video and notes*Cauchy's Integral Formula Extended*- video and notes*Cauchy's Inequality and Liouville's Theorem*- [recording failed] and notes*The Fundamental Theorem of Algebra*- video and notes*Outtake: A Little Topology*- video [no notes]*Harmonic Functions*- video and notes*A Quick Review of Sequences and Series*- video and notes*Convergence of Sequences and Series of Functions*- video and notes*Convergence of Power Series*- video and notes*Taylor Series*- video and notes*Power Series & Holomorphic Functions*- [recording failed] and notes*Taylor's Formula*- video and notes*Laurent Series*- video and notes*Laurent Series II*- video and notes*Laurent Series III*- video and notes*Singularities & Residues*- [recording failed] and notes

Maintained by Stefan Bilaniuk. Last updated 2022-05-04.