Trent University

Mathematics 3770H

*Complex Analysis*

Archive Page

**Winter 2024**

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

Originally downloaded from https://matthbeck.github.io/complex.html . 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
*Lecture Videos*(webm format)- 2024-01-08: Basics of the complex numbers.
- 2024-01-09: Open and closed sets, connectedness and path-connectedness, and continuity.
- 2024-01-10: Limits of complex functions. [Video failed; audio only.]
- 2024-01-16: Derivatives of complex functions.
- 2024-01-17: Complex derivatives and the Cauchy-Riemann equations.
- 2024-01-22a: Complex derivatives and the Cauchy-Riemann equations II.
- 2024-01-22b: More on complex derivatives, fractional linear and Mobius transformations.
- 2024-01-24: Mobius transformations as compositions of geometric transformations.
- 2024-01-31: Complex exponential, logarithmic, and trigonometric functions.
- 2024-02-05a: Path integrals of complex functions.
- 024-02-05b: The Fundamental Theorem of Calculus for complex functions. [Recording failed.
- 2024-02-07: Another form of the Fundamental Theorem of Calculus for complex functions.
- 2024-02-12a: Another form of the Fundamental Theorem of Calculus for complex functions II.
- 2024-02-12b: Homotopic paths, statement of Cauchy's Theorem.
- 2024-02-14: Sketch of a proof of Cauchy's Theorem based on Cauchy's Triangle Theorem.
- 2024-02-26a: Cauchy's Integral Formula.
- 2024-02-26b: Cauchy's Integral Formula extended.
- 2024-02-28: Cauchy's Inequality, Liouville's Theorem, and the Fundamental Theorem of Algebra.
- 2024-03-04a: The Fundamental Theorem of Algebra continued.
- 2024-03-04b: Sequences and series of complex numbers and convergence thereof. [Recording failed.]
- 2024-03-06: Uniform convergence and continuity.
- 2024-03-11a: Uniform convergence and integration, Weierstrauss M-test. [Recording failed.]
- 2024-03-11b: Complex power series, absolute convergence, radius of convergence.
- 2024-03-18a: Analytic functions are holomorphic.
- 2024-03-18b: Holomorphic functions are analytic.
- 2024-03-20: Holomorphic functions are analytic II.
- 2024-03-25a: Missed due to illness. The lecture from 2022-03-29 was provided to cover it:
*Laurent Series*- video and notes. - 2024-03-25b: Missed due to illness. The lecture from 2022-03-30 was provided to cover it:
*Laurent Series II*- video and notes. - 2024-03-27: Laurent series and convergence thereof. [Recapitulates material that should have been done on 2024-03-25.]
- 2024-04-01a: Missed due to illness. The lecture from 2022-04-05 was provided to cover it:
*Laurent Series III*- video and notes. - 2024-04-01b: Missed due to illness. The notes from the unrecorded lecture from 2022-04-06 were provided to cover it:
*Singularities, residues, and the Residue Theorem.*- notes.

**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 2024-05-01.