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, 2e, 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, 2e, 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.