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, 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 2022-05-04.