MATH-GA2450 Complex Variables I, Fall 2024 Calendar
Week Date Topics Links
1 Tuesday
9/3/2024
  • Prerequisites
  • Complex Numbers
  • Complex Functions
 Slides
Thursday
9/5/2024
  • Topology of \(\mathbb{C}\)
  • Limit of Sequence
  • Convergent and Cauchy Sequences
 Slides
2 Tuesday
9/10/2024
  • Compact Sets
  • Limit of Function
  • Continuity and Uniform Continuity
 Slides
Thursday
9/12/2024
  • Complex Differentiability
  • Cauchy-Riemann Equations
 Slides
3 Tuesday
9/17/2024
  • Holomorphic Implies Conformal
  • Series
  • Power Series
 Slides
Thursday
9/19/2024
  • Algebra of Formal Power Series
  • Laurent Series
 Slides
4 Tuesday
9/24/2024
  • Ratio of Convergence for Product of Power Series
  • Analytic Functions
  • Uniqueness of Power Series
 Slides
Thursday
9/26/2024
  • Algebra of Analytic Functions
  • Binomial Series
  • Differentiation of Power Series
 Slides
5 Tuesday
10/1/2024
  • Contour Integral
  • Fundamental Theorem of Calculus
 Slides
Thursday
10/3/2024
  • Contour Integrals
 Slides
6 Tuesday
10/8/2024
  • Contour Integral Around Closed Curve of Laurent Series
 Slides
Thursday
10/10/2024
  • Polar Form of Piecewise \(C^1\) Curve
  • Winding Number of Closed Curve Around Point
  • Cauchy Integral Formula for Laurent Series
 Slides
7 Tuesday
10/15/2024		 No class
Thursday
10/17/2024
  • Homotopic Curves
  • Homotopy Forms of Cauchy Theorem
 Slides
8 Tuesday
10/22/2024
  • Homology Form of Cauchy Theorem
Thursday
10/24/2024
  • §5.3: Isolated Singularities
9 Tuesday
10/29/2024
  • §5.3: Isolated Singularities
  
Thursday
10/31/2024
    Midterm Exam
10 Tuesday
11/5/2024
  • §6.1: The Residue Formula
Thursday
11/7/2024
  • §6.2: Evaluation of Definite Integrals
11 Tuesday
11/12/2024
  • Chapter 7: Conformal Mappings
Thursday
11/14/2024
  • Chapter 8: Harmonic Functions
12 Tuesday
11/19/2024
Thursday
11/21/2024
13 Tuesday
11/26/2024
Thursday
11/28/2024
    No class
14 Tuesday
12/3/2024
Thursday
12/5/2024
15 Tuesday
12/10/2024
Thursday
12/12/2024
  TBA Final Exam Warren Weaver Hall 1302