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
    Cancelled
Thursday
10/24/2024
    Cancelled
9 Tuesday
10/29/2024
  • Cauchy Integral Formula
  • Lax's Proof
 Slides
Thursday
10/31/2024
  • Local Cauchy Integral Formula
  • Holomorphic Implies Analytic
  • Radius of Convergence for Holomorphic Function
 Slides
10 Tuesday
11/5/2024
  • Bound on Derivatives of Holomorphic Function
  • Liouville' Theorem
  • Fundamental Theorem of Algebra
  • Orientation of Curve
  • Contour Integral of Oriented Curve
 Slides
Thursday
11/7/2024
    Midterm Exam
11 Tuesday
11/12/2024
  • Winding Number of Closed Curve
  • Homologous Curves
  • Chains
  • Contour Integral Along Chain
  • Winding Number of Chain
  • Homologous Forms of Cauchy's Theorem and Cauchy Integral Formula
 Slides
Thursday
11/14/2024
    Laurent Series
Slides
12 Tuesday
11/19/2024
  • Isolated Singularities
  • Poles
  • Meromorphic Functions
  • Esential Singularities
 Slides
Thursday
11/21/2024
  • Residue Formula
  • Order of Meromorphic Function at Point
 Slides
13 Tuesday
11/26/2024
  • Counting Zeros and Poles
  • Evaluation of Definite Integrals
 Slides
Thursday
11/28/2024
    No class
14 Tuesday
12/3/2024
  • Analytic Isomorphisms
 Slides
Thursday
12/5/2024
  • Maximum Modulus Principle
  • Schwarz Lemma
 Slides
15 Tuesday
12/10/2024
  • Automorphisms of Disk
  • Fractional Linear Transformations
 Slides
Thursday
12/12/2024
  • Geometry of Sphere
  • Stereographic Projection of Sphere
  • Isometries and Conformal automorphisms of Sphere
  • Geometry of Hyperbolic Plane
  • Stereographic Projection of Hyperbolic Plane
  • Isometries and Conformal automorphisms of Hyperbolic Plane
Slides
  Thursday
12/19/2024
8am-9:50pm		 Final Exam (Warren Weaver Hall 1302)