Complex Analysis

Infinite sequences and series; algebra and geometry of complex numbers; analytic functions; integration; power series; residue calculus; conformal mapping, applications.

Week 1 (1/13 - 1/17)

Monday Wednesday Friday
  • Introduction
  • Sections 1.1-1.3
  • Algebra and Geometry
  • Section 1.4
  • Topology

Week 2 (1/20 - 1/24)

Monday Wednesday Friday
  • Martin Luther King Day
  • No Class
  • Section 2.1
  • Complex Functions
  • Section 2.2
  • Differentiability and Holomorphicity

Week 3 (1/27 - 1/31)

Monday Wednesday Friday
  • Section 2.3
  • Cauchy Riemann Equations
  • Section 2.4
  • Constant Functions
  • Section 3.1
  • Mobius Transformations

Week 4 (2/3 - 2/7)

Monday Wednesday Friday
  • Section 3.2
  • Infinity and the Cross Ratio
  • Section 3.3
  • Stereographic Projection
  • Section 3.4
  • Exponential and Trig Functions

Week 5 (2/10 - 2/14)

Monday Wednesday Friday
  • Section 3.5
  • Logarithm and Complex Exponential
  • Review I
  • Exam I

Week 6 (2/17 - 2/21)

Monday Wednesday Friday
  • Section 4.1
  • Complex Integration
  • Secion 4.2
  • Antiderivatives
  • Section 4.3
  • Cauchy's Theorem

Week 7 (2/24 - 2/28)

Monday Wednesday Friday
  • Section 4.4
  • Cauchy's Integral Formula
  • Section 5.1
  • Variations of a Theme
  • Section 5.2
  • Antiderivatives Again

Week 8 (3/3 - 3/7)

Monday Wednesday Friday
  • Section 5.3
  • Taking Cauchy's Formula to the Limit
  • Review II
  • Exam II

Week 9 (3/10 - 3/14)

Monday Wednesday Friday
  • Spring Break
  • No Class
  • Spring Break
  • No Class
  • Spring Break
  • No Class
  • Spring Break
  • No Class

Week 10 (3/17 - 3/21)

Monday Wednesday Friday
  • Section 6.1
  • Harmonic Functions
  • Section 6.2
  • Mean Value Theorem and Maximum Principle
  • Section 7.1
  • Sequences and Completeness

Week 11 (3/24 - 3/28)

Monday Wednesday Friday
  • Section 7.2
  • Series
  • Section 7.3
  • Sequences and Series of Functions
  • Section 7.3
  • Sequences and Series of Functions

Week 12 (3/31 - 4/4)

Monday Wednesday Friday
  • Section 7.4
  • Regions of Convergence
  • Section 8.1
  • Power Series
  • Section 8.2
  • Classification of Zeros

Week 13 (4/7 - 4/11)

Monday Wednesday Friday
  • Section 8.3
  • Laurent Series
  • Section 9.1
  • Classification of Singularities
  • Section 9.2
  • Residues

Week 14 (4/14 - 4/18)

Monday Wednesday Friday
  • Section 9.3
  • Argument Principle and Rouche's Theorem
  • Review III
  • Exam III

Week 15 (4/21 - 4/25)

Monday Wednesday Friday
  • Research Day
  • Research Day
  • Research Day

Week 16 (4/28 - 5/2)

Monday Wednesday Friday
  • Research Day
  • Final Presentations
  • Final Presentations