Notes - Math 29142

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• Week 1
  • 1.1 Complex Numbers [Video]
  • 1.2 Arithmetic [Video]
  • 1.3 Sequences
  • 1.4 Series
• Week 2
  • 2.1 Paths
  • 2.2 Domains
  • 2.3 Functions
  • 2.4 Continuous Functions
• Week 3
  • 3.1 Power Series
  • 3.2 Holomorphic Functions
  • 3.3 The Cauchy-Riemann Equations
  • 3.4 A Cauchy-Riemann Converse
• Week 4
  • 4.1 Differentiating Power Series
  • 4.2 The Exponential Function
  • 4.3 The Trigonometric Functions
  • 4.4 Contours
• Week 5
  • 5.1 Contour Integration
  • 5.2 Antiderivatives
  • 5.3 The Principal Logarithm
• Week 6
  • 6.1 Cauchy's Theorem in a Rectangle
  • 6.2 Winding Numbers
  • 6.3 Cauchy's Theorem
• Week 7
  Coursework this week. No new material!
• Week 8
  • 8.1 Cauchy's Integral Formula
  • 8.2 Taylor's Theorem
  • 8.3 Applications
• Week 9
  • 9.1 Laurent Series
  • 9.2 Examples of Laurent Series
  • 9.3 Isolated Singularities
• Week 10
  • 10.1 Poles
  • 10.2 Cauchy's Residue Theorem
  • 10.3 Calculating Residues
• Week 11
  • 11.1 Infinite Real Integrals
  • 11.2 Evaluating Series
• Week 12
  Review this week. No new material!