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Exercises in Complex Analysis

Hisashi Yokota

• Complex numbers
  • complex numbers and complex plane
  • DeMoivre's theorem and Euler's formula
  
  
• Complex functions
  • Complex function
  • Fractional transformation
  • Elementary functions
    • meromorphic function
  • Inverse function of elementary function
  
  
• Holomorphic function
  • Limit and Continuity
  • Analytic function,holomorphic function
    • Differntial coefficients and derivatives
  
  
• Complex integration
  • Line integral and Green's theorem
  • Complex integration
  • Cauchy's integral theorem
  • Cauchy's integral formula
  
  
• Expansion and residue
  • Laurent's expansion
  • Residue
  • Application to real integration
  
  
• Solution
  • 1.1 Complex numbers and complex plane
  • 1.2 DeMoivre's theorem and Euler's formula
  • 2.1 Complex function
  • Linear function
  • 2.3 Elementary functions
  • 2.4 Inverse function of an elementary function
  • Limit and continuity
  • 3.2 Analytic function
  • 4.1 Line integral and Green's theorem
  • 4.2 Complex integral
  • 4.3 Cauchy's integral theorem
  • 4.4 Cauchy's integral formula
  • 5.1 Laurent expansion
  • 5.2 Residue
  • 5.3 Application of real integral
  
  
• Index
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