• About complex numbers
  • Euler’s formula
  • de Moivre’s theorem
  • Roots of complex numbers
  • Triangle inequality
  • Schwarz inequality
• Functions of complex variables
  • Limits and continuity
  • Analyticity and Cauchy-Riemann conditions
  • Harmonic function
  • Examples of analytic functions
  • Singular functions
    • Poles
    • Branch points
    • Order of singularity
    • Branch cut
• Integration of a function of a complex variable
  • Cauchy’s inequality
  • Cauchy’s integral formula
  • Residues and residue theorem
  • Application in solving definite integrals
• Simply and multiply connected regions
• Laurent and Taylor series expansions

Acknowledgment

My understanding of complex analysis has been mostly developed during the excellent classes by Prof. Carl Bender and before that by Prof. Gautam Mukhopadhyay. During the preparation of these notes, I have consulted the class notes of Prof. Bender.

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