- Introduction – why do we need complex numbers
- The field of complex numbers
- Continuity and derivatives
- The Cauchy Riemann equations
- Elementary functions
- Complex integrals
- Cauchy’s formula
- Applications of Cauchy’s formula (Average, Maximum principal and Lioville’s theorem)
- Infinite sums of functions
- Taylor and Laurent expansions
- Singularities
- The residue theorem
- Computing real integrals
- And even more real integrals

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