CHAPTER 19
Complex Analysis
Complex numbers and geometry
The complex plane, modulus, argument, polar and exponential forms.
Complex functions and limits
Limits, continuity and mappings in the complex plane.
Complex differentiation
Analytic functions and the Cauchy–Riemann equations.
Contour integration
Complex line integrals, Cauchy's theorem and integral formula.
Series and residues
Taylor and Laurent series, singularities and the residue theorem.
Conformal mappings
Angle-preserving maps and applications.