Techniques — notation, the principal theorems, and criteria for holomorphy, constancy, singularities, zeros, and estimates.
Precalculus preliminaries — conic sections, parameterizations, and trigonometric values.
Calculus preliminaries — the contraction principle, the implicit and inverse function theorems, line integrals, and convergence of series and functions.
Series reference — factorial notation, the standard power series, finite sums, and inversion of power series.
Complex arithmetic — problems on complex arithmetic and holomorphy, and algebraic identities.
Summation by parts and Abel's theorem — Dirichlet’s test, Abel’s theorem, and summation by parts.
Holomorphic functions are treated in Holomorphic functions.