Complex Analysis:

Analytic and harmonic functions; Cauchy-Riemann equations; power series; Cauchy's Theorem, Cauchy's Formula; Liouville's Theorem; Taylor's Theorem; The Maximum Modulus Theorem; Morera's Theorem; the theory of isolated singularities: Cassardi-Weierstrass Theorem; Laurent expansion, the residue theorem, application to definite integrals; elementary functions and their mapping properties; analytic continuation; Riemann mapping theorem.