Complex Analysis Complex Function Theory by Felix Wong
File Type :PDF Number of Pages :109
Description The note covers an
introductory undergraduatelevel sequence in complex analysis, starting from
basics notions and working up to such results as the Riemann mapping theorem or
the prime number theorem. Topics covered includes: Riemann Sphere,
ComplexDifferentiability, and Convergence, Power Series and CauchyRiemann
Equations, The Closed Curve Theorem and Cauchy’s Integral Formula, Applications
of Cauchy’s Integral Formula, Liouville Theorem, Mean Value Theorem, Mean Value
Theorem and Maximum Modulus Principle, Generalized Closed Curve Theorem and
Morera’s Theorem, Morera’s Theorem, Singularities, and Laurent Expansions,
Meromorphic Functions and Residues , Winding Numbers and Cauchy’s Integral
Theorem, The Argument Principle, Fourier Transform and Schwarz Reflection
Principle, Riemann Mapping Theorem, Analytic Continuation of Gamma and Zeta,
Zeta function and Prime Number Theorem, Prime Number Theorem, Elliptic
Functions, Weierstrass’s Elliptic Function and an Overview of Elliptic
Invariants and Moduli Spaces.



