Complex analysis /
The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. The first part comprises the basic core of a course in complex analysis for junior and senior undergraduates. The second part includes various more specialized topics as th...
Table of Contents:
- Complex plane and elementary functions
- Analytic functions
- Line integrals and harmonic functions
- Complex integration and analyticity
- Power series
- Laurent series and isolated singularities
- Residue calculus
- Logarithmic integral
- Schwarz Lemma and hyperbolic geometry
- Harmonic functions and the reflection principle
- Conformal mapping
- Compact families of meromorphic functions
- Approximation theorems
- Some special functions
- Dirichlet problem
- Riemann surfaces.