desc.txt

An introductory course in complex analysis for incoming graduate students. Created to teach Math 5283 at Oklahoma State University. The book has somewhat more material than could fit in a one-semester course, allowing some choices. There are also appendices on metric spaces and some basic analysis background to make for a longer and more complete course for those that have only had an introduction to basic analysis on the real line.

Table of contents:

Introduction
1. The Complex Plane
2. Holomorphic and Analytic Functions
3. Line Integrals and Rudimentary Cauchy Theorems
4. The Logarithm and Cauchy
5. Counting Zeros and Singularities
6. Montel and Riemann
7. Harmonic Functions
8. Weierstrass Factorization
9. Rational Approximation
10. Analytic Continuation
Appendix A. Metric Spaces
Appendix B. Results From Basic Analysis
Appendix C. Basic Notation and Terminology

Jiří Lebl is a Professor of Mathematics at the Oklahoma State University.