### Overview

**Riemann-Hilbert problems** are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann-Hilbert problem.

This book, the most comprehensive one to date on the applied and computational theory of Riemann-Hilbert problems, includes:

- an introduction to computational complex analysis,
- an introduction to the applied theory of Riemann-Hilbert problems from an analytical and numerical perspective,
- a discussion of applications to integrable systems, differential equations, and special function theory, and six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann-Hilbert method, each of mathematical or physical significance or both.

You will find Mathematca code for these examples on this webpage along with a collection of errata. See the RHPackage section below for preliminaries. Then you will find Mathematica notebooks to solve the Riemann-Hilbert problems that are discussed in Chapter 1, Sections 5.3, 5.5, 6.3, 6.4, and Chapters 8-11.

This book is intended for graduate students and researchers interested in a computational or analytical introduction to the Riemann-Hilbert method.