Complex Variables and Applications

The 9th edition of “Complex Variables and Applications” by James Ward Brown is a widely-used textbook for undergraduate courses on complex analysis. It typically covers core topics such as complex numbers, analytic functions, Cauchy’s integral formula, series, residues, and conformal mappings. The book is known for its clear explanations, numerous examples, and exercises of varying difficulty, making it a popular choice for students learning this fundamental area of mathematics and its applications. This edition likely includes updates to examples, problems, and perhaps coverage, based on developments in the field or user feedback.

Table of Contents

1 Complex Numbers

2 Analytic Functions

3 Elementary Functions

4 Integrals

5 Series

6 Residues and Poles

7 Applications of Residues

8 Mapping by Elementary Functions

9 Conformal Mapping

10 Applications of Conformal Mapping

11 The Schwarz- Christoffel Transformation

12 Integral Formulas of the Poisson Type

About the Author

James Ward Brown is a notable mathematician recognized for his contributions to mathematics, particularly in the field of applied mathematics and control theory. He is well-known for co-authoring the book “Matrix Inequalities” with his colleague, which has been influential in various mathematical applications.