Complex Variables (2nd Edition) by Robert B. Ash
Complex Variables (2nd Edition) - Table of Contents
1. Introduction
2. The Elementary Theory
3. The General Cauchy Theorem
4. Applications of the Cauchy Theory
5. Families of Analytic Functions
6. Factorization of Analytic Functions
7. The Prime Number Theorem
What You Will Learn in Complex Variables (2nd Edition)
"Complex Variables (2nd Edition)" by "Robert B. Ash" and "W. P. Novinger" is a rigorous yet accessible textbook on "complex analysis", designed for advanced undergraduates and beginning graduate students. The book begins with the fundamentals of complex numbers, the topology of the complex plane, and the "Cauchy–Riemann equations", carefully explaining the connection between real differentiability and complex differentiability. Students are introduced to analytic functions and the key properties that make them central to the theory of complex variables.
The text develops core results such as "Cauchy’s theorem", Cauchy’s integral formula, and Liouville’s theorem, before moving on to applications including "residue theory", contour integration, and conformal mapping. Later chapters explore families of analytic functions, the Riemann mapping theorem, and advanced applications like the "Prime Number Theorem", demonstrating the power of complex methods in solving both classical and modern mathematical problems.
Rich in examples, exercises, and solutions, this second edition balances theory and application, making it ideal for "self-study", coursework, or as a reference for researchers. Its careful exposition, combined with numerous exercises, equips students with strong proof-writing skills and a deep understanding of analytic functions, residues, and broader "complex variable" techniques applicable across mathematics, physics, and engineering.
Book Details & Specifications
Title:
Complex Variables (2nd Edition) by Robert B. Ash
Publisher:
Dover Publications
Year:
2007
Pages:
220
Type:
PDF
Language:
English
ISBN-10 #:
0486462501
ISBN-13 #:
978-0486462509
License:
University Educational Resource
Amazon:
Amazon
About the Author: Robert B. Ash
The author
Robert B. Ash
is a well-known mathematician and educator recognized for his work in "complex analysis", "real analysis", and advanced mathematics education. His textbooks are valued for their clear structure, logical proofs, and accessibility for advanced undergraduates and graduate students. Ash focuses on building deep conceptual understanding without sacrificing rigor. "W. P. Novinger" is a mathematician with expertise in "mathematical analysis" and university-level teaching. His collaboration with Ash strengthens the book’s clarity and depth. Together, they present complex analysis in a well-organized, student-friendly manner, making the subject approachable while maintaining strong theoretical foundations.
Read or Downloadable Complex Variables (2nd Edition)
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