Complex Variables and Applications

A thoroughly revised and classic textbook on complex analysis, this edition emphasizes real-world applications—especially residues and conformal mapping—while maintaining clarity and rigor. Key updates include a completely rewritten form of the extended Cauchy integral formula for derivatives, enhanced mathematical induction explanations, clearer guidance on handling complex exponents, and a deeper discussion of residues at infinity. The text separates advanced topics into their own sections for better structure, and includes footnotes linking to deeper proofs for readers with varied calculus backgrounds. It is widely used in introductory courses in applied complex analysis.