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ISBN 10: 0763714372
ISBN 13: 9780763714376
Author: Dennis G Zill and Patrick D Shanahan
A First Course in Complex Analysis with Applications is designed as an accessible, application-oriented introduction to the field of complex analysis for undergraduate students. The book assumes knowledge of calculus but no prior exposure to complex analysis, making it suitable for beginners.
The text begins with the fundamentals of complex numbers and the complex plane, gradually moving to more advanced topics such as analytic functions, complex integration, series expansions, residues, and conformal mappings. Each topic is presented with clear explanations, step-by-step examples, and illustrative diagrams, emphasizing both theoretical understanding and practical applications in engineering, physics, and applied mathematics.
One of the book’s key strengths is its integration of applications and problem-solving exercises, which demonstrate the relevance of complex analysis in real-world contexts while helping students develop computational skills and mathematical maturity. It balances rigor with readability, making complex concepts accessible without oversimplifying.
Complex Numbers
Analytic Functions
Elementary Functions
Complex Integration
Series Representations of Analytic Functions
Residues and Poles
Applications of Complex Analysis
Conformal Mapping
Complex Dynamics and Further Topics
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Tags: Dennis G Zill and Patrick D Shanahan, Course, Complex