- Published Year: 2003
- Page count: 660
- File Size: 7 Mb
- Language: English
- Published by: Cambridge University Press
- Visited by: 6
- Rating/Review: 4.5
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ISBN:
0521534291
9780521534291
Keywords:
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Each download or ask from book AI costs 2 points. To earn more free points, please visit the Points Guide Page and complete some valuable actions.Introduction
"Complex Variables: Introduction and Applications" by Mark J. Ablowitz and Athanassios S. Fokas is a pivotal resource for understanding the intricate world of complex analysis. With a comprehensive approach, it delves into the practical and theoretical aspects of complex variables, offering readers both foundational knowledge and a glimpse into advanced applications. Whether you are a student entering the field or a professional seeking to refresh your understanding, this book provides an invaluable perspective on complex functions, conformal mapping, and more.
Detailed Summary of the Book
The book begins with an introduction to the basic concepts of complex numbers and gradually builds up to cover complex functions. The initial chapters lay down the groundwork by explaining the algebra and geometry of complex numbers while introducing concepts such as limits and continuity. Subsequent chapters expand on differentiability and the Cauchy-Riemann equations, which form the backbone of any exploration into complex analysis.
The authors place special emphasis on exploring series expansions, highlighting Taylor and Laurent series, which are crucial for various applications. Topics such as residue theory, contour integration, and the calculus of residues are explored in depth, making them accessible to students as well as useful to practitioners. Furthermore, the book incorporates applications ranging from fluid dynamics to electromagnetics, showcasing the real-world relevance of complex analysis.
Each chapter is bundled with well-crafted examples and exercises, designed to reinforce the understanding of key concepts. This pedagogical approach ensures that readers are not only presented with dry theory but are also exposed to practical problem-solving techniques.
Key Takeaways
- Comprehensive coverage of complex numbers, functions, and their applications.
- Clear and rigorous exposition of the Cauchy-Riemann equations and their implications.
- Understanding power series, Taylor series, and Laurent series in depth.
- Insightful examination of residue calculus and its applications in evaluating complex integrals.
- Practical applications emphasized in fields like engineering and physics.
Famous Quotes from the Book
"Complex analysis is one of the most beautiful as well as useful branches of mathematics."
"The power of complex variables reflects in the elegance of conformal mappings and the strength of theorems derived from Cauchy's integral formula."
Why This Book Matters
"Complex Variables: Introduction and Applications" stands out as a robust pedagogical tool for both beginners and advanced learners. By balancing theory with application, it closes the gap between mathematical rigor and practical utility. The book fulfills a critical role in educating aspiring mathematicians, engineers, and physicists, elucidating how complex analysis can solve real-world problems with elegance and precision. Furthermore, the engaging style of the authors makes these sophisticated topics approachable, ensuring that readers not only learn but also appreciate the beauty inherent in complex variables.
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