Functions of a Complex Variable (Classic Reprint)

E. J. Townsend

ISBN 10: 144005598X / ISBN 13: 9781440055980

Editore: Forgotten Books, 2018

Riguardo questo articolo

Print on Demand. This book delves into the fascinating world of complex numbers and functions, a field of mathematics that has revolutionized our understanding of numbers and their relationships. The author takes the reader on a journey through the evolution of the concept of numbers, starting with the familiar integers and fractions, then expanding to explore irrational numbers, which cannot be expressed as simple ratios. The book's core focus is on complex numbers, which involve the imaginary unit "i," the square root of -1. By introducing this new unit, the book demonstrates how mathematics extends beyond the realm of real numbers, opening up a whole new dimension of possibilities. The author skillfully navigates the complex arithmetic of adding, subtracting, multiplying, and dividing complex numbers, providing clear explanations and geometric interpretations. The book then delves into the key concept of functions of a complex variable, exploring their properties and classifications, such as rational, irrational, algebraic, and transcendental functions. The book explores essential concepts like limits and convergence, laying the groundwork for a deeper understanding of the behavior of complex functions. It also highlights the importance of mapping and linear fractional transformations, demonstrating their practical applications in various fields. Ultimately, this book offers a comprehensive and accessible introduction to the captivating world of complex variables and functions, revealing the elegance and power of this fundamental branch of mathematics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Codice articolo 9781440055980_0

Dati bibliografici

• Titolo: Functions of a Complex Variable (Classic Reprint)
• Editore: Forgotten Books
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 144005598X
• ISBN 13: 9781440055980
• Rilegatura: Paperback
• Condizione: New
• Tipo di libro: print-on-demand item
• Cataloghi dei venditori:
  • Calculus

Descrizione articolo

Riassunto

A clear, student-friendly introduction to complex variables, built from the ground up. This book guides readers from basic ideas of complex numbers to the core concepts of analytic functions, with a steady progression that emphasizes practical understanding over abstraction. It introduces integration early and shows how the key results follow from formal definitions, making the subject approachable for those new to complex analysis.

The text frames the material around what functions of a complex variable can do, including mapping, conformal transformations, and applications in physics. It covers both single-valued and multiple-valued functions, with chapters on series, analytic continuation, and the geometry of mappings. The approach balances theory with concrete examples to help readers connect ideas to real problems.

• Foundations of complex numbers and holomorphic functions, including integral criteria and the Cauchy-Goursat framework


• Mapping, conformal transformation, and linear fractional transformations with geometric interpretation


• Infinite series, power series, and analytic continuation with applications to physics


• Introduction to multiple-valued functions and the beginnings of Riemann surfaces

Ideal for readers of introductory complex analysis and for students applying these tools in physics or engineering.