The book contains material that is not considered in other popular complex analysis texts. This book is intended to serve as a text for first and second year courses in single variable complex analysis.
The Story of √-1 Paul J. Nahin. Figure 7.5. Approximating a simply connected region with arbitrarily many rectangles. ... Then f(z)/(z zo) is also analytic everywhere in that region except at z zo, where f(z)/(z zo) blows ...
Applications, primary motivations for this text, are presented hand-in-hand with theory enabling this text to serve well in courses for students in engineering or applied sciences.
The text offers numerous worked examples and problems representing a wide range of real-world uses, from determining hydrostatic pressure on a retaining wall to measuring current, voltage, and energy stored in an electrical capacitor.
A working knowledge of real calculus and familiarity with complex numbers is assumed. This book is useful for graduate students in calculus and undergraduate students of applied mathematics, physical science, and engineering.
The book may serve as a text for an undergraduate course in complex variables designed for scientists and engineers or for mathematics majors interested in further pursuing the general theory of complex analysis.
The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty.
H. BEHNKE and F. SOMMER [1] Theorie der analytischen Funktionen einer komplexen Veränderlichen (Grundlehren, Bd. 77, Berlin, 1955) Kap. IV, §§ 3–5. W. BENZ [1] Über Möbiusebenen, Ein Bericht. Jahresbericht der deutschen Mathematiker ...
The book divided in ten chapters deals with: " Algebra of complex numbers and its various geometrical properties, properties of polar form of complex numbers and regions in the complex plane.
The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.