9781330190555 - a comparison of different line, geometric representations for functions of a complex variable a dissertation submitted to the faculty of the ogden ... of philosophy, (department or mathematics) di gibbens, gladys e. c. (3 risultati)
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Paperback. Condizione: New. Print on Demand. This book introduces two methods for constructing a congruence of lines determined by a functional relation between two complex variables, enabling readers to visualize the properties of the function by studying the properties of the resulting congruence. In the first method, two comp…lex variables are represented upon two distinct planes, parallel to each other and a unit apart. If points on the first plane are joined to points on the second plane that correspond to them via a given functional relation, a two-parameter family, or congruence, of straight lines is obtained. The second method uses a Riemann sphere. The two complex variables are projected upon the same sphere, and points of the sphere corresponding to each other via the function are joined by lines. The congruences obtained by either method always have real focal sheets and developables, making them more interesting than those obtained by the first method. The author demonstrates that there are other methods of constructing congruences of lines that impose less drastic restrictions upon the reference planes or spheres. The book then goes on to study the properties of the congruences resulting from these generalizations, including an extension of the method of the Riemann Sphere. By introducing complex variables into the study of lines and geometry, this book sheds new light on a subject of great mathematical interest. 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. print-on-demand item.
