Elements of Complex Variables by Louis L. Pennisi (Hardcover) 1963

Description: Elements of COMPLEX VARIABLES LOUIS L. PENNISI University of Illinois, Chicago With the Collaboration of LOUIS I. GORDON and SIM LASHER University of Illinois, Chicago HOLT, RINEHART AND WINSTON New York - Chicago - San Francisco - Toronto - London Hardcover Signs of pre ownership & slight wear on this vintage book, I found no notes, highlighting or tears. Preface: Students enrolled in a first course in the theory of functions of a complex variable usually present a variety of backgrounds and degrees of mathematical maturity. Consequently, the author has ineluded a good deal of elementary material accessible to the student who is taking his first course beyond caleulus. It seemed also desirable to present the material in sufficient detail in order to minimize a sense of vagueness which is apt to disturb the beginning student when only the highlights of the argument are given. In undertaking to prove theorems in full detail there is, of course, the danger of the text becoming too ponderous. 'To circumvent this difliculty, the device of separating auxiliary arguments and stating them in the form of exercises has been used. 'These exercises, in turn, have been supplied with liberal hints or complete solutions. Chapters 1, 3, and 4 are devoted to the algebraic properties of complex numbers, the notion of an analytic function, and an extenaive treatment of elementary functions. Chapter 2 and the beginning of Chapter 3 contain a presentation of those basic concepta associated with the notions of limit and continuity that are used in later chapters. 'The latter part of Chapter 5 and Chapters 6 and 7 deal mainly with the Cauchy integral formula and ita con-sequences, the 'Taylor and Laurent expansions and the residue theorem together with its applications. The first part of Chapter 5 in devoted to contour integration and a proof of the Cauchy integral theorem based on the concept of winding number. Chapter 8 contains a discussion of the mapping properties of analytio functions and some examples of conformal mapping. Chapter 9 deala with application of analytic functions to the theory of flows. In a one-semester course, Chapters 1, 3, 4, 5, 6, and 7 would constitute the main part, and the remaining chapters may be dealt with more lightly. 'To provide an opportunity for the student to assimilate and familiarizo himself with the subject matter, a considerable number of examples have been incorporated into the body of the text, and a large variety of exercises have been placed at the end of various sections. Answers and hints to many of these exercises will be found in the back of the book. The numbering system is according to chapter and section. For example, the sixth section of Chapter 3 is designated by 3.6; the second theorem of Section 3.6 is designated by Theorem 3.6.2, and so on. In general, in order to facilitate references, results are stated as theorems. The author wishes to acknowledge his indebtedness to his colleagues Roger G. Hill, Lawrence R. Sjoblom, and Nicholas C. Scholomiti, whose counsel he has enjoyed during the writing of this book and who have read the manuscript making valuable suggestions and contributions. Also, he wishes to express his appreciation to Professor Haim Reingold of Illinois Institute of Technology for making possible the use of the text in mimeographed form during the evening classes. While acknowledging the contributions of his collaborators and his colleagues, the author assumes full responsibility for the contents of the book. November 1962 L.L.P. Chicago, Illinois

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