Publication Date: October 18, List Price: This basic book on functions of a complex variable represents the irreducible minimum of what every scientist and engineer should know about this important subject. From a preliminary discussion of complex numbers and functions to key topics such as the Cauchy theory, power series, and residues, distinguished mathematical writer Richard Silverman presents the fundamentals of complex analysis in a concise manner designed not to overwhelm the beginner. The author's lively style and simplicity of approach enable the reader to grasp essential topics without being distracted by secondary issues.
Markushevich's masterly three-volume "Theory of Functions of a Complex Variable. Richard Silverman, the editor and translator of the original, has prepared this shorter version expressly to meet the needs of a one-year graduate or undergraduate course in complex analysis. In his selection and adaptation o Introductory Complex Analysis is a scaled-down version of A.
In his selection and adaptation of the more elementary topics from the original larger work, he was guided by a brief course prepared by Markushevich himself.
The book begins with fundamentals, with a definition of complex numbers, their geometric representation, their algebra, powers and roots of complex numbers, set theory as applied to complex analysis, and complex functions and sequences. The notions of proper and improper complex numbers and of infinity are fully and clearly explained, as is stereographic projection.
Individual chapters then cover limits and continuity, differentiation of analytic functions, polynomials and rational functions, Mobius transformations with their circle-preserving property, exponentials and logarithms, complex integrals and the Cauchy theorem , complex series and uniform convergence, power series, Laurent series and singular points, the residue theorem and its implications, harmonic functions a subject too often slighted in first courses in complex analysis , partial fraction expansions, conformal mapping, and analytic continuation.
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Elementary functions are given a more detailed treatment than is usual for a book at this level. Also, there is an extended discussion of the Schwarz-Christolfel transformation, which is particularly important for applications. There is a great abundance of worked-out examples, and over three hundred problems some with hints and answers , making this an excellent textbook for classroom use as well as for independent study.
Best Reference Books – Vector Calculus and Complex Analysis
A noteworthy feature is the fact that the parentage of this volume makes it possible for the student to pursue various advanced topics in more detail in the three-volume original, without the problem of having to adjust to a new terminology and notation. In this way, Introductory Complex Analysis serves as an introduction not only to the whole field of complex analysis, but also to the magnum opus of an important contemporary Russian mathematician. Get A Copy.
Paperback , pages. Published May 1st by Dover Publications first published April 16th More Details Original Title. Other Editions 4.
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Community Reviews. Showing Average rating 3. Rating details. More filters. Sort order. Start your review of Introductory Complex Analysis. Oct 07, Julia rated it did not like it Shelves: math.
Dick Tinto rated it liked it Nov 03, The author's lively style and simplicity of approach enable the reader to grasp essential topics without being distracted by secondary issues. Abundant exercise material and examples, as well as section-by-section comments at the end of each chapter make this book especially valuable to students and anyone encountering complex analysis for the first time.
Richard A. Silverman: Dover's Trusted Advisor Richard Silverman was the primary reviewer of our mathematics books for well over 25 years starting in the s. And, as one of the preeminent translators of scientific Russian, his work also appears in our catalog in the form of his translations of essential works by many of the greatest names in Russian mathematics and physics of the twentieth century.
Publisher Series: Dover Books on Mathematics
During the Silverman years, the Dover math program attained and deepened its reach and depth to a level that would not have been possible without his valuable contributions. Convert currency. Add to Basket. Book Description Dover Publications, Condition: New. Never used!. Seller Inventory More information about this seller Contact this seller. Brand New!.
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