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Complex Variables and Applications 9/e

作者：James Ward Brown, Ruel V. Churchill (deceased)
原價：NT$ 1,600

ISBN：9781259072772
版次：9
年份：2014
出版商：McGraw-Hill
頁數/規格：480頁/平裝單色

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Description
Complex Variables and Applications, 9e will serve, just as the earlier editions did, as a textbook for an introductory course in the theory and application of functions of a complex variable. This new edition preserves the basic content and style of the earlier editions. The text is designed to develop the theory that is prominent in applications of the subject. You will find a special emphasis given to the application of residues and conformal mappings. To accommodate the different calculus backgrounds of students, footnotes are given with references to other texts that contain proofs and discussions of the more delicate results in advanced calculus. Improvements in the text include extended explanations of theorems, greater detail in arguments, and the separation of topics into their own sections.

Features

Exercise sets occur more frequently than in earlier editions.

Some sections that can be skipped or postponed without disruption are more clearly identified. The statements of Taylora€™s and Laurenta€™s theorems, for example, now appear in sections that are separate from the sections containing their proofs.

The treatment of the extended form of the Cauchy integral formula for derivatives has been completely rewritten, with special attention to its immediate consequences.

Other improvements include more details in arguments involving mathematical induction, greater emphasis on rules for using complex exponents, some discussion of residues at infinity, and a clearer exposition of real improper integrals and their Cauchy principal values.

Some important material is presented in a more focused way by placing it in separate sections. For instance, the discussion of upper bounds of moduli of contour integrals is now entirely in one section, and there is a separate section devoted to the definition of isolated singular points.

A revised Studenta€™s Solutions Manual with solutions for a large number of exercises in Chapters 1-7 is available.

Table of Contents
Chapter 1. Complex Numbers
Chapter 2. Analytic Functions
Chapter 3. Elementary Functions
Chapter 4. Integrals
Chapter 5. Series
Chapter 6. Residues and Poles
Chapter 7. Applications of Residues
Chapter 8. Mapping by Elementary Functions
Chapter 9. Conformal Mapping
Chapter 10. Applications of Conformed Mapping
Chapter 11. The Schwarz-Christoffel Transformation
Chapter 12. Integral Formulas of the Poisson Type

James Ward Brown
is Professor Emeritus of Mathematics at The University of Michigan–Dearborn. He earned his A.B. in physics from Harvard University and his A.M. and Ph.D. in mathematics from The University of Michigan in Ann Arbor, where he was an Institute of Science and Technology Predoctoral Fellow. He is coauthor with Dr. Churchill of Fourier Series and Boundary Value Problems, now in its eighth edition. He has received a research grant from the National Science Foundation as well as a Distinguished Faculty Award from the Michigan Association of Governing Boards of Colleges and Universities. Dr. Brown is listed in Who's Who in the World.

Ruel V. Churchill, (deceased)
was, at the time of his death in 1987, Professor Emeritus of Mathematics at The University of Michigan, where he began teaching in 1922. He received his B.S. in physics from the University of Chicago and his M.S. in physics and Ph.D. in mathematics from The University of Michigan. He was coauthor with Dr. Brown of Fourier Series and Boundary Value Problems, a classic text that he first wrote almost 75 years ago. He was also the author of Operational Mathematics. Dr. Churchill held various offices in the Mathematical Association of America and in other mathematical societies and councils.

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