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Complex variables and applications
This book is a thorough revision of its earlier eighth edition, which was published in 2009. That edition has served, just as the earlier ones did, as a textbook for a one-term 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 ones, the first two of which were written by the late Ruel V. Churchill alone. The book has always had two main objectives.
1. The first is to develop those parts of the theory that are prominent in applications of the subject.
2. The second objective is to furnish an introduction to applications of residues and conformal mapping. The applications of residues include their use in evaluating real improper integrals, finding inverse Laplace transforms, and locating zeros of functions. Considerable attention is paid to the use of conformal mapping in solving boundary value problems that arise in studies of heat conduction and fluid flow. Hence the book may be considered as a companion volume to the authors' text Fourier Series and Boundary Value Problems, where another classical method for solving boundary value problems in partial differentia] equations is developed.
The first nine chapters of this book have for many years formed the basis of a three-
course given each term at The University of Michigan. The final three chapters have
changes and are mostly intended for self-study and reference. The classes using
book have consisted mainly of seniors concentrating in mathematics, engineering,
one of the physical sciences. Before taking the course, the students have completed at
ast a three-term calculus sequence and a first course in ordinary differential equations.
mapping by elementary functions is desired earlier in the course, one can skip to
immediately after Chap. 3 on elementary functions and then return to Chap. 4
integrals.
We mention here a sample of the changes in this edition, some of which were
nested by students and people teaching from the book. A number of topics have
n moved from where they were. For example, although harmonic functions are still
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