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Hundreds of solved examples, exercises, and applications help students gain a firm understanding of the most important topics in the theory and applications of complex variables. Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, and transform methods. Perfect for undergrads/grad students in science, mathematics, engineering. A three-semester course in calculus is sole prerequisite. 1990 edition. Appendices.
Posted August 11, 2006
Fisher¿s book is ideal for a first course in complex variables: the complex plane, geometry of the plane, analytic functions (zeros, singularities, residue computations), Cauchy-and residue theorems, harmonic functions, conformal mappings, boundary value problems, applications, and a lovely last chapter on transform theory, Fourier, Laplace etc, and using contour integration. Pedagogical features: The figures and illustrations are lovely! The exercises are many and well designed. Inclusion of solutions to odd-numbered exercises represents a good compromise. The book will work well for a mixed audience, students in math, in science, and in engineering alike. The presentation starts with a review of complex numbers functions and sequences, moves quickly to central aspects of complex function theory, elementary geometry, Mobius transformations, and conformal maps. The book was published first in 1990, but reprinted since by Dover, starting in 1999. It is suitable as a text or as a supplement in a beginning course in complex function theory, at the undergraduate level. And it is suitable for self-study. While it contains the standard elements in such a course, we note that a systematic treatment of physical problems comes relatively late, in Section 4.2, beginning on page 254 (a little past halfway into the book.) Some readers might want to begin with that. There are other Dover titles on the same subject, also elementary and suitable for a first course. They are slanted differently, and in particular, they point to different applications. Fisher¿s inclusion of transform theory gives this book an edge. See however also Churchill-Brown. Other Dover books: We recommend the books by Fisher, Volkovyskii et al, Silverman, Schwerdtfeger, and Flanigan all inexpensive! These books cover the fundamentals in functions of a single complex variable: analytic, harmonic, conformal mappings, and related applications. Further, there are non-Dover books such as: (a) R. V. Churchill ¿ J. W. Brown, and (b) J. E. Marsden - M. J. Hoffman both a lot more expensive. Review by Palle Jorgensen, August, 2006.Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.
Posted May 6, 2004
This book is terrible. All explanations are vague at best, and at worst insufficient information is given. One particular proof was so vague, it took the instructor three boards to fill in the missing information. Don't buy this book.Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.
Posted November 5, 2003