Complex Variables with Applications

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September 2006



Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. The authors explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, while simultaneously examining their analytic and geometric characteristics, using geometry to illustrate analytic concepts and employing analysis to unravel geometric notions. The engaging exposition is replete with discussions, remarks, questions, and exercises, motivating not only understanding on the part of the reader, but also developing the tools needed to think critically about mathematical problems. This focus involves a careful examination of the methods and assumptions underlying various alternative routes that lead to the same destination. The material includes numerous examples and applications relevant to engineering students, along with some techniques to evaluate various types of integrals. The book may serve as a text for an undergraduate course in complex variables designed for scientists and engineers or for mathematics majors interested in further pursuing the general theory of complex analysis. The only prerequistite is a basic knowledge of advanced calculus. The presentation is also ideally suited for self-study.


Algebraic and Geometric Preliminaries.
Topological and Analytic Preliminaries.
Bilinear Transformations and Mappings.
Elementary Functions.
Analytic Functions.
Power Series.
Complex Integration and Cauchy's Theorem.
Applications of Cauchy's Theorem.
Laurent Series and the Residue Theorem.
Harmonic Functions.
Conformal Mapping and the Riemann Mapping Theorem.
Entire and Meromorphic Functions.
Analytic Continuation.


"A good point of the book is the selections of questions and exercises at the end of each section. They are very carefully selected and will help students with reading comprehension and with application of the material of the current section. Most of the time the exercises progress nicely from simple applications of concepts to problems that will expand the student's horizons." -MAA Reviews
"By using this book the reader can get a good background on complex analysis and become ready for further study of deeper chapters of Complex Analysis and its Applications."-Zentralblatt Math
EAN: 9780817644574
ISBN: 0817644571
Untertitel: Auflage 2006. Sprache: Englisch.
Erscheinungsdatum: September 2006
Seitenanzahl: 513 Seiten
Format: gebunden
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