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Table of contents:
Calculus with Complex Numbers offers a practical course in complex calculus with an emphasis on applications rather than theory. While assuming an acquaintance with complex numbers and a working knowledge of real calculus, the author begins with a concise but thorough introduction to the complex number system and complex functions. He then presents derivatives and integrals, discussing all of the usual topics and proving some of the simpler results.The second half of the book explores applications, primarily those of complex integrals. Here the author explains complex variable techniques for evaluating finite and infinite real integrals and for series summation. The final chapter presents a proof of the fundamental theorem of algebra. Each chapter includes several examples and exercises, and the solutions of these are given at the end of the book. Appendices provide proof of Cauchy's theorem and the half-residue theorem.Clear, concise, and well written, Calculus with Complex Numbers is an outstanding introduction to the subject. While not intended to replace standard texts on complex analysis but rather to complement them, this accessible, straightforward presentation prepares and motivates its readers to pursue the study of complex calculus at a higher, more formal level.
Contents:
Complex NumbersComplex FunctionsDerivativesIntegralsEvaluation of Finite Real IntegralsEvaluation of Infinite Real IntegralsSummation of SeriesFundamental Theorem of Algebra Solutions to ExamplesAppendicesIndex of SymbolsGeneral IndexBibliography
Brief Description:
This text is a practical course in complex calculus that covers the applications, but does not assume the full rigour of a real analysis background. Topics covered include algebraic and geometric aspects of complex numbers, differentiation, contour
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