Calculus with Complex Numbers

that they are too verbose, too much geared toward teaching everything to everyone (rather than teaching the basics to everyone), too heavy, and too expensive. This little slim volume is in some sense an optimal solution to this problem. It covers the very basics of complex analysis in such a way that a typical engineering student could read the book cover to cover in a short time and come away with a basic understanding of the field. The reader would then be empowered to read up on more specialized topics (e.g., the use of phasors, nyquist stabilty criterion, inverse laplace transforms) or to apply the theory in an engineering class. For comparison, I usually tell others that my favorite textbook on complex variables is the book by Wunsch. Although I still like Wunsch's book it has gotten fatter and thicker as it has morphed into the current third edition. Its sheer bulk and scope might discourage the student from delving into the book who was not required to by taking a class. Most engineers have to become "self-learners" throughout their career and books like this really help facilitate the process of lifelong learning. This text is a practical course in complex calculus that covers the applications, but does not assume the full rigor of a real analysis background. Topics covered include algebraic and geometric aspects of complex numbers, differentiation, contour integration, evaluation of finite and infinite real integrals, summation of series and the fundamental theorem of algebra. The Residue Theorem for evaluating complex integrals is presented in such a way that those wishing to study the subject at a deeper level should not need to unlearn anything presented here. A working knowledge of real calculus is assumed as is an acquaintance with complex numbers. This will be of interest to undergraduate students of applied mathematics, physical sciences and engineering.

this Practical Treatment Explains The Applications Complex Calculus Without Requiring The Rigor Of A Real Analysis Background. The Author Explores Algebraic And Geometric Aspects Of Complex Numbers, Differentiation, Contour Integration, Finite And Infinite Real Integrals, Summation Of Series, And The Fundamental Theorem Of Algebra. The Residue Theorem For Evaluating Complex Integrals Is Presented In A Straightforward Way, Laying The Groundwork For Further Study. A Working Knowledge Of Real Calculus And Familiarity With Complex Numbers Is Assumed. This Book Is Useful For Graduate Students In Calculus And Undergraduate Students Of Applied Mathematics, Physical Science, And Engineering.

"This text is a practical course in complex calculus with an emphasis on the applications rather than the theory. It is not intended to replace existing texts on complex calculus, but rather to complement them by acting as preparation for and motivation towards further study of complex calculus at a more formal level." "Prerequisites are a working knowledge of real calculus and an acquaintance with complex numbers. The book should be accessible to any student who has studied calculus at upper-school level and should be of interest to university students of applied mathematics, physical sciences and engineering."--Jacket Complex numbers Complex functions Derivatives Integrals Evaluation of finite real integrals Evaluation of infinite real integrals Summation of series Fundamental theorem of algebra.