Calculus with Complex Numbers 1st Edition by John B. Reade (PDF)

Description

This practical course in complex calculus explains the applications, 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 sciences and engineering.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a great short introduction to complex analysis. It doesn’t cover all of the topics that might be covered in a college course, but the topics it does cover it covers clearly and with many good examples. There are exercises, but not an inordinate amount;just enough to practice what the author is teaching you.I reread this over the summer and I had forgotten how much I like this book. In fact, I wish I owned a copy of it the first time I took complex analysis.

⭐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 studentcould 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 intothe 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.

⭐I have to say that I am a huge fan of John Reade after reading this book. I recently read his much earlier Analysis book and was so impressed I wanted to find what else he had written. Unfortunately, as far as I can tell, this was the only other book he produced. And it is a work of genius. Its pedagogical value is unmatched by any competitor in this field and I would heartily recommend it to anyone looking for an introduction to Complex Analysis.There are 8 short chapters and it took me about three weeks to get through it, doing most of the exercises. At 100 pages it is very brief but I have to say that my knowledge of this area has improved vastly.I also feel that I have a powerful tool at my disposal for working with infinite integrals and of just how well complex numbers can produce in the most counterintuitive ways extremely productive results.

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