Schaum's Outline of Complex Variables

This book no longer need a review. It is so popular among the academics and the students for its lucid way of treating complex variables I used this book as my reference for complex variables for the graduate mathematical methods course. This book helped me a lot with lots of examples and interesting exercise problems. It is also very good for students who wants to have a fast glance at the concepts. Overall, I would strongly recommend this book to any student who wants to learn complex variables in the most simple way with all kinds of examles to solve problems and score high grades.

Complaints seem to abound in regard to how this Schaum's outline is too theoretical and has too few problems involving applications. You must remember that this particular outline was meant to complement an undergraduate mathematics course in complex variables, not an applied physics or engineering course using complex variables. Thus, the purpose of this book is to develop the calculus of functions of a complex variable. This is one of those Schaum's outlines that has sufficient explanation, figures, and examples that it can double as a cheap textbook on the subject. However, remember that the emphasis is on theorems and proofs of theorems versus applications. However, there are some sections of the outline that are excellent at illustrating some applications of the subject matter. In particular, chapter 9, "Physical Applications of Conformal Mapping" contains applications from physics using those equations that are defined by a potential, including the electromagnetic field, the gravitational field, and, in fluid dynamics, potential flow, which is an approximation to fluid flow assuming constant density, zero viscosity, and irrotational flow. By choosing an appropriate mapping, the outline demonstrates clearly how one can transform the inconvenient geometry of one set of these equations into a much more convenient one. The equations are solved in this new "convenient" geometry, and then transformed back into the old one. One example of a fluid dynamic application of a conformal map that is detailed is the Joukowsky transform. If you are not looking for a book to complement a mathematics course on complex variables and you are looking for something more applied, you might look at "Complex Variables: Introduction and Applications". That book has the first part dedicated to theory and the second part dedicated to applications at a reasonable price.

I like this book very much. First, you can go through solved examples or you can try to solve them yourself and compare your solution against the presented one. If you want to get deeper, there are theorems to be proved and again, proofs are shown or indicated, you will not be left alone. Then the book presents number of examples to be solved.

When I took complex variables, the required text was Churchill's book. It was overpriced, overrated, and dull. I used Murray Spiegel's 1st edition instead and found it covered everything in Churchill's but with more interesting problems, better typography, and better presentation. The proofs are straight-forward and clear with illustrations.

I purchased this book for my undergraduate class in Complex Analysis because I was not overly impressed with the required text by Little and Brown. I found that the examples were well chosen, the explanations were easy to follow and the solved problems were informative in their step by step approach. I have compared this to several other texts and while none are perfect, this is at the very least an excellent supplement to any of them.