Customer Reviews

Schaum's Outlines: Complex Variables (With an Introduction to Conformal Mapping and Its Applications)

5 star:		(11)
4 star:		(6)
3 star:		(1)
2 star:		(2)
1 star:		(1)

 

 

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.

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.

This text discusses several things to help you start working with complex variables. The chapters covered are complex numbers; functions, limits, and continuity; complex differentiation and the Cauchy-Riemann equations; complex integration and Cauchy's Theorem; Cauchy's integral formulas and related theorems; infinite series (Taylor and Laurent); the Residue Theorem; and an introduction into conformal mapping and its physical applications.

The author takes the time to explain the terms and everything is easy to refer to. He walks you through several problems, and then you can test yourself with some supplementary problems. Although the answers to the particular problems are not there, you can many times compare it with a problem discussed previously in the chapter. It is still difficult to know if you got it right, but you will have a good idea.

I would recommend this.

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.

The first graduate level course in mathematics that I took was complex variables. Despite having been very successful as an undergraduate, I felt a bit of trepidation, as the rumor was that graduate school was much, much harder. To help ease the transition, I bought this book as a crutch, which was a wise move. I found problems similar to the assigned homework problems in here and by working through them; I was able to figure out how to do the homework. As a consequence, I was able to do nearly every homework problem, missing only a few points due to minor errors.

That work also led to my achieving very high scores on the exams and getting an A for the course. I strongly recommend this book to anyone who is taking complex variables and is having a bit of difficulty.

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.

It contains little theory, and a lot of solved problems. Therefore it is an excellent reference to the field of complex variables. Further, since the book is rather complete, from the 'real number system' to 'conformal mapping', it may also serve as a study book.

I never took a course in complex variables so a professor recommended this book to me. The format is simple and straighforward. Every chapter begins with a terse exposition of the subject matter to be covered. Immediately following is a longer section of "solved problems," where the theory is put into use. The final section consists of problems for the student to solve. The techniques necessary to solve these problems are covered in the earlier "solved problems" section. It is apparently intended as a supplementary textbook, although to me the book seems perfectly adequate by itself for self teaching. No good if you like to learn through reading alone, but for the hands-on type it is very good.

I am a huge fan of Schaum's outlines, but I was disappointed by this book.

The reason, like most people who disliked it, is that the examples do not deal with the mechanics of problem solving. For instance, early in the book, there is not a lot of material on parametrization, and this is a key part of integration in the complex plane. Not everyone who reads this book will go on to be an advanced mathematician; many people taking the class need reviews on problem solving mechanics that they missed in other classes.

Moreover, the theoretical exercises may be extensive, but they are not necessarily relevant. Each professor likes to teach the class in a different way, and though there are admittedly an abundance of theoretical exercises, I have found many problems in my book that do not have an analogue in Schaum's. Also, when one gets to series representation of analytic functions and beyond, the proofs are not as detailed and extensive as they should be.

I can't recommend actually not buying a Schaum's outline to anyone, and perhaps my review is based on lack of understanding of the material. But I can say that I think that this Schaum's outline is lower quality and less relevant than other ones that I have.