Complex Analysis (Universitext) 2nd Edition by Eberhard Freitag (PDF)

Description

All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumedProvides a more in-depth introduction to the subject than other existing books in this areaOver 400 exercises including hints for solutions are included

User’s Reviews

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

⭐Several very good textbooks (usually in two volumes) are available to study Complex Analysis. Each offers something a little bit different. Conway makes things as easy as possible, but not easier. It is well organized and makes learning as simple as possible. So, it is often chosen as “the” right modern text. Elias Stein has an introductory text that is very insightful, a single volume (slightly dependent on a previous volume on Harmonic Analysis), and arranged for true beginners. Berenstein and Gay have two volumes that are very demanding and give a very sophisticated introduction, intended to connect students as quickly as possible to the research frontier. It is probably not very accessible to an undergraduate student, although, in principle, it starts from the beginning. In the Springer Series, there is an excellent two volume treatise by Remmert and Schumacher. It is ideal in the sense that it gives a very complete view of the whole field of analysis of a single complex variable. It gives its viewpoint in the same way that the originators themselves understood it. It is, in its own way, a very great masterpiece, and greater than this volume. It is much more detailed and precise than Conway. It seems superior in most ways, not just to this volume, but to most treatises. This volume is not a slouch. It simply has masterful works of scholarship as its competitors. This book is very, very desirable because it gives a clear and concise introduction to the great bulk of complex analysis quite quickly, in the first four chapters. So, it wastes no time and is completely rigorous. It is the “Joe Friday” “just the facts Ma’am” approach to learning complex analysis. After this introduction, it gives several chapters of extremely useful study on more specialized topics (modular functions) that is difficult to find elsewhere. It is not just difficult to find, but very difficult to find done so well. I really prefer Remmert Schumacher for most things, but RS is not available in English. I think this (paired) volume has a place on the bookshelf of any serious student of complex analysis.

⭐Written in a clear, modern style, “Complex Analysis” is an outstanding addition to the huge crop of existing books on the beautiful field of complex analysis. The authors have done a great service to any student who takes the time and care to study the book. What distinguishes this one is its choice of material. Obviously written by authors with a love for analytic number theory, in 130+ pages they give one of the clearest expositions of elliptic functions, the Modular Group, modular forms, and the Zeta function available. I don’t want to be misunderstood. They certainly cover the basic elements of complex variables, but, to me, the introductory material merely serves as a foundation for this later work. The fascinating area of elliptic functions and modular forms is all too often neglected in the current university curriculum and it is nice to see it return to the forefront in an elementary text.That said, one looks in vain for other classical topics. For example the Dirichlet problem and Poisson formula are virtually absent.I would say that the current text along with Conway’s excellent pair of offerings cover very thoroughly all you need to know about one complex variable in order to do real research. At a much higher level of detail and sophistication, I would recommend the volumes by Berenstein and Gay in place of Conway.For those interested in a pleasant introduction to the basics of modular forms — which historically have been a favorite tool for number theorists but recently seem to be cropping up in various areas of physics, such as black hole theory — I highly recommend the YouTube videos of Keith Conrad and Don Zagier.

⭐My first objection (which I should have checked out first, MY BAD there . The text is huge. The binding is over 2.0 in. which is prohibitive when it comes to carrying it around. It is a struggle to consult it without compromising the binding. There really should be some sort of warning about the size of the text despite its description. My other objection is that the print is far too light. I have to constantly refer to a font that is just too light to read, especially while trying to study . For the price, along with Springer’s reputation for poor bindings.

⭐Well written. Clever. Thought provoking.

⭐Good

⭐Nice, concise summary of Complex Analysis topics. Convenient paper back.

⭐This book was originally written in German, and the German version is just incredible: a real gem. Good reason to translate it! Unfortunately, this is one of the worst translations from German I have seen. Some of it is just awkward grammar, which the reader may be able to ignore. But, there are also some words and phrases which are translated incorrectly.For example “Paragraphen” in German does not mean paragraph in English, it means section. But in this book it is translated as paragraph. Try looking for something at the end of a paragraph or in the previous paragraph, when you should actually be looking at the end of the section or in the previous section. An example of this can be found in the explanation of the addition theorem for complex exponents (p. 27). The English text claims there is a remark concerning this at the end of the “paragraph.” The paragraph ends and there is no remark. Turn to the end of the section (p. 31) and you will find the remark just above the exercises.My advice is, if you can read German, get the German version! If you can’t read German, you can still get the English version, but you will have to be very patient with the mistakes incurred in the translation (not to be found in the German original). If you own this book, you should systematically go through it and replace “paragraph” everywhere with “section.” Most of the other translation mistakes can be figured out by context.

⭐That by Remmert or Lang slightly better

⭐The binding and pages were not glued together well.

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