The guiding principle of this presentation of “Classical Complex Analysis” is to proceed as quickly as possible to the central results while using a small number. Complex Analysis. Eberhard Freitag and Rolf Busam basic ideas of complex analysis: the complex plane, the Cauchy-Riemann equations. Complex Analysis has 11 ratings and 0 reviews. All needed notions are developed within Eberhard Freitag,. Rolf Busam. · Rating details · 11 ratings · 0.
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All needed notions are developed within the book: Thus the prerequisites for understanding this book are minimal; only elementary facts of calculus and algebra are required. Interesting introductions, over four compelx exercises with hints or solutions, historical remarks, and over figures make this book very appropriate analsyis attractive for students at all levels. Overall, this is quite an attractive book. No doubt, this excellent, comprehensive, and nearly self-contained textbook on complex analysis deserves a wide international audience of readers, who will profit a great deal from studying it.
The idea of this book is to give an extensive description of the classical complex analysis, here ”classical” means roughly that sheaf theoretical and cohomological methods are omitted.
The first four chapters cover the fgeitag core of complex analysis presenting their fundamental results. After this standard material, the authors step forward to elliptic functions and to elliptic modular functions including a taste of all most beautiful results of this field.
The book is rounded by applications to analytic number theory including distinguished pearls of this fascinating subject as for instance the Prime Number Theorem. Great importance is attached to completeness, all needed notions are developed, only minimal prerequisites elementary facts of calculus and algebra are required. More than exercises including hints for solutions and many figures make this an attractive, indispensable book for students who would like to have a sound introduction to classical complex analysis.
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Add both to Cart Add both to Freitqg. These items are shipped from and sold by different sellers. Buy the selected items together This item: Ships from and sold by Amazon. Husam from and sold by allnewbooks. Customers who bought this item also bought. Freitay 1 of 1 Start over Page 1 of 1. Complex Analysis Graduate Texts in Mathematics. An Introduction to Manifolds: Complex Variables Dover Books on Mathematics. Review From the reviews: For the second edition the authors have revised the text carefully.
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Bsam of 6 reviews. Top Reviews Buaam recent Top Reviews. There was a problem filtering reviews right now. Please try again later. 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 Analysisand arranged for true beginners.
Complex Analysis – Eberhard Freitag, Rolf Busam – Google Books
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 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. 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.
Complex Analysis by Eberhard Freitag, Rolf Busam
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.
Nice, concise summary of Complex Analysis topics. I was truly delighted to find this text. It starts off with ordinary complex analysis at the level of sophomore undergraduate students and proceeds well into graduate-level complex analysis analytic number theory, elliptic functions, abels theorem, etc. The ‘advanced’ results are shown using standard methods, so it was a great way for someone who learned the nuts and bolts of contour integration to move into theta functions, the prime number theorem, etc etc This book was originally written in German, buzam the German version is just incredible: 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 anxlysis 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. The English text claims there is a remark concerning this at the end of the “paragraph. Turn to the end of the section p. 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.
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Complex Analysis 2nd Edition by Eberhard Freitag, Rolf Busam – Paperback
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