Theory Of Functions Of A Complex Variable - Vol 1
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MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Can someone recommend a good textbook on functions of one complex variable which have good chapters on geometric theory, in English? An excellent texbook by A.
Hurwitz with collaboration of R. An excellent [though smaller] textbook by B. Shabat, "Introduction to complex analysis, vol. Both books were never translated into English, besides a few chapters from the 2nd book, which were translated by Lenya Ryzhik. As I said in the remark there is no book comparable to the Russian edition of Hurwitz-Courant Evgrafov was the editor of the Russian translation who improved the original very much. There are 2 comprehensive Russian books covering much of geometric theory; both exist in English translation: Markushevich and Goluzin. Another book which covers a lot of geometric theory is Caratheodory 2 vols.
None of these has the theory of compact Riemann surfaces, but Shabat which you like also does not have it. I would say that Markushevich is a good replacement of Shabat. Goluzin can serve as a source of graduate courses. Wilhelm Schlag turned his notes from a first-year graduate course into a book of sorts. It covers a lot of the topics you listed and it has a bunch of good problems. It is especially well-written and cover a lot of topics, from elementary ones volume I to more advanced volume II.
There are many wonderful books on complex analysis in English. In fact it is the one subject on which I used to say one could pick almost any book and be well served. Probably this is because it was well treated in the beginning and most books simply recast the classical theory. My favorite is by Henri Cartan, superb and cheap. Another nice more elementary book is by Frederick Greenleaf. The book of Lang is also excellent.
As to geometry the book by Jones and Singerman: Complex functions, an algebraic and geometric viewpoint, is very well done. The classic book by Ford on Automorphic functions is also recommended. Probably everything is in the two volumes of Einar Hille, the only basic reference I know to include the big Picard theorem. I said this before , but the best book ever in any subject is Ahlfors'. The chapter on the Weierstrass function e.
I have always claimed that the best way to study Complex Analysis correctly is to read Ahlfors for the theory, and Marsden for the worked examples and long list of computational exercises. BTW, you will also find much interesting material in "Visual complex analysis" by T. It is full of geometric insights, although on the elementary side and it takes loooong to get to the harder material. Remmert, Reinhold Classical topics in complex function theory. Translated from the German by Leslie Kay. Graduate Texts in Mathematics, Springer-Verlag, New York, ISBN: It is divided into three parts: A.
Infinite product and partial fraction series. Mapping theory. Selecta including e. I suggest McMullen's lectures: complex analysis and advanced complex analysis in McMullen's homepage , also there is a book: Hand book of complex analysis geometric function theory in 2 vols by R. Sign up to join this community. The best answers are voted up and rise to the top. More information about this seller Contact this seller 2. Condition: Near Fine.
Selected Russian Publications in the Mathematical Sciences series. Inked name on front pastedown, 1" closed tear to rear panel dj with light wear to edges and lightly rubbed front panel same.
Clean, tight and strong binding with no underlining, highlighting or marginalia. Black cloth with gilt lettering. Seller Inventory More information about this seller Contact this seller 3. Published by PH About this Item: PH, Condition: Used: Very Good. More information about this seller Contact this seller 4. About this Item: PH. Condition: Very Good. Previous Owner name inside, Gently used with modest show of wear.
Functions of a Complex Variable and Some of Their Applications - 1st Edition
For Additional Information or pictures, Please Inquire. Seller Inventory SKU More information about this seller Contact this seller 5. Seller Inventory ZB More information about this seller Contact this seller 6. Published by Prentice-Hall From: Ammareal Grigny, France. About this Item: Prentice-Hall, Condition: Bon. Edition Tome 3. Former library book.
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Functions of a Complex Variable and Some of Their Applications
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Condition: Near Fine to Fine. Volume I: pp. Volume II: pp. Volume III: pp. Tightly bound. Corners not bumped. Text is free of markings. More information about this seller Contact this seller 9. Published by Prentice-Hall. About this Item: Prentice-Hall.
First Printing Black cloth hardcover with gold lettering. No Dust Jacket. Name written inside cover, otherwise clean. Hinges slightly loose. Seller Inventory MA. More information about this seller Contact this seller Published by Chelsea Publishing co. From: edconroybooks Troy, NY, U.