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Title: Complex Analysis (4th Ed) (Graduate Texts in Mathematics, 103) by Serge Lang ISBN: 0-387-98592-1 Publisher: Springer Verlag Pub. Date: 15 January, 1999 Format: Hardcover Volumes: 1 List Price(USD): $69.95 |
Average Customer Rating: 4 (3 reviews)
Rating: 3
Summary: A good book, but not for beginners.
Comment: if you want an introduction to complex analysis, I advise you to pass on this book, and read Churchill and Brown's introductory book. Having said this, part I of Lang's book will seem mostly review if you follow my advice. Part II, on Geometric Function Theory, is more advance material that is presented reasonably well.
Rating: 4
Summary: Not TOO complex
Comment: A person with absolutely no knowledge of complex numbers could begin with page one of this book. However, I think that some exposure to analysis is helpful before finishing the first chapter, but not necessary. I found this book easier to read & understand than some real analysis books, yet it helped me further understand real analysis in the process. I'm sure this is due to mere repetition of some of those concepts over a different field. As the author mentions in his foreword, the first half of the book can be used as an undergraduate text (Jr/Sn years) and the second half can also, but I would NOT have enjoyed it in undergraduate studies. I found it worthy of a first course in complex numbers at the graduate level. I especially liked it after studying real numbers. The placement of the chapter subject matter can be altered (to some degree) to ones liking. I think Lang has provided good examples & problems. There's a solutions manual (by Rami Shakarchi) for this text somewhere.
A brief discription of the chapters (some of them at least):
Chp 1: basic definitions & operations, polar form, functions, limits, compact sets, differentiation, Cauchy-Riemann eqs, angles under holomorphic ("differentiable") maps.
Chp 2: formal & convergent power series, analytic functions, inverse & open mapping thms., local maximum modulus principle
Chp 3: connected sets, integrals over paths, primitives ("antiderivatives"), local Cauchy thm, etc
Chp 4: winding numbers, global Cauchy Thm, Artin's proof
Chp 5: Applications of Cauchy's integral formula, Laurent series
Chp 6: Calculus of residues, evaluation of complex definate integrals, Fourier transforms, etc (fun stuff)
Chp 7: Comformal mapping, Schwarz lemma, analytic automorphisms of the Disc
Chp 8: Harmonic functions; Chp 9: Schwarz reflection; Chp 10: Riemann mapping theorem; (11): Analytic continuation along curves; (12) applications of Maximum Modulus Principle an Jensen's Formula; (13) Entire & Meromorphic functions; (14) elliptic functions; (15) Gamma & Zeta functions; (16) The Prime Number Theorem; and a handy appendix.
Rating: 5
Summary: Wrong book!
Comment: I have tried to tell you guys. My review you have published above is of the book of same name and publisher (but 2nd ed) by Bak and Newman! I did not review Serge Lang's book!
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Title: Problems and Solutions for Complex Analysis by Rami Shakarchi, Serge Lang ISBN: 0387988319 Publisher: Springer Verlag Pub. Date: December, 1999 List Price(USD): $44.95 |
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Title: Algebra by Serge Lang ISBN: 038795385X Publisher: Springer Verlag Pub. Date: 08 January, 2002 List Price(USD): $69.95 |
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Title: Visual Complex Analysis by Tristan Needham ISBN: 0198534469 Publisher: Clarendon Pr Pub. Date: June, 2000 List Price(USD): $65.00 |
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Title: Counterexamples in Analysis by Bernard R. Gelbaum, John M. H. Olmsted ISBN: 0486428753 Publisher: Dover Pubns Pub. Date: 04 June, 2003 List Price(USD): $14.95 |
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Title: Elementary Theory of Analytic Functions of One or Several Complex Variables by Henri Cartan ISBN: 0486685438 Publisher: Dover Pubns Pub. Date: 06 July, 1995 List Price(USD): $11.95 |
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