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Complex Analysis (Graduate Texts in Mathematics, nr. 103)

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en Limba Engleză Carte Hardback – 30 Jul 2003
The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. The first half, more or less, can be used for a one-semester course addressed to undergraduates. The second half can be used for a second semester, at either level. Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra read- ing material for students on their own. A large number of routine exer- cises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recommend to anyone to look through them. More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues.
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Specificații

ISBN-13: 9780387985923
ISBN-10: 0387985921
Pagini: 489
Ilustrații: 139 Abb.
Dimensiuni: 155 x 235 x 33 mm
Greutate: 0.89 kg
Ediția: 4th ed. 1999. Corr. 3rd printing 2003
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics

Locul publicării: New York, NY, United States

Public țintă

Graduate

Recenzii

"The very understandable style of explanation, which is typical for this author, makes the book valuable for both students and teachers."
EMS Newsletter, Vol. 37, Sept. 2000
Fourth Edition
S. Lang
Complex Analysis
"A highly recommendable book for a two semester course on complex analysis."
—ZENTRALBLATTMATH

Caracteristici

Written by a well-known and somewhat controversial Springer author whose writing style has achieved a considerable following
Unique approach should appeal to those who want to obtain new results in this field
Goes beyond the basic material to present special topics of current interest
Additional topics covered in the second part give readers a great deal of flexibility in structuring their learning of the subject
Extensively revised edition, includes new examples and exercises, and hundreds of minor improvements throughout

Cuprins

I: BASIC THEORY. 1: Complex Numbers and Functions. 2: Power Series. 3: Cauchy's Theorem, First Part. 4: Winding Numbers and Cauchy's Theorem. 5: Applications of Cauchy's Integral Formula. 6: Calculus of Residues. 7: Conformal Mappings. 8: Harmonic Functions. II: GEOMETRIC FUNCTION THEORY. 9: Schwarz Reflection. 10: The Riemann Mapping Theorem. 11: Analytic Continuation Along Curves. III: VARIOUS ANALYTIC TOPICS. 12: Applications of the Maximum Modulus Principle and Jensen's Formula. 13: Entire and Meromorphic Functions. 14: Elliptic Functions. 15: The Gamma and Zeta Functions. 16: The Prime Number Theorem.