BeschreibungThis is the fourth edition of Serge Lang's Complex Analysis. The first part of the book covers the basic material of complex analysis, and the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more systematically than in other texts, and the proofs using these methods often shed more light on the results than the standard proofs do. The first part of Complex Analysis is suitable for an introductory course on the undergraduate level, and the additional topics covered in the second part give the instructor of a graduate course a great deal of flexibility in structuring a more advanced course. This is a revised edition, new examples and exercises have been added, and many minor improvements have been made throughout the text.
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.
Pressestimmen"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
"A highly recommendable book for a two semester course on complex analysis."
Untertitel: 'Graduate Texts in Mathematics'. 4. Auflage, korr. Nachdruck 2001. 139 Abbildungen. Sprache: Englisch.
Verlag: Springer-Verlag GmbH
Erscheinungsdatum: September 1999