Description
Book SynopsisOne Basic Theory.- I Complex Numbers and Functions.- II Power Series.- III Cauchy's Theorem, First Part.- IV Winding Numbers and Cauchy's Theorem.- V Applications of Cauchy's integral Formula.- VI Calculus of Residues.- VII Conformal Mappings.- VIII Harmonic Functions.- Two Geometric Function Theory.- IX Schwarz Reflection.- X The Riemann Mapping Theorem.- XI Analytic Continuation Along Curves.- Three Various Analytic Topics.- XII Applications of the Maximum Modulus Principle and Jensen's Formula.- XIII Entire and Meromorphic Functions.- XIV Elliptic Functions.- XV The Gamma and Zeta Functions.- XVI The Prime Number Theorem.- 1. Summation by Parts and Non-Absolute Convergence.- 2. Difference Equations.- 3. Analytic Differential Equations.- 4. Fixed Points of a Fractional Linear Transformation.- 6. Cauchy's Theorem for Locally Integrable Vector Fields.- 7. More on Cauchy-Riemann.
Trade Review"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
Table of ContentsI: 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.
