Introduction to Complex Analysis: Second EditionIt really is a gem, both in terms of its table of contents and the level of discussion. The exercises also look very good. —Clifford Earle, Cornell University This book has a soul and has passion. —William Abikoff, University of Connecticut This classic book gives an excellent presentation of topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem. The two quotes above confirm that the book can be successfully used as a text for a class or for self-study. |
Contents
| 1 | |
GENERAL PROPERTIES OF RATIONAL FUNCTIONS | 23 |
LINEAR TRANSFORMATIONS | 37 |
MAPPING BY RATIONAL FUNCTIONS OF SECOND ORDER | 60 |
THE EXPONENTIAL FUNCTION AND ITS INVERSE THE GENERAL POWER | 65 |
THE TRIGONOMETRIC FUNCTIONS | 78 |
INFINITE SERIES WITH COMPLEX TERMS | 95 |
INTEGRATION IN THE COMPLEX DOMAIN CAUCHYS THEOREM | 108 |
HARMONIC FUNCTIONS | 184 |
ANALYTIC CONTINUATION | 213 |
ENTIRE FUNCTIONS | 225 |
PERIODIC FUNCTIONS | 242 |
THE EULER ΓFUNCTION | 278 |
THE RIEMANN ζFUNCTION | 289 |
THE THEORY OF CONFORMAL MAPPING | 305 |
| 345 | |
CAUCHYS INTEGRAL FORMULA AND ITS APPLICATIONS | 131 |
THE RESIDUE THEOREM AND ITS APPLICATIONS | 167 |
Back Cover | 351 |
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Common terms and phrases
analytic function angle apply arbitrary assume boundary boundary point bounded branch points choose circle closed complex condition conformally connected consider constant contains continuous converges corresponds curve defined definition denote derivative determined differentiable disk domain G equal equation Exercise exists expansion expression finite fixed follows formula function w(z given half-plane Hence holds imaginary infinite integral interior inverse joining limit linear transformation mapping means neighborhood obtain one-to-one origin parallelogram path periodic plane point z poles positive primitive principle problem proof properties Prove radius of convergence rational function real axis regular remains respect result Riemann surface right-hand side satisfies segment sequence simply single-valued slit takes tends theorem triangle uniformly unit disk vanishes vector w₁ write z-plane z₁ zero