Classical Complex AnalysisCRC Press, 24.09.1991 - 792 Seiten Text on the theory of functions of one complex variable contains, with many elaborations, the subject of the courses and seminars offered by the author over a period of 40 years, and should be considered a source from which a variety of courses can be drawn. In addition to the basic topics in the cl |
Inhalt
Preface | 1 |
Complex Numbers | 7 |
223 | 69 |
2 | 87 |
Functions Limits and Continuity Arcs and Curves | 125 |
Sequences and Series | 173 |
Elementary Functions | 214 |
4 | 248 |
Differentiation | 308 |
Integration | 409 |
Applications | 458 |
Sequences and Series of Functions Series | 520 |
Singularities The Calculus of Residues | 650 |
| 759 | |
Häufige Begriffe und Wortgruppen
absolutely convergent algebra analytic function b₁ bilinear transformation C₁ called Cauchy Cauchy-Goursat theorem circle closed contour coefficients compact complex function complex numbers complex plane conjugate consider constant contained continuous function converges absolutely Corollary corresponding Definition denoted derivative differentiable disk diverges equation Example exists f(zo finite number fixed point fn(z fo(z follows formula function f(z ƒ is analytic geometric given graph Hence homotopic implies infinite integral inverse Let f Let f(z limit Math metric space neighborhood obtain open set points z₁ poles polynomial power series Prove r₁ radius of convergence real axis real numbers region Riemann Riemann sphere Riemann surface sequence series converges Show single-valued singularity sinh subset Suppose Theorem topological topological space un(z uniform convergence variable vector w-plane w₁ zero