By Professor Dr. Eberhard Freitag, Dr. Rolf Busam (auth.)

ISBN-10: 3540257241

ISBN-13: 9783540257240

ISBN-10: 3540308237

ISBN-13: 9783540308232

The guideline of this presentation of ``Classical complicated Analysis'' is to continue as fast as attainable to the imperative effects whereas utilizing a small variety of notions and ideas from different fields. therefore the necessities for knowing this e-book are minimum; in simple terms trouble-free evidence of calculus and algebra are required.

The first 4 chapters hide the basic center of advanced analysis:

- differentiation in C (including ordinary proof approximately conformal mappings)

- integration in C (including complicated line integrals, Cauchy's imperative Theorem, and the fundamental Formulas)

- sequences and sequence of analytic functions, (isolated) singularities, Laurent sequence, calculus of residues

- development of analytic functions: the gamma function, Weierstrass' Factorization Theorem, Mittag-Leffler Partial Fraction Decomposition, and -as a selected spotlight- the Riemann Mapping Theorem, which characterizes the easily attached domain names in C.

Further issues incorporated are:

- the idea of elliptic services in keeping with the version of K. Weierstrass (with an tours to older ways due to N.H. Abel and C.G.J. Jacobi utilizing theta series)

- an advent to the idea of elliptic modular functions and elliptic modular forms

- using advanced research to acquire quantity theoretical results

- an explanation of the leading quantity Theorem with a susceptible kind of the error term.

The ebook is mainly suited to graduated scholars in arithmetic and complicated undergraduated scholars in arithmetic and different sciences.

Motivating introductions, greater than 400 routines of all degrees of trouble with tricks or recommendations, historic annotations, and over one hundred twenty figures make the general presentation very beautiful. The constitution of the textual content, together with abstracts starting every one bankruptcy and highlighting of the most effects, makes this publication very applicable for self-guided research and an critical relief in getting ready for tests.

This English version is predicated at the fourth impending German edition.