Theory of complex functions

Series: Graduate Texts in Mathematics, Vol. 122

Rheinhold Remmert

450 pages, parution le 30/04/1990

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Résumé

The material from function theory, up to the residue calculus, is developed in a lively and vivid style, well motivated throughout by examples and practice exercises. Additionally, there is ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations (original language together with English translation) from their classical works.

Yet the book is far from being a mere history of function theory. Even experts will find here few new or long forgotten gems, like Eisenstein's novel approach to the circular functions. This book is destined to accompany many students making their way into a classical area of mathematics which represents the most fruitful example to date of the intimate connection between algebra and analysis. For exam preparation it offers quick access to the essential results and an abundance of interesting inducements. Teachers and interested mathematicians in finance, industry and science will also find reading it profitable, again and again referring to it with pleasure.

Sommaire

Historical Introduction.
- Chronological Table.
- A. Elements of Function Theory.
- 0. Complex Numbers and Continuous Functions.
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- §1. The field of complex numbers.
- 1. The field
- 2. -linear and -linear mappings
- 3. Scalar product and absolute value
- 4. Angle-preserving mappings.
- §2. Fundamental topological concepts.
- 1. Metric spaces
- 2. Open and closed sets
- 3. Convergent sequences. Cluster points
- 4. Historical remarks on the convergence concept
- 5. Compact sets.
- §3. Convergent sequences of complex numbers.
- 1. Rules of calculation.
- 2. Cauchy's convergence criterion. Characterization of compact sets.
- §4. Convergent and absolutely convergent series.
- 1. Convergent series of complex numbers
- 2. Absolutely convergent series
- 3. The rearrangement theorem
- 4. Historical remarks on absolute convergence
- 5. Remarks on Riemann's rearrangement theorem
- 6. A theorem on products of series.
- §5. Continuous functions.
...

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Rheinhold Remmert
Parution	30/04/1990
Nb. de pages	450
Couverture	Cartonné
Intérieur	Noir et Blanc
EAN13	9780387971957
ISBN13	978-0-3879-7195-7