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Rannacher, Rolf: Analysis 1: Differential- und Integralrechnung für Funktionen einer Veränderlichen, Heidelberg: Heidelberg University Publishing, 2018. DOI: 10.17885/heiup.317.431

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ISBN 978-3-946054-69-6 (PDF)
ISBN 978-3-946054-68-9 (Softcover)

Published 02/12/2018 .

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Rolf Rannacher

Analysis 1

Differential- und Integralrechnung für Funktionen einer Veränderlichen

Lecture Notes

This introductory text is based on lectures within a three-semester cycle on "Real Analysis" given by the author at Heidelberg University. The present first part is devoted to the classical calculus of differentiation and integration for functions of one real variable. Content and presentation are particularly oriented towards the needs of the application in the theory of differential equations, in Mathematical Physics and in Numerical Analysis.
For supporting self-study each chapter contains exercises with solutions collected in the appendix.

Rolf Rannacher, retired Professor of Numerical Mathematics at Heidelberg University – study of Mathematics at the University of Frankfurt/Main, doctorate 1974, postdoctorate 1978 at Bonn University – 1979/1980 Vis. Assoc. Professor at the University of Michigan (Ann Arbor, USA), thereafter Professor at Erlangen and Saarbrücken, in Heidelberg since 1988 – field of interest “Numerics of Partial Differential Equations”, especially the “Finite Element Method” and its applications in the Natural Sciences and Engeneering; more than 160 scientific publications.

Contents
PDF
Front Matter
Inhaltsverzeichnis
Bibliography
0 Vorwort
1 Grundlagen der Analysis
2 Die reelen und die komplexen Zahlen
3 Zahlenfolgen und Reihen
4 Funktionen und Stetigkeit
5 Differentiation
6 Integration
7 Fourier-Analysis
A Lösungen der Übungsaufgaben
Index