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Rannacher, Rolf: Numerik 0: Einführung in die Numerische Mathematik, Heidelberg: Heidelberg University Publishing, 2017. DOI: 10.17885/heiup.206.281

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978-3-946054-27-6 (PDF)

978-3-946054-30-6 (Softcover)

Published 04/26/2017.

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Rolf Rannacher

Numerik 0

Einführung in die Numerische Mathematik

Lecture Notes

This introductory text is based on courses on “Numerical Mathematics” given by the author at Heidelberg University within a multi-semester cycle over a period of 25 years. The present first part covers fundamental concepts of numerical methods for solving ordinary analysis and linear algebra problems. Both theoretical and practical aspects are considered. The understanding of the contents requires only that prior knowledge as is usually provided in the basic Analysis and Linear Algebra courses. For facilitating self-learning the book contains theoretical and practical exercises with solutions.

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
Titelei
Inhaltsverzeichnis
Literaturverzeichnis
Einleitung
Kapitel 1: Fehleranalyse
Kapitel 2: Interpolation und Approximation
Kapitel 3: Numerische Integration
Kapitel 4: Lineare Gleichungssysteme I (Direkte Verfahren)
Kapitel 5: Nichtlineare Gleichungen
Kapitel 6: Lineare Gleichungssysteme II (Iterative Verfahren)
Kapitel 7: Eigenwertaufgaben
Kapitel 8: Lineare Optimierung
Kapitel A: Lösungen der Übungsaufgaben
Index