Any good calculus texts in German?

Question

I am looking for a good text on calculus written (or translated) in German. It is difficult to judge which books are best so I am hoping for people who have experience to recommend something.

Edit:

I am not new to calculus so abstraction/density should not be a problem.

Answer 1

Walter has also written very nice texts. Another standard book for lectures is Königsberger. Heuser is very expansive, but once was also a standard.

In my opinion, Foster is a very good reference book for Analysis, short, to the point. But hardly suited for self study.

A collection of reviews and recommendations of of Analysis related books by the mathematical community of the portal matheplanet.com

Answer 2

If you want a good ( very abstract) introduction in analysis, I would suggest Herbert Amann, Joachim Escher : Analysis I .

This is the textbook we used in our introductory course for Analysis at TU Ilmenau. It is very well written, but also very abstract. It certainly won't be easy to understand on the first try, but the authors have a very nice style in my opinion.

Answer 3

I can recommend the books by Otto Forster.

He has written the books

• Analysis 1, 11th revision, Springer 2013, ISBN 978-3-658-00316-6
• Analysis 2, 10th revision, Springer 2013, ISBN 978-3-658-02356-0
• Analysis 3, 6th revision, Vieweg + Teubner 2011, ISBN 978-3-8348-1232-2

Also much recommended by our professor at University of Regensburg.

Answer 4

As Stefan indicated, it depends on the style you prefer. Besides Amann Escher, which is quite abstract, you could have a look at Forster, which is a standard textbook used by many lecturers in Germany.

Answer 5

I have always liked Bröcker's Analysis in three volumes (I-III) very much. It is however possibly a bit too condensed as an only text if you are learning the material for the first time.

The books have been out of print for some time now, but they can be bought used. Until recently PDF's were available on his page at the University of Regensburg, but sadly Prof. Bröcker has passed away since this question was asked.

Answer 6

I have Zorich's books, which I find very good. They have basically everything you need to know on the subject in them (an I would hope so, considering they total at more than 1000 pages of calculus...)

Answer 7

Peter Dombrowski, Differentialrechnung I und Abriss der Linearen Algebra, BI Hochschulskripten 743/743a, Mannheim 1970. Das Buch ist wohl nur noch antiquarisch zu erhalten, ist aber ein “must have”.

Answer 8

The following has been used at ETH Zurich many times, it's for free:

http://www.math.ethz.ch/~blatter/dlp.html