Additional literature for the first-year analysis courses:

 
This list contains some Analysis textbooks that I can recommend to interested students for various reasons and purposes. They are not compulsory, and some of them cover much more material than our lectures. It is a somewhat arbitrary, necessarily incomplete choice from an enormous bulk of texts, with the purpose of giving some orientation:



T. W. Körner, A Companion to Analysis , Graduate Studies in Mathematics 62, AMS 2004,
ISBN: 0-8218-3447-9

Ik like the text's style. The level of abstraction is slightly higher, and more material is covered than in our lectures.

W.R. Wade, An Introduction to Analysis, Pearson 2004, ISBN 0-13-124683-6,
TUE-Bibl.: CKB 2004 WAD

For the 1D part, the book is comparable to Kosmala, the multidimensional part is more comprehensive. Nice, but sometimes relatively difficult exercises.


W. Rudin: Principles of mathematical analysis, McGraw-Hill, 1976,
TUE-Bibl.: CLB 64 RUD

A classic, originating from the 1950s. The text is quite short due to its elegant and concentrated style, but covers the essence.

A. van Rooij: Analyse voor Beginners, Epsilon Uitgaven 6, 2003, ISBN 978-90-5041-005-2
TUE-Bibl.: CKB 2003 ROO

A text in Dutch, aimed to facilitate the step from highschool to university. The explanations are very comprehensive, and lots of examples are given. Lots of attention is given to teaching proof techniques.


R. A. Kortram, A. van Rooij: Analyse: Functies van meer veranderlijken,
Epsilon uitgaven 16, 1990, ISBN 978-90-5041-024-3
TUE-Bibl.: CLE 90 KOR

Continuation of "Analyse voor Beginners".

H. Heuser, Analysis Teil 1/Teil 2, Teubner 1980, ISBN 978-3519422358 / 978-3519422341
TUE-Bibl.: CLB 80 HEU

For those who are not deterred by German language. A popular beginner's analysis text at German universities. Comprehensive and with lots of examples. The second part is going further and deeper than we do.


H. Amann, J. Escher: Analysis I-III, Birkhäuser, 1998-2001, ISBN 3-7643-5976-5 (I). - 3-7643-6134-4 (II). - 3-7643-6613-3 (III)
TUE-Bibl.: CKB 98 AMA

Available in German  and English. My personal favorite. For our courses, Part I and some of Part II are of interest. The level of abstraction is higher, and the theory is set up in a general framework from the beginning. If one got used to this, this is quite enlightening. Warning: There are not many simple, concrete examples, and the exercise problems are often relatively difficult.


R.A. Adams: Calculus, Pearson 2006, ISBN 0-321-27000-2
TUE-Bibl.: CAB 2006 ADA

The book you know from the basis Calculus course. Differing from the other books on this list, it is centered on calculations and elementary concepts, and proofs play a minor role. You find a large number of worked out examples and problems to train your calculation abilities.

There are lots of Calculus texts with these purposes, this certainly belongs to the better ones.


Moreover, here you find a literature list for a complete study of (pure) mathematics.

For us, the sections on Calculus and (introductory) Analysis are relevant. They also contain material that is freely available on the net.