This is the first part of a three semester introduction into the basic mathematical field of Analysis. Differential and integral calculus in a real variable will be covered.
Topics: - the real numbers, - the concept of limits (sequences and series) – functions (continuity and differentiability) – minima and maxima of differentiable functions, extreme value calculation – the Riemann integral, Fourier series – ordinary differential equations.

The lecture follows the script Analysis I

Further literatur:

• Blatter, Ch.: Analysis 1. Springer-Verlag. xi+369 S.

• Forster, O.: Analysis 1. Differential- und Integralrechnung einer Veränderlichen. Vieweg. viii+208 S.

• Fritzsche, K.: Grundkurs Analysis 1 - Differentiation und Integration in einer Veränderlichen. Spektrum Verlag. xii+372 S.

Many examples, applications and useful comments can be found in

• Arens, T. , et al.: Mathematik. Heidelberg: Spektrum Akademischer Verlag. 2008. xiv+1496 S.

The following book develops Analysis  using a historical context

• Körle, H.-H.: Die phantastische Geschichte der Analysis. Ihre Probleme und Methoden seit Demokrit und Archimedes. Dazu die Grundbegriffe von heute. Oldenbourg. 2009. xiv+217 S.