i6.010 | ## Vorlesung und Übung: Analysis I |
L |

WS 2019 | Prof. Dr. Michael Gnewuch | |

6h/wk 9 ECTS |
B.Sc modules:CS-BP-MAT - Mathematics CS-BWP-MAT - Mathematics KOGW-PM-MAT - Mathematics KOGW-WPM-MAT - Mathematics |
Tue: 10-12
Thu: 10-12 Fri: 10-12 |

Students will have encountered some concepts and applications of calculus at high school. The aim of this course is to extend and deepen this knowledge systematically, because the material covered and the form of reasoning is necessary for later studies and applications.|Although the course uses some basic understanding of numbers and functions, it begins anew with the discussion of numbers, natural numbers, integers, rationals, reals, and complex numbers. Proofs by induction are also discussed here. This is followed by the concept of functions. The idea of a limit is at the heart of calculus. Thus sequences, series, and continuity for functions of a real variable are studied in detail. Then differential calculus of one variable and the basic functions, exponentials, logarithms, and the trigonometric functions can be studied. Integration is usually introduced in the form of the Riemann integral or by means of primitive functions.|