Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-02-13a-K-1

Mathematics für Socioinformatics: Analysis (2V+2U, 5.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 5.0 CP 94 h
2 V Lecture 28 h
2 U Exercise class (in small groups) 28 h
(2V+2U) 5.0 CP 56 h 94 h

Basedata

SWS 2V+2U
CP, Effort 5.0 CP = 150 h
Position of the semester 1 Sem. in SuSe
Level [1] Bachelor (General)
Language [DE] German
Lecturers
Böhm, Janko, Dr. (WMA | DEPT: MAT)
Kämmerer, Florentine, Dr. (WMA | DEPT: MAT)
Kunte, Michael, Dr. (WMA | DEPT: MAT)
+ further Lecturers of the department Mathematics
Area of study [MAT-Service] Mathematics for other Departments
Livecycle-State [NORM] Active

Notice

The lecture is identical with the lecture in [MAT-02-13-K-1]. Additionally, a dedicated exercise programme (small group exercises) is offered for students of socioinformatics.

Possible Study achievement

  • Verification of study performance: proof of successful participation in the exercise classes (incl. written examination, ungraded)
  • Examination number (Study achievement): 80217 ("Mathematics für Sozioinformatics: Analysis")
  • Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

Contents

  • integer and rational numbers, countability,
  • sequences, convergence, Cauchy sequences, convergence criteria, application: existence and calculation of square roots, real numbers,
  • series, geometric series, convergence and divergence criteria, Cauchy product of series, functions, continuity,
  • intermediate value theorem, power series, exponential function and functional equation, sine and cosine,
  • differentiability, rules of derivation, derivation of power series, Taylor series, extreme values, mean value theorem, rule of l'Hospital,
  • Riemann integral, antiderivative and fundamental theorem of calculus, integration rules,

inverse function, logarithm, general powers, derivative of the inverse function,

  • outlook on ideas and concepts of multivariate analysis: limit values and continuity in several variables, partial derivatives, gradient and Hesse matrix, Taylor formula and local extrema.

Literature

  • O. Forster: Analysis 1, Analysis 2,
  • H. Heuser: Lehrbuch der Analysis, Teil 1 und Teil 2,
  • M. Barner, F. Flohr: Analysis I, Analysis II,
  • K. Königsberger: Analysis 1, Analysis 2,
  • B. Kreußler, G. Pfister: Mathematik für Informatiker: Algebra, Analysis, Diskrete Strukturen.

Materials

Further literature will be announced in the lecture(s); exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

Prior or parallel participation in the course [MAT-02-11a-K-1] is expected.

Requirements for attendance (formal)

None

References to Course [MAT-02-13a-K-1]

Module Name Context
[MAT-02-90-M-1] Mathematics for Socioinformatics: Linear Algebra and Analysis P: Obligatory 2V+2U, 5.0 LP