Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-02-13-K-1

Mathematics for Computer Science Students: 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 WiSe/SuSe
Level [1] Bachelor (General)
Language [DE] German
Lecturers
Area of study [MAT-Service] Mathematics for other Departments
Livecycle-State [NORM] Active

Possible Study achievement

  • Verification of study performance: proof of successful participation in the exercise classes (ungraded)
  • Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

Contents

  • integer and rational numbers, countability,
  • sequences, convergence, real numbers, decimal fractions, Cauchy sequences, convergence criteria, application: existence and calculation of square roots,
  • Series, geometric series, convergence and divergence criteria, Cauchy product of series,
  • Functions, continuity, application: nested intervals and existence of zeros, intermediate value theorem,
  • power series, exponential function and functional equation, sine and cosine,
  • differentiability, derivation rules, derivation of power series, Taylor series, extreme values, mean value theorem, rule of l'Hospital, application (e.g. Newton's method),
  • Riemann integral, antiderivative and fundamental theorem of calculus, integration rules,
  • inverse function, logarithm, general powers, derivative of the inverse function, application: runtime analysis of algorithms,
  • outlook on ideas and concepts of multivariate analysis: limit values and continuity in several variables, curves in ℝn, partial derivatives, gradient and Hesse matrix, Taylor formula and local extrema, applications (e.g. geometric modelling).

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)

A previous or parallel participation in the course [MAT-02-11-K-1] "Mathematics for Computer Science Students: Algebraic Structures" is assumed.

Requirements for attendance (formal)

None

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

Module Name Context
[MAT-02-13-M-1] Mathematics for Computer Science Students: Analysis P: Obligatory 2V+2U, 5.0 LP