Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-02-13-M-1

Mathematics for Computer Science Students: Analysis (M, 5.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-02-13-M-1 Mathematics for Computer Science Students: Analysis 5.0 CP (150 h)

Basedata

CP, Effort 5.0 CP = 150 h
Position of the semester 1 Sem. in WiSe/SuSe
Level [1] Bachelor (General)
Language [DE] German
Module Manager
Lecturers
Area of study [MAT-Service] Mathematics for other Departments
Reference course of study [INF-82.79-SG] B.Sc. Computer Science
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+2U MAT-02-13-K-1
Mathematics for Computer Science Students: Analysis
P 56 h 94 h
U-Schein
ja PL1 5.0 WiSe/SuSe
  • About [MAT-02-13-K-1]: Title: "Mathematics for Computer Science Students: Analysis"; Presence-Time: 56 h; Self-Study: 94 h
  • About [MAT-02-13-K-1]: The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.
    • It is a prerequisite for the examination for PL1.

Examination achievement PL1

  • Form of examination: written exam (Klausur) (75-105 Min.)
  • Examination Frequency: each semester
  • Examination number: 80214 ("Mathematics for Computer Science Students: Analysis")

Evaluation of grades

The grade of the module examination is also the module grade.


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).

Competencies / intended learning achievements

Upon successful completion of this module, the students have achieved the following learning outcomes:
  • The students know and understand the basic concepts, statements and methods of one-dimensional analysis, and know applications of them in computer science.
  • Based on an outlook, they have developed a basic understanding of the generalization of these concepts to multivariate analysis.
  • They are trained in analytical thinking and their capacity for abstraction has been promoted.
  • Using a structure-oriented approach, they have learned to comprehend mathematical proofs and to independently prove or disprove mathematical statements in simple examples.
  • By working on the given exercises, they have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture.
  • In addition, their abilities to present and to work in a team were promoted.

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.

Registration

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

Requirements for attendance of the module (informal)

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

Requirements for attendance of the module (formal)

None

References to Module / Module Number [MAT-02-13-M-1]

Course of Study Section Choice/Obligation
[INF-82.79-SG] B.Sc. Computer Science [Compulsory Modules] Theoretical Foundations [P] Compulsory