- 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).
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 |
+ further Lecturers of the department Mathematics
|
| 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
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 (informal)
Prior or parallel participation in the course [MAT-02-11-K-1] is assumed.
Requirements for attendance (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 | Theoretical Foundations | [P] Compulsory |