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 |
+ further Lecturers of the department Mathematics
|
| 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 |