 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 ℝ^{n}, partial derivatives, gradient and Hesse matrix, Taylor formula and local extrema, applications (e.g. geometric modelling).
Module MAT0213M1
Mathematics for Computer Science Students: Analysis (M, 5.0 LP)
Module Identification
Module Number  Module Name  CP (Effort) 

MAT0213M1  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  [MATService] Mathematics for other Departments 
Reference course of study  [INF82.79SG] B.Sc. Computer Science 
LivecycleState  [NORM] Active 
Courses
Type/SWS  Course Number  Title  Choice in ModulePart  PresenceTime / SelfStudy  SL  SL is required for exa.  PL  CP  Sem.  

2V+2U  MAT0213K1  Mathematics for Computer Science Students: Analysis
 P  56 h  94 h 
USchein
 ja  PL1  5.0  WiSe/SuSe 
 About [MAT0213K1]: Title: "Mathematics for Computer Science Students: Analysis"; PresenceTime: 56 h; SelfStudy: 94 h
 About [MAT0213K1]: The study achievement [USchein] 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) (75105 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 onedimensional 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 structureoriented 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.unikl.de)
Requirements for attendance (informal)
Prior or parallel participation in the course [MAT0211K1] is assumed.
Requirements for attendance (formal)
None
References to Module / Module Number [MAT0213M1]
Course of Study  Section  Choice/Obligation 

[INF82.79SG] B.Sc. Computer Science  Theoretical Foundations  [P] Compulsory 