Module 24-B-NU Numerical Analysis

Faculty

Person responsible for module

Regular cycle (beginning)

Every summer semester

Credit points and duration

10 Credit points

For information on the duration of the modul, refer to the courses of study in which the module is used.

Competencies

Non-official translation of the module descriptions. Only the German version is legally binding.

Students master the fundamentals of numerical mathematics and scientific computing, i.e: They can deal with the basic concepts and methods of numerical mathematics in a technically correct manner, successfully transfer them to new problems, independently carry out proofs in these areas and implement procedures algorithmically. They are able to confidently apply the knowledge and skills required in advanced courses in numerical mathematics.

In the tutorials, students demonstrate the acquisition of skills in the basic techniques of mathematical work in the field of numerical mathematics and scientific computing, in particular the analysis, application and implementation of numerical methods and the performance of mathematical proofs under supervision, as well as presentation and communication skills and perseverance as basic mathematical skills through the study requirements . The final exam demonstrates students' advanced understanding of the relationships and concepts, their ability to carry out proofs independently and their confidence in applying the methods to new problems.

Content of teaching

Rounding errors and error propagation,
Interpolation and approximation,
Discrete Fourier transform,
Numerical integration and differentiation,
Solving linear systems of equations: direct and iterative methods,
balancing problems and linear optimisation,
Solving non-linear systems of equations: iterative methods,
Eigenvalue problems

Recommended previous knowledge

Knowledge of analysis and linear algebra

Necessary requirements

—

Explanation regarding the elements of the module

The module cannot be studied together with module 24-B-NU-5

Module structure: 1 SL, 1 bPr 1

Courses

Numerical Analysis I
Type lecture
Regular cycle SoSe
Workload5 60 h (60 + 0)
LP 2 [Pr]
Tutorials for Numerical Analysis I
Type exercise
Regular cycle SoSe
Workload5 90 h (30 + 60)
LP 3 [SL]

Study requirements

Allocated examiner Workload LP2
Teaching staff of the course Tutorials for Numerical Analysis I (exercise)

Regular completion of the exercises, each with a recognisable solution approach, as well as participation in the exercise groups for the module's lecture. As a rule, participation in the exercise group includes presenting solutions to exercises twice after being asked to do so as well as regular contributions to the scientific discussion in the exercise group, for example in the form of comments and questions on the proposed solutions presented. The organiser may replace some of the exercises with face-to-face exercises.

 see above see above

Examinations

e-portfolio with final oral examination o. e-portfolio with final written examination o. portfolio with final oral examination o. portfolio with final written examination
Allocated examiner Teaching staff of the course Numerical Analysis I (lecture)
Weighting 1
Workload 150h
LP2 5

The (e-)portfolio is passed if

  • a sufficient number of correctly solved exercises, which are completed as part of the study requirements , are demonstrated, usually by at least 50% of the points achievable in the semester for solving the exercises, and
  • a final exam in the form of a final written exam (usually 90 min) or a final oral exam (usually 30 min) is passed. The final exam relates to the content of the lecture and the tutorial and is used for assessment.

A remote electronic written examination is not permitted as a final exam.

The module is used in these degree programmes:

Degree programme Version Profile Recom­mended start 3 Duration Manda­tory option 4
Extension subject / Master of Education Erweiterungsfach [Prüfungsordnung vom 21.03.2023 mit Änderungen vom 30.11.2023 und 26.04.2024] Mathematics (Subject-specific Regulations from 2019): Extension subject Master of Education Continuation Minor Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule')) 3. o. 4. one semester Compul­sory optional subject
Mathematical and Theoretical Physics / Master of Science [FsB vom 26.04.2024 mit Änderungen vom 29.05.2024 und 10.12.2024 und der Berichtigung vom 01.04.2025] Admission Track Profile B 1. o. 2. one semester Compul­sory optional subject
Mathematics / Bachelor of Science [FsB vom 28.02.2025] Major Subject (Academic) 3. o. 4. o. 5. o. 6. one semester Compul­sory optional subject
Mathematics / Bachelor [FsB vom 28.02.2025] Minor Subject (Academic), 60 CPs 4. o. 5. o. 6. one semester Compul­sory optional subject
Mathematics / Bachelor of Science [FsB vom 28.02.2025] Major Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule')) 3. o. 4. o. 5. o. 6. one semester Compul­sory optional subject
Mathematics / Bachelor of Science [FsB vom 30.09.2016 mit Änderung vom 10.12.2024] Major Subject (Academic) 3. o. 4. one semester Compul­sory optional subject
Mathematics / Bachelor of Science [FsB vom 30.09.2016 mit Änderung vom 10.12.2024] Major Subject (Academic) Strukturierte Ergänzung des fw Bachelor KF 3. o. 4. o. 5. one semester Compul­sory optional subject
Mathematics / Bachelor [FsB vom 30.09.2016 mit Änderung vom 10.12.2024] Minor Subject (Academic), 60 CPs 3. o. 4. o. 5. one semester Compul­sory optional subject
Mathematics / Bachelor of Science [FsB vom 30.09.2016 mit Änderung vom 10.12.2024] Major Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule')) 3. o. 4. one semester Compul­sory optional subject
Mathematics / Master of Education [FsB vom 01.03.2019 mit Änderung vom 10.12.2024] Continuation Major Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule')) 3. o. 4. one semester Compul­sory optional subject
Mathematics / Master of Education [FsB vom 01.03.2019 mit Änderung vom 10.12.2024] Continuation Minor Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule')) 3. o. 4. one semester Compul­sory optional subject
Informatics for the Natural Sciences / Bachelor of Science [FsB vom 01.04.2025] Bachelor with One Core Subject (Academic) 2. o. 4. one semester Compul­sory optional subject
Informatics for the Natural Sciences / Master of Science [FsB vom 01.04.2025] 2. o. 4. one semester Compul­sory optional subject
Mathematical Economics / Bachelor of Science [FsB vom 28.02.2025 mit Berichtigung vom 30.04.2025] Bachelor with One Core Subject (Academic) 3. o. 4. o. 5. o. 6. one semester Compul­sory optional subject
Mathematical Economics / Bachelor of Science [FsB vom 30.09.2016 mit Berichtigung vom 10.01.2017 und Änderungen vom 15.05.2017, 01.03.2018, 01.03.2019, 16.09.2019, 02.03.2020 und 10.12.2024] Bachelor with One Core Subject (Academic) Business Administration 3. o. 4. o. 5. one semester Compul­sory optional subject
Mathematical Economics / Bachelor of Science [FsB vom 30.09.2016 mit Berichtigung vom 10.01.2017 und Änderungen vom 15.05.2017, 01.03.2018, 01.03.2019, 16.09.2019, 02.03.2020 und 10.12.2024] Bachelor with One Core Subject (Academic) Political Economy 3. o. 4. o. 5. one semester Compul­sory optional subject

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Legend

1
The module structure displays the required number of study requirements and examinations.
2
LP is the short form for credit points.
3
The figures in this column are the specialist semesters in which it is recommended to start the module. Depending on the individual study schedule, entirely different courses of study are possible and advisable.
4
Explanations on mandatory option: "Obligation" means: This module is mandatory for the course of the studies; "Optional obligation" means: This module belongs to a number of modules available for selection under certain circumstances. This is more precisely regulated by the "Subject-related regulations" (see navigation).
5
Workload (contact time + self-study)
SoSe
Summer semester
WiSe
Winter semester
SL
Study requirement
Pr
Examination
bPr
Number of examinations with grades
uPr
Number of examinations without grades
This academic achievement can be reported and recognised.

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Elements of the module

Courses

Study requirements

Examinations

Programme of lectures (eKVV)

Programme of lectures (eKVV)

Show lists of modules

Mathematics (Subject-specific Regulations from 2019) (Extension subject) / Master of Education Erweiterungsfach: Extension subject Master of Education Continuation Minor Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule'))

Mathematical and Theoretical Physics / Master of Science // Admission Track Profile B

Mathematics / Bachelor of Science: Major Subject (Academic)

Mathematics / Bachelor: Minor Subject (Academic), 60 CPs

Mathematics / Bachelor of Science: Major Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule'))

Mathematics / Bachelor of Science: Major Subject (Academic) [FsB vom 30.09.2016 mit Änderung vom 10.12.2024]

Mathematics / Bachelor of Science: Major Subject (Academic) // Strukturierte Ergänzung des fw Bachelor KF [FsB vom 30.09.2016 mit Änderung vom 10.12.2024]

Mathematics / Bachelor: Minor Subject (Academic), 60 CPs [FsB vom 30.09.2016 mit Änderung vom 10.12.2024]

Mathematics / Bachelor of Science: Major Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule')) [FsB vom 30.09.2016 mit Änderung vom 10.12.2024]

Mathematics / Master of Education: Continuation Major Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule'))

Mathematics / Master of Education: Continuation Minor Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule'))

Informatics for the Natural Sciences / Bachelor of Science: Bachelor with One Core Subject (Academic)

Informatics for the Natural Sciences / Master of Science

Mathematical Economics / Bachelor of Science: Bachelor with One Core Subject (Academic)

Mathematical Economics / Bachelor of Science: Bachelor with One Core Subject (Academic) // Business Administration [FsB vom 30.09.2016 mit Berichtigung vom 10.01.2017 und Änderungen vom 15.05.2017, 01.03.2018, 01.03.2019, 16.09.2019, 02.03.2020 und 10.12.2024]

Mathematical Economics / Bachelor of Science: Bachelor with One Core Subject (Academic) // Political Economy [FsB vom 30.09.2016 mit Berichtigung vom 10.01.2017 und Änderungen vom 15.05.2017, 01.03.2018, 01.03.2019, 16.09.2019, 02.03.2020 und 10.12.2024]