# Mathematics by tonze.danzel

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```									                                Public Management Bachelor Programme

Module                  41 – Mathematics
Examination             QMI I (Quantitative Methods and Computer Sciences)
Semester                1st semester (winter semester)
Courses                 a) Mathematics (L) DE
b) Mathematics – Exercise (E) DE
Workload                4 SPW 4 credits 120 workload hours (45 attendance hours, 75 self study hours)
Module coordinator      Dr. Georg Baumbach

1. Learning outcomes
Students will be familiar with the fundamental mathematical tools that form the basis of economic theories. They
will be in a position to model standard economic problems with a mathematical background, to thus determine a
solution and to interpret its values in economic terms. They will have mastered the essential processes of linear
algebra and analysis needed for this. They will have the expertise required to use methods of financial mathe-
matics that form the basis of all types of financing. At the end of the course, participants will be in a position to
make content-related and methodical associations with other modules in the field of quantative methods and with
the overall course curriculum.

2. Recommended prior knowledge and skills
General knowledge of mathematics (A-level equivalent in mathematics – elementary course)

3. Contents
 Financial mathematics
 Computation of interest (linear, compound interest, equivalence principle)
 Annuities (hire purchase agreements, capital and annuity, perpetuities)
 Sinking fund calculations (methods of repayment, repayment plans)
 Applications in investment (net present values, annuities, internal interest rate)
 Linear algebra
 Linear equation systems (solvability and solution structure, Gauss algorithm)
 Vectors and matrices
 Determinants
 Analysis
 Functions (one-dimensional and multi-dimensional, limit and continuity)
 One-dimensional differential calculus (limit function, elasticities and optimal values)
 Multi-dimensional differential calculus (partial derivatives, extrema with and without constraints)
 (ordinary) differential equations

4. Modes of teaching and learning, workload
Lecture (22,5 hrs); practical exercises (22,5 hrs); preparation and revision of lectures (20 hrs); sample questions
and test exam (25 hrs), discussion of test exam answers during the practical exercises; exam preparation (30 hrs).

5. Type of examination
Written exam (120 minutes)

6. Literature
TIETZE, Jürgen: Einführung in die Finanzmathematik, 8. Auflage, Wiesbaden 2008; TIETZE, Jürgen: Übungsbuch
zur Finanzmathematik, 5. Auflage, Wiesbaden 2008; FÜHRER, Christian: Kompakt-Training Wirtschaftsmathema-
tik, 2. Auflage, Ludwigshafen (Rhein) 2008; TIETZE, Jürgen: Einführung in die angewandte Wirtschaftsmathema-
tik, 14. Auflage, Wiesbaden 2008; TIETZE, Jürgen: Übungsbuch zur angewandten Wirtschaftsmathematik, 6. Auf-
lage, Wiesbaden 2006; LUDERER, Bernd; WÜRKER, Uwe : Einstieg in die Wirtschaftsmathematik, 6. Auflage,
Wiesbaden 2005; ROMMELFANGER, Heinrich: Mathematik für Wirtschaftswissenschaftler, Band 1, 6. Auflage, Hei-
delberg 2004; ROMMELFANGER, Heinrich: Mathematik für Wirtschaftswissenschaftler, Band 2, 5. Auflage, Heidel-
berg 2001.

Stand: 30.06.2009

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