MKM_MAT2 Mathematics

Autumn 2020
Extent and Intensity
26/0/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
Ing. Lukáš Kokrda (lecturer)
Ing. Mgr. Markéta Matulová, Ph.D. (lecturer)
Guaranteed by
Ing. Mgr. Markéta Matulová, Ph.D.
Department of Applied Mathematics and Computer Science - Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Department of Applied Mathematics and Computer Science - Faculty of Economics and Administration
Prerequisites
Knowledge of calculus and linear algebra according to syllabus of the course BKM_MATE
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to prepare students to use advanced mathematical apparatus in specialized courses (Financial Mathematics, Microeconomics 2, Macroeconomics 2, etc.) so that they know not only how but also why these mechanisms work.
Learning outcomes
After completion of the course students will be able to:
- Analyze the behavior of economic systems and handle quantitative relationships between economic variables.
- Apply the tools required for static and dynamic economic modelling
- Foster mathematical and geometric intuition for understanding principals of financial mathematics, microeconomics, etc.
- Effectively use available software tools for symbolic and numeric computations
Syllabus
• Topics of tutorials with links to the respective chapters of Essential mathematics for economic analysis (EMEA) and Further mathematics for economic analysis (FMEA)
• 1. Advanced linear algebra: rank of matrix, linear dependence, eigenvalues and eigenvectors, quadratic forms [FMEA, kap. 1]
• Multivariate calculus: limit, gradient, Hessian, direction derivative, convexity, Taylor polynomial [EMEA 11.4-11.8, FMEA 2.1-2.6]
• Multivariate optimization [FMEA, 3.1-3.2]
• 2. Multivariate optimization with equality constraints [EMEA, 14, FMEA, 3.3 - 3. 4]
• Multivariate optimization with inequality constraints [FMEA 3.5-3.8]
• Introduction to linear programming [EMEA, 17]
• 3. Implicit function, envelope theorem, comparative statics [FMEA 2.8, EMEA 12, 13.7, 14. 7]
• Improper integration [EMEA, 9.7]
• Double integration [FMEA, 4]
• 4. Differential equations I [FMEA, 5]
• Differential equations II [FMEA, 6,7]
• Difference equations [FMEA, 11]
Literature
required literature
• SYDSÆTER, Knut, Peter J. HAMMOND, Arne STRØM and Andrés CARVAJAL. Essential mathematics for economic analysis. Fifth edition. Harlow: Pearson, 2016. xvi, 807. ISBN 9781292074610. info
• SYDSÆTER, Knut. Further mathematics for economic analysis. 2st ed. Harlow: Prentice-Hall, 2008. xi, 616. ISBN 9780273713289. info
recommended literature
• HOY, Michael. Mathematics for economics. 3rd ed. Cambridge, Mass.: MIT Press, 2011. xiv, 959. ISBN 9780262516228. info
• SIMON, Carl P. and Lawrence BLUME. Mathematics for economists. 1st ed. New York: W.W. Norton, 1994. xxiv, 930. ISBN 0393957330. info
• BAUER, Luboš, Hana LIPOVSKÁ, Miloslav MIKULÍK and Vít MIKULÍK. Matematika v ekonomii a ekonomice (Mathematics in Economics and Economy). první vydání. Praha: Grada Publishing, a.s., 2015. 352 pp. ISBN 978-80-247-4419-3. info
Teaching methods
The course is divided into four tutorials. Students are expected to selfstudy, to do the homework and pass through four auto-correction tests.
Assessment methods
The course is ended by an examination. The rating is determined by point gain from
-the final test
- auto-correction tests
- homework
Any copying, recording or leaking tests, use of unauthorized tools, aids and communication devices, or other disruptions of objectivity of exams (credit tests) will be considered non-compliance with the conditions for course completion as well as a severe violation of the study rules. Consequently, the teacher will finish the exam (credit test) by awarding grade "F" in the Information System, and the Dean will initiate disciplinary proceedings that may result in study termination.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught: in blocks.
Note related to how often the course is taught: 12 hodin.
General note: Přednášky jsou dostupné online a ze záznamu.
Information on the extent and intensity of the course: tutorial 12 hodin.
Information on course enrolment limitations: Předmět nebude v daném semestru vypsán, pokud se nezapíše min.30 studentů.
The course is also listed under the following terms Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019.
• Enrolment Statistics (recent)