#
ESF:MKM_MAT2 Mathematics - Course Information

## MKM_MAT2 Mathematics

**Faculty of Economics and Administration**

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**- Finance (programme ESF, N-FIN)
- Finance (programme ESF, N-FU)
- Business Management (programme ESF, N-EKM)
- Business Management (programme ESF, N-PEM)

**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**- 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

*required 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

*recommended literature*- SYDSÆTER, Knut, Peter J. HAMMOND, Arne STRØM and Andrés CARVAJAL.
**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.

- Enrolment Statistics (recent)

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