Course detail

Mathematical modeling

FP-KmmPAcad. year: 2024/2025

The subject is focused on precise mathematical formulation of economic models and at the same time appropriate economic interpretation of these models.

Language of instruction

Czech

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

doc. Mgr. Veronika Novotná, Ph.D.

Department

Institute of Informatics (ÚI)

Entry knowledge

Basic knowledge of Mathematics 1 and 2: properties of numbers, derivative, integral, function of one variable, function analysis of two variables
Basic knowledge of microeconomics and macroeconomics.

Rules for evaluation and completion of the course

The form of the exam is written and the teacher reserves the right to the oral examination. The maximum number of points in the exam is 100 points, and the student must earn at least 50 points in order to obtain a rating of at least E..
Attendance at lectures is optional.

Aims

Learning outcomes of the course unit The aim of the course is to acquaint students with models of mathematical economics and economic models using mathematical apparatus and with precise mathematical formulation in the field of economic models and at the same time appropriate economic interpretation of these models.
Objective of the course - learning outcomes and competences: Students will be able to understand and describe solutions of selected economic problems using previous and newly acquired knowledge of mathematical,
The student is able to apply both existing and newly acquired mathematical knowledge in solving selected economic problems

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

GROS, I.; DYNTAR, J. Matematické modely pro manažerské rozhodování. 2. upravené a rozšířené vyd. Praha: Vysoká škola chemicko-technologická v Praze, 2015. 303 s. ISBN 978-80-7080-910-5.
GROS, I.; DYNTAR, J. Matematické modely pro manažerské rozhodování. 2. upravené a rozšířené vyd. Praha: Vysoká škola chemicko-technologická v Praze, 2015. 303 s. ISBN 978-80-7080-910-5.
MEZNÍK, I. Úvod do matematické ekonomie pro ekonomy. 2. vyd. Brno: CERM, s.r.o., 2017. 189 s. ISBN 978-80-214-5512-2.
MEZNÍK, I. Úvod do matematické ekonomie pro ekonomy. 2. vyd. Brno: CERM, s.r.o., 2017. 189 s. ISBN 978-80-214-5512-2. (CS)

Recommended reading

BUTCHER, J. C. (John Charles). Numerical methods for ordinary differential equations. Third edition. Chichester: Wiley, 2016. 513 s. ISBN 978-1-119-12150-3.
BUTCHER, J. C. (John Charles). Numerical methods for ordinary differential equations. Third edition. Chichester: Wiley, 2016. 513 s. ISBN 978-1-119-12150-3.
CHIANG, A. C.; WAINWRIGHT, K. Fundamental methods of mathematical economics. 4th ed. Boston: McGraw-Hill/Irwin, 2005. 688 s. ISBN 0-07-010910-9.
CHIANG, A. C.; WAINWRIGHT, K. Fundamental methods of mathematical economics. 4th ed. Boston: McGraw-Hill/Irwin, 2005. 688 s. ISBN 0-07-010910-9.
PRAŽÁK, P. Diferenční rovnice s aplikacemi v ekonomii. Hradec Králové: Gaudeamus, 2013. 360 s. ISBN 978-80-7435-268-3.
PRAŽÁK, P. Diferenční rovnice s aplikacemi v ekonomii. Hradec Králové: Gaudeamus, 2013. 360 s. ISBN 978-80-7435-268-3.

Classification of course in study plans

  • Programme BAK-EP Bachelor's 2 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

Upon successful completion of this course, students will be able to use mathematics as a tool for deeper understanding of economics and apply acquired mathematical knowledge in solving selected economic problems.

1. Mathematical modeling in economics. Classification of economic-mathematical models.
2. Mathematical modeling in economics - basic mathematical means for exploring functions in economics.
3. Interpolation and function approximation. Interpolation with algebraic polynomials. Lagrange interpolation method. Approximate least squares method.
4. Mathematical Analysis of Selected Economic Addictions - Consumer Decision Making.
5. Mathematical analysis of selected economic dependencies - production model with multiple inputs.
6. Methods of mathematical analysis and mathematical programming. Models of imperfect markets. Evaluation of production efficiency.
7. Flow variable in economy - investment and accumulation of capital. Analysis of selected economic functions.
8. Functional dependence as a tool for modeling macroeconomic phenomena. Static equilibrium models. Static concept of multiplier, accelerator. Mathematical derivation of the IS-LM model.
9. Mathematical basis of continuous dynamic models in economics. Analogue Discrete and Continuous Models. Differential equations as a tool for modeling continuous macroeconomic dynamic processes.
10. Differential equations as a tool for modeling of continuous microeconomic dynamic processes.
11. Mathematical basis of discrete dynamic models in economics. Differential equations as a tool for modeling discrete macroeconomic dynamic processes.
12. Differential equations as a tool for modeling discrete microeconomic dynamic processes.
13. Application of differential and differential equations in selected microeconomic models. Continuous and discrete models in logistics.