151-0435/04 – Mathematics in Economics (ME435)

Gurantor department	Department of Mathematical Methods in Economics	Credits	5
Subject guarantor	doc. Ing. Petr Seďa, Ph.D.	Subject version guarantor	doc. Ing. Petr Seďa, Ph.D.
Study level	undergraduate or graduate
		Study language	Czech
Year of introduction	2009/2010	Year of cancellation
Intended for the faculties	EKF	Intended for study types	Follow-up Master

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
SED02	doc. Ing. Petr Seďa, Ph.D.

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Part-time	Credit	6+6

Subject aims expressed by acquired skills and competences

The main aim of the course is to teach students how to use mathematics effectively and to increase knowledge and understanding of microeconomic and macroeconomic problems. Students will get the following knowledge, skills and abilities: • will be able to use mathematics as a tool for deeper understanding of microeconomics and macroeconomics, • will be able to study economics effectively, • will learn how to apply methods and procedures of mathematical analysis to solve practical economic problems at the microeconomic and macroeconomic level, • will be able to describe solutions of selected economic problems using mathematical tools, check individual steps of given solution, generalize conclusions and evaluate the correctness of results with respect to given conditions.

Teaching methods

Lectures

Summary

This course connects the existing knowledge of mathematics and economics obtained at bachelor level of study so that students apply the knowledge of mathematics in the area of microeconomics and macroeconomics. The aim of this course is to enable students to understand the benefits of using mathematics as a very useful tool for understanding objective economic reality using mathematical abstraction. Students should discover connections and relationships by comparing economic phenomena having different content but same formal description. This approach allows students to achieve a deeper knowledge of economics.

Compulsory literature:

DOWLING, Edward T. Schaum's Outline of Introduction to Mathematical Economics. New York: McGraw-Hill, 2011. 552 s. ISBN 978-0071762519. KLEIN, Michael. Mathematical Methods for Economics. London: Pearson College, 2019. 580 s. ISBN 978-0201726268. MAVRON, Vassilis a Timothy PHILLIPS. Elements of Mathematics for Finance. London: Springer, 2007. 322 s. ISBN 978-3-540-05117-6.

Recommended literature:

CHIANG, Alpha a Kevin WAINWRIGHT. Fundamental Methods of Mathematical Economics. New York: McGraw-Hill/Irwin, 2004. 704 s. ISBN 0-07-066219-3. SYDSAETER, Knut a Peter HAMMOND. Essential Mathematics for Economic Analysis. London: Pearson College, 2008. 721 s. ISBN 978-0273713241. YU Kam. Mathematical Economics: Prelude to the Neoclassical Model. Heidelberg: Springer, 2019. 227 s. ISBN 978-3030272913.

Additional study materials

Study supports in the EduDocs system

Way of continuous check of knowledge in the course of semester

Knowledge is controlled through 2 written tests and tasks according to specification of teachers.

E-learning

The course is supported by on-line LMS (Learning Management System).

Other requirements

Not required by teachers.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Topics for selfstudy: 1. Introduction. Mathematical modelling in economics. Classification of economic and mathematical models. Functional dependency. 2. Approximation of real functions. Interpolation by algebraic polynomials. Lagrange interpolation method. Approximation by the least squares method. 3. Differential calculus of functions of one variable in economic applications. Economic functions and their properties, the slope of a function. Total, average and marginal variables in economics, elasticity of a function. 4. Differential calculus of multivariable functions in economic applications I. The methods of optimizing the multivariable functions in economics - the substitution method, the method of Lagrange multipliers, the method of comparison of marginal rates of substitutions. 5. Differential calculus of multivariable functions in economic applications II. Constrained extrema of multivariable functions in economics. Model with multiply inputs. Evaluation of efficiency. 6. Differential calculus of multivariable functions in economic applications III. The methods of optimization in imperfect models markets. 7. Integral calculus in economics. Application of definite and indefinite integrals in economics. Flow quantities in economics and their accumulation over time. 8. Functional dependence as a tool for modelling static economic phenomena. Models of static equilibrium. Models of comparative statics in economics. 9. Mathematical basis of discrete linear dynamic models in economics I. Difference equation – a mathematical tool for modelling the discrete macroeconomic dynamic processes in economics. 10. Mathematical basis of continuous linear dynamic models in economics I. Analogy of discrete and continuous models. Differential equations - a mathematical tool for modelling the continuous macroeconomic dynamic processes in economics. 11. Mathematical basis of discrete linear dynamic models in economics II. Difference equations - mathematical tool for modelling the discrete microeconomic dynamic processes in economics. 12. Mathematical basis of continuous linear dynamic models in economics II. Differential equations – a mathematical tool for modelling the continuous microeconomic dynamic processes in economics. Tutorials: 1. Mathematical modelling in economics. Differential calculus in economic applications. Economic functions and their properties. Total, average and marginal variables in economics, elasticity of function. 2. Mathematical analysis of selected multivariable functions in economic applications. Models with multiple inputs. Integral calculus in economics. 3. Mathematical basis of discrete and continuous dynamic models in economics. Differential equations. Continuous dynamic processes in economics. Difference equations. Discrete dynamic processes in economics.

Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Credit	Credit	100 (100)	52	2
Test 1	Written test	50	26	2
Test 2	Written test	50	26	2

Mandatory attendence participation: Attendance at tutorials is recommended.

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Conditions for subject completion and attendance at the exercises within ISP: Attendance at tutorials is recommended. It is necessary to pass 2 written tests, just like in the case of students without ISP.

Show history

Occurrence in study plans

Academic year	Programme	Branch/spec.	Spec.	Form	Study language	Tut. centre	Year	Type of duty
2023/2024	(N0311A050012) Applied economics	(S02) Economic Development		K	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(N0311A050012) Applied economics	(S02) Economic Development		K	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(N0311A050012) Applied economics	(S02) Economic Development		K	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration		K	Czech	Ostrava	1	Compulsory	study plan
2020/2021	(N0311A050012) Applied economics	(S02) Economic Development		K	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(N0311A050012) Applied economics	(S02) Economic Development		K	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration		K	Czech	Ostrava	1	Compulsory	study plan
2018/2019	(N6208) Economics and Management	(6208T037) Management		K	Czech	Ostrava	1	Compulsory	study plan
2018/2019	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration		K	Czech	Ostrava	1	Compulsory	study plan
2018/2019	(N6208) Economics and Management	(6208T020) Business Economics		K	Czech	Ostrava	1	Compulsory	study plan
2017/2018	(N6208) Economics and Management	(6208T037) Management		K	Czech	Ostrava	1	Compulsory	study plan
2017/2018	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration		K	Czech	Ostrava	1	Compulsory	study plan
2017/2018	(N6208) Economics and Management	(6208T020) Business Economics		K	Czech	Ostrava	1	Compulsory	study plan
2016/2017	(N6208) Economics and Management	(6208T020) Business Economics		K	Czech	Ostrava	1	Compulsory	study plan
2016/2017	(N6208) Economics and Management	(6208T037) Management		K	Czech	Ostrava	1	Compulsory	study plan
2016/2017	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration		K	Czech	Ostrava	1	Compulsory	study plan
2015/2016	(N6208) Economics and Management	(6208T020) Business Economics		K	Czech	Ostrava	1	Compulsory	study plan
2015/2016	(N6208) Economics and Management	(6208T037) Management		K	Czech	Ostrava	1	Compulsory	study plan
2015/2016	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration		K	Czech	Ostrava	1	Compulsory	study plan
2014/2015	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration		K	Czech	Ostrava	1	Compulsory	study plan
2014/2015	(N6208) Economics and Management	(6208T020) Business Economics		K	Czech	Ostrava	1	Compulsory	study plan
2014/2015	(N6208) Economics and Management	(6208T037) Management		K	Czech	Ostrava	1	Compulsory	study plan
2013/2014	(N6208) Economics and Management	(6208T037) Management		K	Czech	Ostrava	1	Compulsory	study plan
2013/2014	(N6208) Economics and Management	(6208T037) Management	(02) Management	K	Czech	Ostrava	1	Compulsory	study plan
2013/2014	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration		K	Czech	Ostrava	1	Compulsory	study plan
2013/2014	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration	(02) Public Economics and Administration	K	Czech	Ostrava	1	Compulsory	study plan
2013/2014	(N6208) Economics and Management	(6208T020) Business Economics		K	Czech	Ostrava	1	Compulsory	study plan
2013/2014	(N6208) Economics and Management	(6208T020) Business Economics	(02) Business Economics	K	Czech	Ostrava	1	Compulsory	study plan
2012/2013	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration	(02) Public Economics and Administration	K	Czech	Ostrava	1	Compulsory	study plan
2012/2013	(N6208) Economics and Management	(6208T020) Business Economics	(02) Business Economics	K	Czech	Ostrava	1	Compulsory	study plan
2012/2013	(N6208) Economics and Management	(6208T037) Management	(02) Management	K	Czech	Ostrava	1	Compulsory	study plan
2011/2012	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration	(02) Public Economics and Administration	K	Czech	Ostrava	1	Compulsory	study plan
2011/2012	(N6208) Economics and Management	(6208T020) Business Economics	(02) Business Economics	K	Czech	Ostrava	1	Compulsory	study plan
2011/2012	(N6208) Economics and Management	(6202T049) Accounting and Taxes	(02) Účetnictví a daně	K	Czech	Ostrava	1	Compulsory	study plan
2011/2012	(N6208) Economics and Management	(6208T037) Management	(02) Management	K	Czech	Ostrava	1	Compulsory	study plan
2010/2011	(N6202) Economic Policy and Administration	(6210T004) European Integration	(02) European Integration	K	Czech	Ostrava	1	Compulsory	study plan
2010/2011	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration	(02) Public Economics and Administration	K	Czech	Ostrava	1	Compulsory	study plan
2010/2011	(N6208) Economics and Management	(6208T020) Business Economics	(02) Business Economics	K	Czech	Ostrava	1	Compulsory	study plan
2010/2011	(N6209) Systems Engineering and Informatics	(6209T025) System Engineering and Informatics	(02) System Engineering and Informatics	K	Czech	Ostrava	1	Compulsory	study plan
2009/2010	(N6208) Economics and Management	(6208T020) Business Economics	(02) Business Economics	K	Czech	Ostrava	1	Compulsory	study plan
2009/2010	(N6202) Economic Policy and Administration	(6210T004) European Integration	(02) European Integration	K	Czech	Ostrava	1	Compulsory	study plan
2009/2010	(N6202) Economic Policy and Administration	(6202T055) Public Economics and Administration	(02) Public Economics and Administration	K	Czech	Ostrava	1	Compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner
Subject block without study plan - EKF - K - cs	2019/2020	Part-time	Czech				Optional	EKF - Faculty of Economics	stu. block

Assessment of instruction