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Mathematics for Economists

Course developers

Course abstract

The course of study is intended to acquire the mathematical knowledge and practical skills needed to study future special subjects, as well as to acquire skills for applying math techniques to study different entrepreneurship and economic relationships.
The course deals with set theory, mathematical theory of linear economic models, elements of mathematical analysis, a derivative and its application in the study of economic relationships.

Learning outcomes and their assessment

Upon successful completion of this course:
1. Students are able to manage and demonstrate knowledges and critical understanding of linear algebras, calculation of function limits, derivatives of functions. Students manage the application of the acquired topics in practical examples related to the specialty. – tests
2. Students are able to show understanding of the corresponding concept and regularities, to perform necessary caluculations and operations. - practical and laboratory work

3. Working in a group or doing work independently, student is able to apply the mathematical calculations corresponding to the speciality problem situation in economic, entrepreneurship and business management fields, to make a professional assessment and interpretation of the intermediate result of the calculations and the final results. – independent studies

Course Content(Calendar)

1. Set theory. (2 h)
2. Mathematical theory of linear economic models (matrices and determinants). (5 h)
3. Systems of linear equations and their solutions. (3 h)
4. The concept of function. Basic elementary functions. Economic functions: demand function, costs function, revenue function and profit function. (3 h)
Test 1. Linear algebra and economic functions
5. Limit of the function, its properties. Indeterminate forms of limit and their solutions. (4 h)
6. Derivatives, its geometric, physical and economical interpretation. Differentiation rules and formulas. Higher-order derivatives. (4 h)
7. Function elasticity, its economic interpretation. (2 h)
8. Applications of differentiation. Function monotonicity, extrema. Maximization of sales volume and revenue. Minimizing average costs. Profit maximization. (5 h)
9. Concavity of the function. Point of inflection. Differential of function. (2 h)

Test 2. Limit of function, derivative and its use in the study of economic relationships

Requirements for awarding credit points

Four independent works and two tests must be completed.
Assessment: Exam

Description of the organization and tasks of students’ independent work

The following independent work must be completed:
Independent work 1: Elements of Linear algebra
Independent work 2: Economic functions
Independent work 3: Limit theory

Independent work 4: Derivatives of one argument functions and their Economic applications

Criteria for Evaluating Learning Outcomes

Conditions for receiving the assessment of the Accumulative Exam:
- all independent works are completed (all tasks are executed correctly);
- during the semester each test score is at least 4.
Failed tests can be repeated. The student may overwrite unsuccessfully written test work during the study process at times specified by the teaching staff. The student can rewrite the last test and depended independent works in the individual study and examination period at the time indicated by the lecturer.
The accumulative exam mark is the average mark of all tests.
In the case of unsuccessful work in the semester student answers in the Exam for all the topics together in the period of the individual studies and examinations.

Compulsory reading

1. Revina I., Peļņa M., Gulbe M., Bāliņa S. Matemātikā ekonomistiem. Teorija un uzdevumi. Rīga: Izglītības soļi, 2006.
2. Revina I., Peļņa M., Gulbe M., Bāliņa S. Uzdevumu krājums matemātikā ekonomistiem. Rīga, Zvaigzne, 1997.
3. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. I, II daļa. Rīga; Zvaigzne, 1988.
4. Šteiners K., Siliņa B. Augstākā matemātika. II, III daļa. Rīga: Zvaigzne ABC, 1999, 1997.
5. Rosser M. Basic mathematics for economists. Second Edition. Rautledge, 2003.

Further reading

1. Buiķis M. Finansu matemātika.Rīga, 2002. Biznesa izglītības bibliotēka I
2. Grīnglazs L., Kopitovs J. Augstākā matemātika ekonomistiem (ar datoru lietojuma paraugiem uzdevumu risināšanai). Rīga, 2003. Biznesa izglītības bibliotēka III.
3. Hazans M., Jaunzems A. Augstākās matemātikas kursa pamatjēdzienu ekonomiskā interpretācija un realizācija. Rīga: LU, 1980.
4. Mizrahi A., Sullivan M. Mathematics for Buisiness and Social sciences. Wiley&Sons, 1988.
5. Strupule L., Jēgere I. Matemātika ekonomistiem. Programma, lekciju konspekts, uzdevumu risinājumu paraugi un patstāvīgā darba uzdevumi, Ekonomikas fakultātes pilna un nepilna laika studiju programmai. LLU. Jelgava, 2009.
6. Čerņajeva S., Vintere A. Mācību līdzeklis augstākās matemātikas pamatu apguvei. Rīga-Jelgava: 2016. 198 lpp.
7. Buiķis M. Finansu matemātika. Rīga, 2002. Biznesa izglītības bibliotēka I.
7. Grīnglazs L., Kopitovs J. Augstākā matemātika ekonomistiem (ar datoru lietojuma paraugiem uzdevumu risināšanai). Rīga, 2003. Biznesa izglītības bibliotēka III.

Notes

Theoretical basic courses and information technology courses (part B2) for FESD professional Bachelor’s study programme “Entrepreneurship and Business Management”.