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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 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, integral and its application in the determination of production costs, revenues and profits, changes in resource consumption, output/product volume and economic performance.

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, analytic geometry elements, calculation of function limits, derivatives of functions and integration. 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 specialty problem situation, 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
10. Primitive function and definition of indefinite integral. Properties and basic integration rules. (5 h)
11. Economic application of the indefinite integral, cost, revenue, profit. (2 h)
12. Definition of definite integral. Properties and calculation of the definite integral. Integration by substitution and partial integration into the definite integral. (2 h)
13. Application of the definite integral. Calculating the area. Economic applications of the definite integral. Determining resource consumption. Determination of production costs, sales revenue and profit growth. Determination of the volume of production and the quantity of goods sold. Benefits for consumers and benefits for producers. (5 h)
Test 3. Integrals and their Economic interpretation.
14. Function of several variables. Production functions, characteristics, main types, product curves. First and second partial derivatives (4 h)
15. Economic interpretation of partial derivatives. (2 h)
16. Extrema of functions of two variables. Economic-mathematical relationships of two benefits. (6 h)
17. Interest calculations. Simple interest, compound interest. Periodic payments. (4 h)
Test 4. Function of two variables, economic-mathematical relationships on the two-benefit farm and financial calculations.

Requirements for awarding credit points

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 function of one variable and their Economic applications
Independent work 5: Integrals and their Economic interpretation

Independent work 6: Partial derivatives and extrema of two arguments functions

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. 306 lpp.
2. Revina I., Peļņa M., Gulbe M., Bāliņa S. Uzdevumu krājums matemātikā ekonomistiem. Rīga: Zvaigzne, 1997. 167 lpp.
3. Šteiners K., Siliņa B. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 1998. 116 lpp.
4. Šteiners K., Siliņa B. Augstākā matemātika. III daļa. Rīga: Zvaigzne ABC, 1998. 192 lpp.
5. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. I daļa. Rīga: Zvaigzne, 1988. 534 lpp.
6. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. II daļa. Rīga: Zvaigzne, 1988. 527 lpp.
7. Barnett R. A., Ziegler M. R. Applied mathematics for business and economics, life sciences and social sciences. 3rd ed. San Francisco, California, 1989. 1079 p.
8. Silberg E. The Structure of Economics: A Mathematical Analysis. New York: McGraw – Hill Book Company, 1978. 543 p.

Further reading

1. 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. 93 lpp.
2. Čerņajeva S., Vintere A. Mācību līdzeklis augstākās matemātikas pamatu apguvei. Rīga-Jelgava: 2016. 198 lpp.
3. Grīnglazs L., Kopitovs J. Augstākā matemātika ekonomistiem ar datoru lietojuma paraugiem uzdevumu risināšanai. Rīga, 2003. 379 lpp. Biznesa izglītības bibliotēka III.
4. Mizrahi A., Sullivan M. Mathematics for Business and Social sciences. Wiley&Sons, 1988. 876 p.
5. Rosser M. Basic mathematics for economists. Second Edition. Rautledge, 2003. 535 p.
6. Buiķis M. Finansu matemātika. Rīga, 2002. Biznesa izglītības bibliotēka I.
7. Hazans M., Jaunzems A. Augstākās matemātikas kursa pamatjēdzienu ekonomiskā interpretācija un realizācija. Rīga: LU, 1980.

Notes

Compulsory course for Bachelor’s study programme “Economics”.