SubjectsSubjects(version: 928)
Course, academic year 2022/2023
  
Applied mathematics - AB501095
Title: Applied mathematics
Guaranteed by: Department of Economics and Management (837)
Faculty: Central University Departments of UCT Prague
Actual: from 2022
Semester: summer
Points: summer s.:7
E-Credits: summer s.:7
Examination process: summer s.:
Hours per week, examination: summer s.:3/3, C+Ex [HT]
Capacity: unlimited / unlimited (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
Level:  
For type:  
Note: enabled for web enrollment
Guarantor: Vozárová Pavla Ing. Mgr. Ph.D., M.A.
Romanenko Viktoriia doc. Ph.D.
Literature
Last update: Cibulková Jana Ing. (19.12.2022)

Sydsæter, K., Strøm, A., & Berck, P. (2005). Economists' mathematical manual (Vol. 3). Berlin: Springer.

Dowling, E. T. (2001). THEORY AND PROBLEMS OF INTRODUCTION TO MATHEMATICAL ECONOMICS 3rd ed. MC Graw Hill Education.

Sydsæter, K., & Hammond, P. J. (2008). Essential mathematics for economic analysis. Pearson Education.

Bronshtein, I. N., & Semendyayev, K. A. (2013). Handbook of mathematics. Springer Science & Business Media.

Vinogradov V. (1999). A Cook-book of Mathematics. CERGE-EI.

Syllabus
Last update: Cibulková Jana Ing. (19.12.2022)

1. Revision of the analysis of functions of one variable - application to selected economic problems (Cost functions and relationships between them. Maximization of monopoly profit.).

2. Revision of the analysis of functions of multiple variables - application to selected economic problems (Utility function and indifference curves.).

3. Extrema of functions of several variables multiple restrictions (Optimal choice of labor and capital for a firm in the regime of perfect competition).

4. Extrema of functions of multiple variables with restrictions, Lagrange function (Minimization of costs for a given volume of production).

5. Primitive function and its properties. Indefinite integral of elementary functions. (Distribution functions and probability densities.)

6. Method by parts and substitution method for the indefinite integral. (Total versus marginal cost.)

7. Definite integral. Newton's and Riemann's integral. (Lorenz curve and Gini coefficient)

8. Method by parts and substitution method for the definite integral. Improper integral. (Mean values of continuous random variables.)

9. Integral of functions of multiple variables. Fubini theorem. Integral as a function of the upper bound. Leibniz theorem. (Maximizing social welfare.)

10. Sequences and their properties. Sequence limits. Sequence differences. (Financial products.)

11. Series. Basic convergence criteria. (Valuation of bonds. Mean values of discrete random variables.)

12. Differential equations – particular and general solutions, initial conditions. Differential equation of the first order. (Solow model)

13. Higher order differential equation with constant coefficients. Systems of differential equations of the first order. (Dynamic IS-LM model)

14. Difference equations. (A dynamic model of economic growth. An economic model of the web type.)

Course completion requirements
Last update: Cibulková Jana Ing. (19.12.2022)

Requirements for assessment: A combined result of three tests written during the semester of at least 50%, conditional on the teaching assistant agreement to grant credit on the basis of active participation during exercies sessions.

Exam requirements: The grade will be awarded based on the result of the written exam followed by an oral discussion.

 
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