Mathematics in Economics
| Type of study | Follow-up Master |
|---|---|
| Language of instruction | English |
| Code | 151-0535/01 |
| Abbreviation | ME535 |
| Course title | Mathematics in Economics |
| Credits | 5 |
| Coordinating department | Department of Mathematical Methods in Economics |
| Course coordinator | doc. Ing. Petr Seďa, Ph.D. |
Subject syllabus
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.
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.
E-learning
The course is supported by on-line LMS (Learning Management System).
Literature
CHIANG, Alpha C. and Kevin WAINWRIGHT. Fundamental Methods of Mathematical Economics. McGraw-Hill/Irwin, 2013. ISBN 978-1259097348 .
MAVRON, Vassilis C. and Timothy N. PHILLIPS. Elements of Mathematics for Finance. Springer, 2023. ISBN 978-3-031-43909-4 .
PENA-LEVANO, Luis Moises. Schaum's Outline of Calculus for Business, Economics and Finance. McGraw-Hill, 2023. ISBN 978-1264266852 .
MAVRON, Vassilis C. and Timothy N. PHILLIPS. Elements of Mathematics for Finance. Springer, 2023. ISBN 978-3-031-43909-4 .
PENA-LEVANO, Luis Moises. Schaum's Outline of Calculus for Business, Economics and Finance. McGraw-Hill, 2023. ISBN 978-1264266852 .
Advised literature
PEMBERTON, Malcom and Nicholas RAU. Mathematics for economists: An introductory textbook. Manchester University Press, 2023. ISBN 978-1526173539 .
PENA-LEVANO, Luis Moises. Schaum's Outline of Mathematical Methods for Business, Economics and Finance. McGraw-Hill, 2021. ISBN 978-1264266876 .
SYDSAETER, Knut and Peter HAMMOND. Essential Mathematics for Economic Analysis. Prentice Hall, 2013. ISBN 978-0-273-76068-9 .
PENA-LEVANO, Luis Moises. Schaum's Outline of Mathematical Methods for Business, Economics and Finance. McGraw-Hill, 2021. ISBN 978-1264266876 .
SYDSAETER, Knut and Peter HAMMOND. Essential Mathematics for Economic Analysis. Prentice Hall, 2013. ISBN 978-0-273-76068-9 .