Economic-mathematical Methods

Garant předmětu:

David Vrba

Lecturer:

Vladimír Rogalewicz, David Vrba

Tutor:

Matouš Brunát, Hana Děcká, David Vrba

Supervisor:

Department of Biomedical Technology

Synopsis:

Selected topics in mathematics to support economic courses

Requirements:

Requirements of the graded assessment:

There will be three partial writen tests during the semester.

It is required that the student gets at lest 50% of points in each test.

It is required that the student has at least 50% of points in the sum of all three partial tests.

The final grade is given according to the study regulation in force.

Syllabus of lectures:

1. Interests and discounting

Simple interest, discounting, compound interest, mixed interest calculation, continuous interest calculation

2. Time value of money

Present value, IIR, present and final value of a rent, debt amortization, calculation of „RPSN“

3. Mathematical solution of the optimizing problem I

Local extremes of functions of one variable, solution using derivatives. Local extremes of functions of two variables.

4. Mathematical solution of the optimizing problem II

Functions of three and more variables. Finding the local extremes of a function subject to equality constraints. Lagrange multipliers.

5. Regression analysis – linear and non-linear regression

Point and interval estimation of regression coefficients, confidence belt. General regression function. Linearization. Correlation coefficient, coefficient of determination. Interpretation. Predictive value of the regression function.

6. Introduction into differential equations

Differential equations as a dynamic model. Solving ordinary differential equations.

Syllabus of tutorials:

1. Interests and discounting

Simple interest, discounting, compound interest, mixed interest calculation, continuous interest calculation

2. Time value of money

Present value, IIR, present and final value of a rent, debt amortization, calculation of „RPSN“

3. Mathematical solution of the optimizing problem I

Local extremes of functions of one variable, solution using derivatives. Local extremes of functions of two variables.

4. Mathematical solution of the optimizing problem II

Functions of three and more variables. Finding the local extremes of a function subject to equality constraints. Lagrange multipliers.

5. Regression analysis – linear and non-linear regression

Point and interval estimation of regression coefficients, confidence belt. General regression function. Linearization. Correlation coefficient, coefficient of determination. Interpretation. Predictive value of the regression function.

6. Introduction into differential equations

Differential equations as a dynamic model. Solving ordinary differential equations.

Study Objective:

Study materials:

Required:

[1].CHIANG, Alpha C. Fundamental methods of mathematical economics. 3rd ed. New York: McGraw-Hill, 1984. ISBN 0-07-010813-7

[2].GILLMAN, Leonard. a Robert H. MCDOWELL. Calculus. [1st ed.]. New York: Norton, 1973. ISBN 9780393093506

[3].CHATFIELD, Christopher. Statistics for technology: a course in applied statistics. 3rd ed. New York: Chapman and Hall, 1983. ISBN 0412253402

Recommended:

Wikipedia

Wolfram MathWorld at http://mathworld.wolfram.com/?source=wordcloud

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Systematic Integration ofPprocesses in Healthcare - combined study (compulsory course)