Differential and Difference Equations.
- Credits: 5
- Ending: Examination
- Range: 2P + 2C
- Semester: winter
- Year: 2
- Faculty of Economic Informatics
Teachers
Included in study programs
Teaching results
Knowledge. In the field of new knowledge, students will get acquainted with the multiply integral, differential and difference equations and their use in various areas of economics.
Students will understand and master not only the basic concepts, but also their properties.
Skills. In the educational process, students will acquire such theoretical and practical skills in the use and solution of differential and difference equations, which they can then use in other subjects and which will help them to solve various professional problems while studying at the University of Economics.
Competences. On the basis of completing the study of the subject, graduates are able not only to continue to actively expand their knowledge and skills, but also to acquire additional competencies in the use of differential and difference equations in various areas of economic theory and practice.
Indicative content
1. Repetition. Double integral, triple integral, multiply integral – definition and properties.
2. Calculation of multiply integral by using iterated integral.
3. Changes of variables – polar, cylindrical and spherical coordinates.
4. Applications of multiply integral. Area and volume.
5. Differential Equations. General, particular and singular solution of differential equation. Separable and homogeneous equations.
6. Linear differential equation of the first order.
7. Some nonlinear differential equation (DE) of first order.
8. Linear DE of higher order with constant coefficients. Wronskian.
9. Nonhomogeneous linear DE. Methods – variation of parameters, typical right sides.
10. Economic applications. Linear differential system. Characteristic equation.
11. Calculus of (finite) differences. First order difference. Differences of some functions. Differences of higher order.
12. Difference equations.
13. Linear difference equation of the first order. Linear system of difference equation.
Support literature
1. SAKÁLOVÁ, K. – STREŠŇÁKOVÁ, A: 2011. Množný integrál a diferenciálne rovnice. Bratislava : Ekonóm EUBA, 2011. 171. ISBN 978-80-225-3189-4.
2. PELLER. F. – PINDA, Ľ. – FECENKO, Ľ.: 2001. Matematika 3. Bratislava : IURA Edition Bratislava, 2001. ISBN 80-88715-97-0.
Syllabus
1. Repetition. Double integral, triple integral, multiply integral – definition and properties. 2. Calculation of multiply integral by using iterated integral. 3. Changes of variables – polar, cylindrical and spherical coordinates. 4. Applications of multiply integral. Area and volume. 5. Differential Equations. General, particular and singular solution of differential equation. Separable and homogeneous equations. 6. Linear differential equation of the first order. 7. Some nonlinear differential equation (DE) of first order. 8. Linear DE of higher order with constant coefficients. Wronskian. 9. Nonhomogeneous linear DE. Methods – variation of parameters, typical right sides. 10. Economic applications. Linear differential system. Characteristic equation. 11. Calculus of (finite) differences. First order difference. Differences of some functions. Differences of higher order. 12. Difference equations. 13. Linear difference equation of the first order. Linear system of difference equation.
Requirements to complete the course
The semester work and the written test – 30 %
The final written test – 70 %
Student workload
Total study load (in hours): 156 hours
26 hours participation in lectures
26 hours participation in exercises
13 hours preparing for exercises
13 hours preparation for course credit
52 hours individual study in preparation for the exam
Language whose command is required to complete the course
slovak
Date of approval: 10.02.2023
Date of the latest change: 15.05.2022