# Course syllabus E15-0104-I - Mathematics and Modeling (FEM - WS 2019/2020)

**Information sheet**Detailed content Timetable ECTS syllabus Slovak

**English**

University: | Slovak University of Agriculture in Nitra | ||||||||||||

Faculty: | Faculty of Economics and Management | ||||||||||||

Course unit code: | E15-0104-I | ||||||||||||

Course unit title: | Mathematics and Modeling | ||||||||||||

Planned types, learning activities and teaching methods: | |||||||||||||

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Credits: | 6 | ||||||||||||

Semester: | Internacional Economics and Development - master (elective), 1. semester International Economics and Development - master (elective), 1. semester International Economics and Development - master (elective), 1. semester International Economics and Development - master (elective), 1. semester | ||||||||||||

Level of study: | 2. | ||||||||||||

Prerequisites for registration: | none | ||||||||||||

Assesment methods : | |||||||||||||

- Partial written tests during the semester for 30 points, - Seminar project and individual project task via LMS Moodle (bonus) for 10 points, - The final exam test for 60 points. It is necessary to obtain (out of 100 points): - at least 93 points for the grade A, at least 86 points for the grade B, at least 79 points for the grade C, at least 72 points for the grade D and at least 64 points for the grade E. | |||||||||||||

Learning outcomes of the course unit: | |||||||||||||

Student will understand the theory of functions of several variables, indefinite and definite integral and differential equations, and use this theory and computational skills to solve mathematical and applied problems and problems in specialized fields. Via mathematical methods students should be able to create and interpret simple mathematical models.
Upon completion of the course, students should be able to: - find partial derivatives of functions of several variables - master differentiation techniques of various types of functions - understand the methods for solving indefinite and definite integrals - solve differential equations - give logical reasoning and interpretation of the obtained results | |||||||||||||

Course contents: | |||||||||||||

1. Introduction and review of the concept, geometric and physical meaning of the derivative, differentiation rules
2. Higher order derivatives, implicit and logarithmic differentiation 3. Applied problems on maxima and minima, optimization problems 4. Real function of n real variables, partial derivatives, total differential. Gradient of a function. 5. Relative and constrained extremes of functions of n variables, necessary and sufficient conditions for maxima and minima, the Hess determinant, applied economic and geometric problems 6. Indefinite integral, antiderivative, review of integration techniques, advanced integration techniques 7. Definite integral, applied economic and geometric problems, mean value theorem 8. Introduction to differential equations, classification of DE, solutions and integral curves, qualitative analysis of 1st order DE 9. Separable DE, explicit and implicit solutions, 10. Linear DE, method of variation of parameters, general and particular solutions 11. Mathematical modeling, meaning of modeling, simple mathematical models and their interpretation 12. Population and growth models 13. Logistic functions and models | |||||||||||||

Recommended or required reading: | |||||||||||||

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Language of instruction: | Slovak, English | ||||||||||||

Notes: | |||||||||||||

Evaluation of course unit: | |||||||||||||

Assessed students in total: 67
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Name of lecturer(s): | Mgr. Norbert Kecskés, PhD. (examiner, instructor, lecturer) doc. RNDr. Dana Országhová, CSc. (examiner, lecturer, person responsible for course) | ||||||||||||

Last modification: | 11. 3. 2019 | ||||||||||||

Supervisor: | doc. RNDr. Dana Országhová, CSc. and programme supervisor |

*Last modification made by Iveta Kunová on 03/11/2019.*