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

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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:
lecture2 hours weekly / 26 hours per semester of study (on-site method)
seminar2 hours weekly / 26 hours per semester of study (on-site method)

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:
1. Carl P. Simon and Lawrence Blume (1994). Mathematics for Economists. W. W. Norton & Company, Inc. New York.
2. Ayres, F. – Mendelson, E.: Calculus. Schaum’s Outlines, McGraw Hill, 2002, ISBN 978-0-07-150861-2.
3. Bronson, R: Differential Equations. Schaum’s Outlines, McGraw Hill 1994, ISBN 0-07-008019-4

Language of instruction: Slovak, English
Evaluation of course unit:
Assessed students in total: 67

17,9 %9,0 %23,9 %25,4 %20,9 %2,9 %
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.

Type of output: