151-0401/03 – Mathematics B (MBKS)
| Gurantor department | Department of Mathematical Methods in Economics | Credits | 4 |
| Subject guarantor | doc. Mgr. Marian Genčev, Ph.D. | Subject version guarantor | RNDr. Simona Pulcerová, Ph.D., MBA |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2006/2007 | Year of cancellation | 2009/2010 |
| Intended for the faculties | EKF | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
The students will be able to master the basic techniques specified by the three main topics (see below, items 1-3). Also, they will be able to freely, but logically correct, discuss selected theoretical units that will allow talented individuals to excel. The student will also have an overview of basic application possibilities of the discussed apparatus in the field of economics.
(1) The student will be introduced to the basics of linear algebra and its application possibilities in economics.
(2) The student will be able to apply the basic rules and formulas for the calculation of integrals, use them to calculate the area of planar regions, and for calculating of improper integrals and integrals of discontinuous functions. The student will be able to discuss the relating application possibilities in economics.
(3) The student will be able to find local extrema of functions of two variables without/with constraints, level curves and total differential, will be able to decide whether the given function is homogeneous. The student will be able to discuss the relating application possibilities and to mention appropriate generalizations for functions of 'n' real variables.
Teaching methods
Lectures
Individual consultations
Tutorials
Practical training
Summary
The course is focused on the practical mastery of selected mathematical methods in the field of linear algebra and calculus, which form the basis for further quantitative considerations in related subjects. The student will also be acquainted with the derivation of basic theoretical findings. This enables the development of logical skills, which form the basis for analytical and critical thinking. For better motivation of students, the presentation in lectures is always connected with appropriate economic problems.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Studenti mají ke každému učivu test, mohou si tak sami ověřit, zda probranému učivu porozuměli či nikoliv. Také mají vzor závěrečné písemné zkoušky, kde si mohou opět vyzkoušet, zda by u zkoušky uspěli či nikoliv.
E-learning
Other requirements
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Témata výkladu zpracovaných v podobě multimediálních studijních opor:
1. Neurčitý integrál – definice a vlastnosti, základní vzorce, pravidla
integrování, metody integrace: substituční metoda, metoda per partes,
integrace racionální lomené funkce, rozklad na parciální zlomky, integrace
některých iracionálních funkcí, integrace některých goniometrických funkcí.
2. Určitý integrál – motivace a jeho zavedení, definice a vlastnosti, Newton-
Leibnizova formule, obsah rovinného obrazce, nevlastní integrál.
3. Funkce dvou proměnných – úvod a základní pojmy, definiční obor, obor
hodnot, graf, parciální derivace prvního řádu, parciální derivace vyšších
řádů, extrémy funkce dvou proměnných: lokální extrémy, vázané extrémy.
4. Obyčejné diferenciální rovnice 1. řádu – úvod a základní pojmy, obecné
řešení, partikulární řešení, separovatelná diferenciální rovnice, homogenní
diferenciální rovnice, lineární diferenciální rovnice homogenní a nehomogenní
(metoda variace konstanty).
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction