151-0337/01 – Mathematics D (Mat D)
| Gurantor department | Department of Mathematical Methods in Economics | Credits | 5 |
| Subject guarantor | doc. Mgr. Marian Genčev, Ph.D. | Subject version guarantor | doc. Mgr. Marian Genčev, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2004/2005 | Year of cancellation | 2009/2010 |
| Intended for the faculties | EKF | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
The aim of the subject Mathematics D is the systematic study and fixation of
immediate knowledges from the theory of real and complex sequences, from
the theory of real and functional infinite series and the basic algorithms for
finding the solution of difference equations.
The student get up to work with the concept (functional) sequence and can
apply it in the theory of infinite seires which offer an interesting apparatus for
further study of certain more sophisticated models in the reality. The
students learn also the method of mathematical induction and the algorithms
used by finding the solution of difference equations. The focal point of this
course will be the concept of the infinite series.
Teaching methods
Summary
The structure of the course Mathematics D developes the basic knowledge
acquired in the courses Mathmatics A and Mathematics B and extends in a
significant manner the theory of sequences in real and complex field, the
theory of real and functional infinite series and introduces the basic
algorithms for finding the solution of certain types of difference equations.
Hence, the subject's structure can afford good resources for further study of
qualitative and quantitative relationships in the economics and helps to
develope the logical thinking.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Diferenciální počet – funkce jedné proměnné, definiční obor, vlastnosti
funkcí, elementární funkce, limita funkce, derivace funkce, průběh funkce.
2. Integrální počet – neurčitý integrál, určitý integrál, nevlastní integrál.
3. Diferenciální rovnice – obyčejná diferenciální rovnice prvního řádu,
obyčejná diferenciální rovnice druhého řádu.
4. Diferenční rovnice – posloupnost, diference posloupnosti, diferenční
rovnice prvního řádu, diferenční rovnice vyšších řádů.
5. Posloupnosti a řady – posloupnost, řada čísel, konvergence řady, absolutní
konvergence řady, divergence řady, kritéria konvergence.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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