Information package & Course catalogue

for academic year 2024/2025
University of West Bohemia

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Course: Selected Aspects of Mathematics Analysis

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Course title	Selected Aspects of Mathematics Analysis
Course code	KMT/VKMA
Organizational form of instruction	Lecture + Tutorial
Level of course	Bachelor
Year of study	2
Semester	Summer
Number of ECTS credits	6
Language of instruction	Czech
Status of course	Compulsory, Compulsory-optional
Form of instruction	Face-to-face
Work placements	This is not an internship
Recommended optional programme components	None

Lecturer(s)
Hora Jaroslav, Doc. RNDr. CSc. Königsmarková Soňa, Mgr. et Mgr. Ph.D.
Course content
Content: 1st ? 4th week: Revision ? elementary techniques for finding primitive function. 5th week: Riemann?s definition of definite integral. 6th ? 8th week: Application of definite integral in geometry. 9th week: Indefinite integral. 10th ? 13th week: Elemental types of first and second order differential equations.
Learning activities and teaching methods
Self-study of literature, Textual studies, Lecture, Practicum Contact hours - 78 hours per semester Preparation for an examination (30-60) - 60 hours per semester Preparation for formative assessments (2-20) - 30 hours per semester
prerequisite
Knowledge
Assumptions Elemental knowledge and usual working techniques on outcome levels of courses KMT/USMA1 and KMT/USMA2 are assumed. Students are able to apply basic knowledge of elementary functions of elementary proof of simple statements, handle simple calculations in the field of mathematical analysis.
learning outcomes
Elementary knowledge of theory and common computer techniques of subjects KMT/MMM2 and KMT/MSB.
rozlišit základní typy integrálů
rozlišit základní metody integrace
vysvětlit pojem určitý a neurčitý, vlastní a nevlastní integrál
popsat možnosti využití integrálů v geometrii a ve fyzice
rozlišit základní typy diferenciálních rovnic
popsat základní metody řešení diferenciálních rovnic
Skills
provést integraci "per partes"
provést integraci pomocí substituce
provést integraci racionálně lomené funkce
provést integraci funkce, již lze převést na integraci racionálně lomené funkce
provést integraci pomocí Eulerovy substituce
provést integraci pomocí goniometrických substitucí
vypočítat zadaný určitý integrál
využít výpočtu určitého integrálu pro řešení úlohy s geometrických obsahem
řešit diferenciální rovnice se separovanými proměnnými
řešit homogenní diferenciální rovnice
řešit Bernoulliho diferenciální rovnice
řešit lineární diferenciální rovnice 1. řádu
řešit jednodušší lineární diferenciální rovnice 2. řádu
teaching methods
Knowledge
Lecture
Practicum
Group discussion
One-to-One tutorial
Skills demonstration
Discussion
Seminar classes
Task-based study method
Skills
Lecture
Practicum
Collaborative instruction
One-to-One tutorial
Skills demonstration
Discussion
Seminar classes
Task-based study method
assessment methods
Knowledge
Oral exam
Written exam
Test
Self-evaluation
Skills demonstration during practicum
Skills
Oral exam
Written exam
Test
Self-evaluation
Skills demonstration during practicum
Recommended literature
Jarník, Vojtěch. Diferenciální rovnice v komplexním oboru. Praha : Academia, 1975. Matvejev, N. M. Zbierka príkladov z obyčajných diferenciálnych rovníc. 2. vyd. Bratislava : Alfa, 1964.

Study plans that include the course

Faculty	Study plan (Version)	Category of Branch/Specialization	Recommended year of study	Recommended semester
Faculty: Faculty of Education	Study plan (Version): Information Technologies in Education (19)	Category: Informatics courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Chemistry in Education (17)	Category: Chemistry courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Technology and Design in Education (17)	Category: Pedagogy, teacher training and social care	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Physics in Education (16)	Category: Physics courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Biology in Education (15)	Category: Biology courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Information Technologies in Education (15)	Category: Informatics courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Geography in Education (1)	Category: Pedagogy, teacher training and social care	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Studies in Mathematics (17)	Category: Mathematics courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Geography in Education (18)	Category: Pedagogy, teacher training and social care	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Studies in Mathematics (18)	Category: Mathematics courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Information Technologies in Education (17)	Category: Informatics courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Geography in Education (15)	Category: Pedagogy, teacher training and social care	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Physics in Education (15)	Category: Physics courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Physics in Education (17)	Category: Physics courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Biology in Education (18)	Category: Biology courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Physics in Education (19)	Category: Physics courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Physical Education in Education (19)	Category: Physical education and sport	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Studies in Mathematics (19)	Category: Mathematics courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Geography in Education (19)	Category: Pedagogy, teacher training and social care	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): English Language in Education (19)	Category: Pedagogy, teacher training and social care	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Biology in Education (17)	Category: Biology courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Geography in Education (17)	Category: Pedagogy, teacher training and social care	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Physical Education in Education (17)	Category: Physical education and sport	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Geography in Education (16)	Category: Pedagogy, teacher training and social care	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Technology and Design in Education (16)	Category: Pedagogy, teacher training and social care	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Chemistry in Education (14)	Category: Chemistry courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Chemistry in Education (19)	Category: Chemistry courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Information Technologies in Education (18)	Category: Informatics courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Biology in Education (16)	Category: Biology courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Chemistry in Education (18)	Category: Chemistry courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Technology and Design in Education (19)	Category: Pedagogy, teacher training and social care	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Technology and Design in Education (18)	Category: Pedagogy, teacher training and social care	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Biology in Education (19)	Category: Biology courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Physical Education in Education (18)	Category: Physical education and sport	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Music in Education (19)	Category: Art and applied art	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Chemistry in Education (16)	Category: Chemistry courses	3	Recommended year of study:3, Recommended semester: Summer
Faculty: Faculty of Education	Study plan (Version): Information Technologies in Education (16)	Category: Informatics courses	3	Recommended year of study:3, Recommended semester: Summer

University of West Bohemia, date of update: 27.07.2024 23:53. Data created for academic year 2024/2025