M2222 Fundamentals of Mathematical Analysis

Faculty of Science
Spring 2023
Extent and Intensity
4/2/0. 6 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Mgr. Jiřina Šišoláková, Ph.D. (seminar tutor)
Guaranteed by
doc. Mgr. Petr Hasil, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 14:00–15:50 MS1,01016, Fri 14:00–15:50 M6,01011
  • Timetable of Seminar Groups:
M2222/01: Fri 16:00–17:50 M6,01011, J. Šišoláková
Prerequisites
! M1100 Mathematical Analysis I && ! M1101 Mathematical Analysis I
High school mathematics
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
This is a basic course of mathematical analysis, where the content is differential and integral calculus and infinite series. Students will understand practical methods and will be able to apply these methods to concrete problems. The course places more emphasis on examples.
Learning outcomes
At the end of the course, students will be able to:
work practically with the derivative and (indefinite and definite) integral;
analyse the behaviour of functions;
understand the use of infinite number series and power series;
understand selected applications of the calculus;
apply the methods of the calculus to concrete problems.
Syllabus
  • Continuous functions and limits
  • Derivatives of functions with applications
  • Indefinite integrals
  • Riemann integral and its applications
  • Series
Literature
    recommended literature
  • HASIL, Petr, Kamila HASILOVÁ and Jiřina ŠIŠOLÁKOVÁ. Sbírka příkladů o nekonečných řadách. Online. 1. vyd. Brno: Masarykova univerzita, 2020. Elportál. ISBN 978-80-280-0006-6. [citováno 2024-04-23] url html PURL info
  • HASIL, Petr and Petr ZEMÁNEK. Sbírka řešených příkladů z matematické analýzy II (Collection of Solved Problems in Mathematical Analysis II). Online. Masarykova univerzita, 2016, [citováno 2024-04-23] URL info
  • ZEMÁNEK, Petr and Petr HASIL. Sbírka řešených příkladů z matematické analýzy I. Online. 3., aktual. vyd. Brno: Masarykova univerzita, 2012. Elportál. ISBN 978-80-210-5882-8. [citováno 2024-04-23] url PURL info
    not specified
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Online. 3. vyd. Brno: Masarykova univerzita, 2013. iv, 113. ISBN 9788021064164. [citováno 2024-04-23] info
  • DOŠLÁ, Zuzana and Jaromír KUBEN. Diferenciální počet funkcí jedné proměnné (Differential Calculus of Functions of One Variable). Online. 2. vyd. Brno: Masarykova univerzita, 2012. vi, 209. ISBN 9788021058149. [citováno 2024-04-23] info
  • DOŠLÝ, Ondřej and Petr ZEMÁNEK. Integrální počet v R (Integral Calculus in R). Online. 1. vydání. Brno: Masarykova univerzita, 2011. 222 pp. ISBN 978-80-210-5635-0. [citováno 2024-04-23] info
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. Online. 1. dotisk 3. vyd. Brno: Masarykova univerzita, 2010. 144 pp. ISBN 978-80-210-4159-2. [citováno 2024-04-23] info
Teaching methods
There are lectures and tutorials
Assessment methods
Four hours of lectures and two hours of seminars. The final exam is written for max 40 points. For successfull examination (the grade at least E), the student needs in total 20 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Spring 2021, Spring 2025.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2023/M2222