M1100 Mathematical Analysis I

Faculty of Science
Autumn 2010 - only for the accreditation
Extent and Intensity
4/2/0. 6 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
Mgr. Michael Krbek, Ph.D. (seminar tutor)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
doc. RNDr. Michal Veselý, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
! M1101 Mathematical Analysis I && !NOW( M1101 Mathematical Analysis I )
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The first course of the mathematical analysis. The content is the differential and integral calculus of functions of one real variable. An attention is paid to the fact that students come from the middle schools with various level of mathematical knowledge. Students will understand theoretical and practical methods from differential and integral calculus of functions of one variable and apply these methods to practical problems.
Syllabus
  • Introduction: real numbers and their basic properties, general properties of real functions, elementary functions, axioms of real numbers and their properties.
  • Limits and continuity.
  • Derivative and its properties, applications, planar curves.
  • Integral calculus in one variable (primitive function, integration of some elementary functions)
  • Riemann integral and its properties, applications.
Literature
  • DOŠLÁ, Zuzana and Jaromír KUBEN. Diferenciální počet funkcí jedné proměnné (Differential Calculus of Functions of One Variable). Brno: Masarykova Univerzita v Brně, 2003, 215 pp. skriptum. ISBN 80-210-3121-2. info
  • NOVÁK, Vítězslav. Integrální počet funkcí jedné proměnné. Vyd. 1. Brno: Rektorát UJEP, 1980, 89 s. info
  • DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 8072005871. info
  • BABULA, Kamil. Protipříklady v matematické analýze (Counterexamples in calculus). Brno: Masarykova univerzita, 2008, 44 pp. Bakalářská práce. info
  • NOVÁK, Vítězslav. Diferenciální počet v R (Differential number in R). Brno: Masarykova univerzita Brno, 1997, 250 pp. ISBN 80-210-1561-6. info
  • Diferenciální počet. Edited by Vojtěch Jarník. Vyd. 6. nezměn. Praha: Academia, 1974, 391 s. URL info
  • Integrální počet. Edited by Vojtěch Jarník. Vyd. 5. nezměn. Praha: Academia, 1974, 243 s. URL info
Teaching methods
Lectures about the theory with illustrative solved problems. Seminar group devoted to solving theoretical and practical numerical problems.
Assessment methods
Two-hour written test and oral examination. The results of exercises (seminars) are partially transfered to the final grade.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.