M1101 Mathematical Analysis I

Faculty of Science
Autumn 2015
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. Mgr. Petr Hasil, Ph.D. (lecturer)
doc. Mgr. Petr Zemánek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 10:00–11:50 M2,01021, Wed 12:00–13:50 M1,01017
  • Timetable of Seminar Groups:
M1101/01: Wed 10:00–11:50 M2,01021, P. Hasil
M1101/02: Thu 10:00–11:50 M4,01024, P. Zemánek
Prerequisites (in Czech)
!OBOR(OM) && !OBOR(STAT) && !OBOR(UM) && !OBOR(FYZ)
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. Attention is paid to the fact that students come from 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.
  • Functions and sequences: Sequences of real numbers, limit and continuity of functions, properties of continuous functions.
  • Differential calculus in one variable: Basic rules of derivative and its properties, geometric interpretation, Taylor formula, behaviour of functions, planar curves.
  • Integral calculus in one variable: Primitive function and its properties, basic methods of integration, special methods of integrations (integrals of goniometric, irrational, and other types of elementary functions).
  • Riemann integral and its properties: Construction of Riemann integral and its calculation (Newton-Leibniz formula), applications of integrals (area of planar objects, length of curves, volume and surface of solids of revolution), Newton integral.
Literature
  • DOŠLÁ, Zuzana and Jaromír KUBEN. Diferenciální počet funkcí jedné proměnné (Differential Calculus of Functions of One Variable). 2. dotisk 1. vyd. Brno: Masarykova univerzita, 2008, 215 pp. ISBN 978-80-210-3121-0. info
  • DOŠLÝ, Ondřej and Petr ZEMÁNEK. Integrální počet v R (Integral Calculus in R). 1. vydání. Brno: Masarykova univerzita, 2011, 222 pp. ISBN 978-80-210-5635-0. info
  • NOVÁK, Vítězslav. Integrální počet funkcí jedné proměnné. Vyd. 1. Brno: Rektorát UJEP, 1980, 89 s. 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
  • ZEMÁNEK, Petr and Petr HASIL. Sbírka řešených příkladů z matematické analýzy I. 3., aktual. vyd. Brno: Masarykova univerzita, 2012. Elportál. ISBN 978-80-210-5882-8. url PURL info
Teaching methods
Standard theoretical lecture with excercise.
Assessment methods
Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week.
3 written intrasemestral tests in seminars (30% of the overall evaluations).
Final exam: Written test (40%) and oral exam (30%).
To pass: 10% of each of the three parts described above and 45% in total.
Results of the intrasemestral tests are included in the overall evaluation. All percentages are given relative to the overall total for the whole semester.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2010 - only for the accreditation, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2016, autumn 2017, Autumn 2018.
  • Enrolment Statistics (Autumn 2015, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2015/M1101