M1101 Mathematical Analysis I

Faculty of Science
Autumn 2018
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. Jan Jekl, Ph.D. (assistant)
Guaranteed by
prof. 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 17. 9. to Fri 14. 12. Mon 10:00–11:50 M1,01017, Tue 10:00–11:50 M1,01017
  • Timetable of Seminar Groups:
M1101/01: Mon 17. 9. to Fri 14. 12. Mon 16:00–17:50 M1,01017, J. Jekl
M1101/02: Mon 17. 9. to Fri 14. 12. Mon 18:00–19:50 M5,01013, J. Jekl
Prerequisites
!OBOR(OM) && !OBOR(STAT) && !OBOR(UM) && !OBOR(FYZ) && !OBOR(NAN) && !OBOR(ASTR)
High school mathematics
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 of differential and integral calculus of functions of one variable and will able to apply these methods to concrete problems.
Learning outcomes
At the end of the course students will be able to:
define and interpret the basic notions from the calculus of functions of one real variable;
formulate relevant mathematical theorems and to explain methods of their proofs;
analyse problems from the topics of the course;
understand to theoretical and practical methods of calculus of functions of one variable;
apply the methods of calculus to concrete 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).
Literature
    recommended 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
    not specified
  • 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
  • ADAMS, R. A. and Christopher ESSEX. Calculus : a complete course. 7th ed. Toronto: Pearson, 2010, xvi, 973. ISBN 9780321549280. info
  • BRAND, Louis. Advanced calculus : an introduction to classical analysis. New York: John Wiley & Sons, 1955, x, 574. info
  • DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 8072005871. info
Teaching methods
Standard theoretical lectures with excercises.
Assessment methods
Two-hour written test and oral examination. The results of exercises (seminars) are partially transferred to the final grade.
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 2015, Autumn 2016, autumn 2017.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2018/M1101