M1100F Mathematical Analysis I

Faculty of Science
Autumn 2019
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)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
Mgr. Marianna Kustyánová (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
Tue 14:00–15:50 A,01026, Wed 18:00–19:50 A,01026
  • Timetable of Seminar Groups:
M1100F/01: Thu 13:00–14:50 F2 6/2012, P. Musilová
M1100F/02: Thu 9:00–10:50 F4,03017, P. Musilová
Prerequisites
!OBOR(AMV) && !OBOR(FINPOJ) && !OBOR(UM) && !OBOR(OM) && !OBOR(STAT)
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 and of the theory and applications of differential equations. 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. Further, the students will be familiar with basic differential equations and the methods of their solution.
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;
understand the problematics of elementary differential equations.
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).
  • Elementary methods of solution of ordinary differential equations: existence and uniqueness, equations of first order (separable equations, linear equations, integrating factors), higher order equations with constant coefficients, systems of linear equations with constant coefficients.
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
  • RÁB, Miloš. Metody řešení diferenciálních rovnic. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1989, 68 s. info
    not specified
  • 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
  • HASIL, Petr a Petr ZEMÁNEK. Sbírka řešených příkladů z matematické analýzy II. https://goo.gl/hSLUV2
  • NOVÁK, Vítězslav. Integrální počet funkcí jedné proměnné. 1. vyd. Brno: Rektorát UJEP Brno, 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
  • DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 8072005871. 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
  • An introduction to ordinary differential equations. Edited by James C. Robinson. New York: Cambridge University Press, 2004, xiv, 399 p. ISBN 0521533910. info
Teaching methods
Standard theoretical lectures with excercises.
Assessment methods
Lectures: 4 hours/week. Seminars (compulsory): 2 hours/week.
3 written intrasemestral tests in seminars (10% of the overall evaluations).
Final exam: Written test (55%) and oral exam (35%).
To pass: at least 5 of 10 points from intrasemestral tests, then 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 2018, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2019, recent)
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