MUC13 Mathematical Analysis 3

Faculty of Science
Autumn 2024
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
prof. RNDr. Zuzana Došlá, DSc. (lecturer)
Mgr. Petr Liška, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Zuzana Došlá, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 8:00–9:50 M1,01017
  • Timetable of Seminar Groups:
MUC13/01: Fri 10:00–11:50 M5,01013, P. Liška
MUC13/02: Wed 18:00–19:50 M5,01013, P. Liška
Prerequisites
KREDITY_MIN(30)
Mathematical Analysis 1 (MUC11), Mathematical Analysis 2 (MUC12)
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 aim of the course is to familiarize the student with the basic parts of differential calculus in more variables and with the elementary methods of solving the basic types of ordinary differential equations. After passing the course, the student will be able to solve extremal problems for functions in more variables and selected types of ordinary differential equations. The student will be able to understand and explain basic notions and techniques of the above-mentioned fields of mathematics including their mutual context.
Learning outcomes
After passing the course, the student will be able:
to understand the differential calculus of functions in more variables (the notation of function, limit, continuability, partial derivatives, local and global extremes);
to solve the basic ordinary differential equations of the first and second order.
Syllabus
  • Differential calculcus of functions of several variables: limits, continuity, partial derivatives, differential, Taylor theorem, local and absolute extrema of functions, implicit function.
  • Ordinary differential equations: elementary methods of solution of first order differential equations, higher order linear differential equations with constant coefficients.
Literature
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. Vyd. 2. přeprac. Brno: Masarykova univerzita, 1999, iv, 143. ISBN 8021020520. info
  • RÁB, Miloš. Metody řešení obyčejných diferenciálních rovnic. 3. vyd. Brno: Masarykova univerzita, 2004, ii, 96. ISBN 8021034165. info
  • Diferenciální počet. Edited by Vojtěch Jarník. Vyd. 3., dopl. Praha: Academia, 1976, 669 s. URL info
  • PLCH, Roman, Zuzana DOŠLÁ and Petr SOJKA. Matematická analýza s programem Maple. Díl 1, Diferenciální počet funkcí více proměnných. (The Multivariable Calculus with program Maple. Part 1, Differencial calculus). prvni. Brno: Masarykova Universita, 1999, 80 pp. ISBN 80-210-2203-5. URL info
Teaching methods
Standard lecture complemented with an excercise to teach students needed computationals skills.
Assessment methods
The course is closed by an exam with both written and oral parts.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2024/MUC13