MUC15 Mathematical Analysis 4

Faculty of Science
Spring 2025
Extent and Intensity
2/2/0. 4 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
prof. RNDr. Zuzana Došlá, DSc. (lecturer)
Mgr. Petr Liška, Ph.D. (seminar tutor)
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
Prerequisites
Mathematical analysis 1. Mathematical analysis 2. Mathematical analysis 3.
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 integral calculus in more variables and systems of differential equations and other topics which will be chosen by students (Fourier series, line integral, difference equations). After passing the course, the student will be able to solve selected types of integral calculus, systems of differential equations and other chosen topics.
Learning outcomes
After passing the course, the student will be able:
to know Riemann integral of functions in more variables;
to use effective techniques of integrating more variable functions;
to apply acquired pieces of knowledge for the solution of specific problems, mainly in geometry;
understand basic concepts connected to systems of differential equations;
use systems of differential equations to model real world phenomenons.
Syllabus
  • Integral calculus of the functions in more variables: measure in the plane and the space, double and triple integrals (Fubini theorem, transformations in polar and cylindric coordinates ), geometric application.
  • Autonomous systems in plane: nullclines, stationary points and their classification, applications.
Literature
    recommended literature
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Metrické prostory : teorie a příklady. 1. dotisk 2. přeprac. vyd. Brno: Masarykova univerzita, 2000, [iii], 83. ISBN 8021013281. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. Fourth edition. New York: Springer, 1993, 578 stran. ISBN 3540978941. info
Teaching methods
Lectures on the given themes.
Assessment methods
Written and oral examination. For admission to exam student need to submit three homeworks.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2025/MUC15