FC1824 Applied Mathematics - Seminar

Faculty of Education
Spring 2024
Extent and Intensity
0/0/2. 3 credit(s). Type of Completion: k (colloquium).
Teacher(s)
Mgr. Ivana Medková, Ph.D. (lecturer)
Guaranteed by
Mgr. Ivana Medková, Ph.D.
Department of Physics, Chemistry and Vocational Education – Faculty of Education
Contact Person: Jana Jachymiáková
Supplier department: Faculty of Education
Prerequisites (in Czech)
FC1022 Applied Mathematics 1
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
Course objectives
The aim of the subject is to expand knowledge of higher mathematics and practice it on practical tasks. Emphasis is placed on the logical structure of this scientific discipline and on deepening the mathematical knowledge and skills needed to master the physics course at university.
Learning outcomes
By completing the course, the student will repeat and deepen the knowledge and skills acquired in the course Applied Mathematics II, namely: Knowledge: Comprehensive overview of knowledge on the topics of differential and integral calculus of functions of multiple variables, differential equations, basics of vector analysis, orthogonal systems, Fourier series. Skills: Be able to use basic definitions and sentences when solving simple and application problems. To understand the connection of the material being discussed with practical physical applications. Be able to perform a qualified estimation of values. Attitudes: Acquire the values of objectivity and the importance of scientific work. ​
Syllabus
  • I. Functions of several variables. • 1. Delineation of the definition field and graphs of functions of two independent variables, calculation of limits. • II.Differential calculus of functions of several variables. 1. Partial derivative of a complex function, partial derivative of the second order, total differential. • III. Integral caculus of functions of several variables. 1. Calculation of double integrals and their applications. 2. Calculation of triple integrals and their applications.• 3. Curve and surface integrals I. and II. kinds. II. Differential equation. • 1. Linear differential equations of the 1st order, their calculations. 2. Linear differential equations of the 2nd order, their calculations. Selected partial differential equations. • III. Basics of vector analysis. • 1. Rotation and divergence operators. 2. Flow of a vector field through a closed surface. 3. Potential vector field. IV. Orthogonal systems, Fourier series. 1. Basic concepts and definitions. 2. Examples of the development of functions in Fourier series.
Literature
    required literature
  • SLÁDEK, Petr and Václav VACEK. Matematika pro fyziky I a II. Elportál. Brno: Masarykova univerzita, 2009. ISSN 1802-128X. URL info
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. 1. dotisk 3. vyd. Brno: Masarykova univerzita, 2010, 144 pp. ISBN 978-80-210-4159-2. info
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných. 1. vyd. Brno: Masarykova univerzita, 2009, vi, 272. ISBN 9788021049758. info
    recommended literature
  • NOVÁK, Vítězslav. Diferenciální počet funkcí více proměnných. Vyd. 1. Brno: Rektorát UJEP, 1983, 159 s. info
  • HÁJEK, Jiří. Cvičení z matematické analýzy : diferenciální počet funkcí více proměnných. 2. vyd. Brno: Masarykova univerzita, 2000, 111 s. ISBN 8021024534. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. info
  • DULA, Jiří and Jiří HÁJEK. Cvičení z matematické analýzy : obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 1998, 74 s. ISBN 8021019751. info
  • JIRÁSEK, František, Eduard KRIEGELSTEIN and Zdeněk TICHÝ. Sbírka řešených příkladů z matematiky. 2. nezměn. vyd. Praha: SNTL - Nakladatelství technické literatury, 1981, 817 s. URL info
  • JIRÁSEK, František, Stanislav ČIPERA and Milan VACEK. Sbírka řešených příkladů z matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1989, 565 s. info
Teaching methods
exercises
Assessment methods
completing online worksheet
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
Information on the extent and intensity of the course: 8 hodin.
The course is also listed under the following terms Spring 2025.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/ped/spring2024/FC1824