# Institute of Information Engineering, Automation, and Mathematics

Course unit code:
N427S2_4B
Course unit title:
Seminar of Mathematics II
Mode of delivery, planned learning activities and teaching methods:
seminar – 2 hours weekly (on-site method)
Credits allocated:
2
Recommended semester:
Biotechnológia – bachelor (full-time, attendance method), 2. semester
Chemical Engineering – bachelor (full-time, attendance method), 2. semester
Chemistry, Medical Chemistry and Chemical Materials – bachelor (full-time, attendance method), 2. semester
Potraviny, výživa, kozmetika – bachelor (full-time, attendance method), 2. semester
Process Control – bachelor (full-time, attendance method), 2. semester
Level of study:
1.
Prerequisites for registration:
none
Assesment methods:
Attendance at all exercises, preparation of interim tasks, final quiz.
Learning outcomes of the course unit:
The seminar is intended to deepen and thoroughly practice the knowledge acquired in the course Mathematics II. After completing the course, the student is better able to solve examples from the topics of differential and integral calculus of functions of several variables, differential equations, line integral theory and can apply calculation methods in chemistry and physics, can use the appropriate mathematical apparatus to solve problems.
Course contents:

The basics of differential and integral calculus of real-valued functions of several real variables, especially of real-valued functions of two real variables. Applications of local extrema in examples from the fields of chemistry and physics. Ordinary differential equations. First- and second-order linear differential equations with constant coefficients and their applications in physics and chemistry. Double integrals. Vector fields, line integrals of vector fields. Applications.

1. a) The basics of differential and integral calculus of real functions of several variables, especially of real functions of two variables (allocated 0/4)
b) Applications of local extrema in examples from the fields of chemistry and physics. (allocated 0/2)
c) Gradient, linearization, tangent plane. (allocated 0/2)

2. a) Ordinary differential equations. First- and second-order linear differential equations with constant coefficients. (allocated 0/6)
b) Applications of differential equations in physics and chemistry. (allocated 0/2)

3. Double integrals and their applications. (allocated 0/4)

4. a) Vector fields, line integrals of vector fields. (allocated 0/2)
b) Calculation methods of line integrals. (allocated 0/2)

Recommended:
• KRAJŇÁKOVÁ, D. Matematika: Zbierka úloh z matematiky. Bratislava : Alfa, 1986. 222 s.
• JASEM, M. KOLESÁROVÁ, A. Matematika II, Zbierka úloh. Bratislava: Nakladateľstvo STU, 2012. 172 s. ISBN 978 80 227 3663 3. [podrobnosti]
• KOLESÁROVÁ, A. BALÁŽ, V. Matematika II. Bratislava: Slovenská technická univerzita v Bratislave, 2011. 261 s. ISBN 978 80 227 3493 6. [podrobnosti]
Language of instruction:
Slovak, English
Assessed students in total:
780

### FX 1.0 %

Name of lecturer(s):
V. Baláž, Ľ. Horanská, M. Jasem, A. Maťašovský, S. Pavlíková, T. Visnyai (2021/2022 – Winter)
V. Baláž, M. Jasem, M. Langerová, S. Pavlíková, T. Visnyai (2020/2021 – Winter)
Ľ. Horanská, M. Jasem, N. Krivoňáková, P. Viceník, T. Visnyai (2019/2020 – Winter)
Š. Boor, Ľ. Horanská, N. Krivoňáková, P. Viceník, T. Visnyai (2018/2019 – Winter)
Š. Boor, M. Gall, Ľ. Horanská, M. Jasem, A. Maťašovský, S. Pavlíková, P. Viceník, T. Visnyai (2017/2018 – Winter)
V. Baláž, Š. Boor, Ľ. Horanská, M. Jasem, A. Maťašovský, S. Pavlíková, P. Viceník, T. Visnyai (2016/2017 – Winter)
Course supervisor:
PaedDr. Tomáš Visnyai, PhD.
Last modification:
15. 7. 2021

Department:
Department of Mathematics