# Institute of Information Engineering, Automation, and Mathematics

Course unit code:
N427D0_4B
Course unit title:
Differential Equations
Mode of delivery, planned learning activities and teaching methods:
lecture – 1 hour weekly (on-site method)
laboratory practice – 1 hour weekly (on-site method)
Credits allocated:
2
Recommended semester:
Chemistry, Medical Chemistry and Chemical Materials – bachelor (full-time, attendance method), 5. semester
Level of study:
1.
Prerequisites for registration:
none
Assesment methods:
test
Learning outcomes of the course unit:
Acquire the theoretical foundations of differential equations, ordinary and partial differential equations and numerical solutions of differential equtions using computer.
Course contents:
1. Selected topics from algebra and mathematical analysis (allowance 1/1)

 a. Determinants, eigenvalues ​​and engenvectors of matrices b. Sequences and infinite series of functions

2. Linear differential equations of any order (allowance 4/4)

 a. Basic properties of solutions of linear differential equations of the n-th order with constant coefficients b. Solution of homogeneous and non-homogeneous linear differential equations of the n-th order with constant coefficients

3. Systems of differential equations (allowance 4/4)

 a. The system of linear differential equations of the first order with constant coefficients- the basic properties b. Homogeneous and non-homogeneous system of linear differential equations of the first order with constant coefficients

4. Partial differential equations (allowance 3/3)

 a. Linear partial differential equations of the second order b. Some methods for solving of linear partial differential equations of the second order c. Heat equation

5. Numerical solution of differential equtions (allowance 1/1)

 a. Euler method, Runge-Kutta method of solving of differential equation b. Numerical solving of diffential system

Basic:
• KOLESÁROVÁ, A. – BALÁŽ, V. Matematika II. Bratislava: Slovenská technická univerzita v Bratislave, 2011. 261 s. ISBN 978-80-227-3493-6.
• KREYSZIG, E. Advanced Engineering Mathematics 7th Edition. Toronto: John Wiley & Sons, Inc., 1993.
Recommended:
• Borelli, R.– Coleman, C. Differential equations, A Modeling Perspective. New York, Toronto: John Wiley & sons, 2004. 453 s. ISBN 0-471-43332-2.
Language of instruction:
Slovak, English
Assessed students in total:
4

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Name of lecturer(s):
V. Baláž (2020/2021 – Winter)
V. Baláž (2019/2020 – Winter)
Ľ. Horanská (2015/2016 – Winter)
Course supervisor: