Course unit code:
N427D0_4B
Course unit title:
Differential Equations
Mode of completion and Number of ECTS credits:
Exm (2 credits)
Course supervisor:
doc. RNDr. Vladimír Baláž, CSc.
Name of lecturer(s):
V. Baláž (2020/2021 – Winter)
V. Baláž (2019/2020 – Winter)
Ľ. Horanská (2015/2016 – Winter)
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.
Prerequisites for registration:
none
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

Recommended or required reading:
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.
Planned learning activities and teaching methods:
The object is realized in the form of lectures and exercises.
Assesment methods and criteria:
credit, examination
Language of instruction:
Slovak, English
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