Advanced Mathematics (ILV)

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Course numberM2.05280.11.931
Course code
Curriculum2016
Semester of degree program Semester 1
Mode of delivery Presencecourse
SPPW3,0
ECTS credits4,5
Language of instruction English

- Understand advanced methods of mathematics for mathematical modelling
- Able to solve such systems
- Able to analyze solutions, calculated with CAS Systems
- Apply advanced methods for modelling physical and technical systems
- Able to evaluate results of modelling
- apply the most common algorithms for solving ODE and systems of linear equations

Systems of Ordinary Differential Equations
- Fundamental matrix, functions exp(A), exp(tA)
- linear systems with variable and constant coefficiants
- non-linear systems, phase plane, phase plane ODE
- automomous systems and stability
Linear Algbra
- LU factorization
- orthonormal matrices, projections, least square method
- Factorization of squared matrices with full set of eigenvectors
- symmetric matrices, positive definite matrices
- similar matrices
- Singular Value Decomposition

E.Kreyszig, Advanced Enginnering Mathematics, Wiley&Sons, 2010
G.Strang, Introduction to Linear Algebra, Wellesley-Cambridge, Press, 2009
Won Y. Yang et al., Applied Numerical Methods Using MATLAB, Wiley, 2005
Uri M. Asher, Linda R.Petzold, Computer methods for Ordinary Differential Equations and Differential-Algebraic Equations, 1998