Linear and euclidean spaces: linear independence,
basis, linear mappings, nullspace and range, matrix
representation, transitional matrix, rank,
eigenvalues and eigenvectors, scalarproduct, norm,
orthogonality, Gram-Schmidt orthogonalisation,
orthogonal projection (vector of best
approximation), Fourier coefficients, least squares method, overdetermined systems, normal system,
regression line.
Numerical linear algebra: numerical computation
and errors, linear systems, matrix decompositions:
LU, QR, SVD.
Graph theory: matrix presentation, isomorphism,
path, cycle, walk, spanning tree, Hamiltonian and
Eulerian cycle, the shortest path problem, weighted
graph, algorithms of Kruskal and Dijkstra.
Ordinary differential equations: linear DE of order n,
LDE with constant coefficients, linear systems of DE
of first order, matrix solution of initial problem,
boundary value problem.
Basics on partial differential equations: equations of
mathematical physics, vibrating string, d'Alembert
solutions. learning outcomes: basic knowledge and understanding of linear
algebra and mathematical analysis
• mastering of basic computational skills
• the achieved mathematical knowledge is used
by the engineering courses
• mathematics is essential for technical studies
• ability of abstract formulation of practical
problems
• capability of critical judgement of data and
obtained numerical results
• capability of systematical, clear and precise
formulation of problems
• ability of reasoning from general to special and
vice versa
• skills in using literatur
