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FEKT-BPC-VMPAcad. year: 2025/2026
In the vector calculus section, the focus is on vector spaces, basic concepts, linear combinations of vectors, linear dependence, independence of vectors, bases, dimensions of vector space. The introduction of the scalar product allows to explain orthogonalization of vectors and to find the orthogonal projection of a vector onto a subspace and to apply this knowledge to the solution of overdetermined systems and the least squares method. In the matrix calculus section, students are introduced to matrix algebra, eigenvalues and eigenvectors are studied and their use to diagonalize matrices and calculate matrix functions and their application, focusing on the exponential of a matrix . The definiteness of matrices is also discussed. The numerical methods section discusses the solution of nonlinear equations and matrix systems of linear equations, approximation of functions by interpolating polynomial, spline and least squares methods, numerical derivation and integration.
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Entry knowledge
The student should be able to apply knowledge of vector calculus in a real-world domain and calculate in a complex domain at the high school level. Similarly, the student should be able to apply basic mathematical analysis at the high school level
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Fundamentals seminar
Computer-assisted exercise