**GENERAL DESCRIPTION OF THE COURSE**

The student chooses eighter Mathematics B Linear Algebra of study program Civil engineering (16U008) or Mathematics B Linear Algebra And Financial Mathematics of study program Industrial engineering – Civil engineering (57U608).

Both courses include the main modul (of 30 hours of lectures and 20 hours of exercises) wich covers basics of Linear algebra. The student will acquire fundamental theoretical and practical knowledge of vectors (on the plane and in 3D-space), lines and planes in 3D, matrices and their interpretations and basics of linear transformations.

The second modul (of 15 hours of lectures and 10 hours of exercesises) is separated for students of different study programs. The modul of study program Civil engineering (16U008) contains more topics of Linear algebra, in particular matrices, linear transformations and applications of spectral theory.

The modul of study program Industrial engineering – Civil engineering (57U608) contains topics of Financial mathematics and their applications.

**COURSE CONTENTS**

The course will cover the following topics:

- linear algebra (16U008, 57U608): vectors on the plane and in 3D-space, products and their interpretation, lines and planes in 3D, rotations, projections, reflections (applications in physics and mechanics), matrices, their interpretations and special classes, determinants, sistems of linear equations, basics of linear transformations
- matrices and linear transformations (16U008): eigenvalues, eigenvectors, spectral theory and Jordan form, spectrums of special types of matrices, applications of spectral theory
- financial mathematics (57U608): compounding of interest, periodical cash flows, annuities and capitalization, value of money, applications of financial mathematics (credits, loans, mortgages,…)

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**STUDY MATERIALS:**

- Kreyszig: Advanced Engineering Mathematics, 10th edition, John Willey and Sons, New York 2011