## MATHEMATICS II - ALgebra

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### Information for students of Civil Engineering and Environmental Engineering

Course Content

- Groups and fields
- The field of complex numbers
- Vector spaces
- Basis and dimension of a vector space
- Matrices. Operations on matrices
- Linear transformations
- Determinants and their properties
- Rank of a matrix. Systems of linear equations
- Eigenvalues and eigenvectors of linear transformations
- Diagonal matrices
- The scalar, vector and triple scalar product of vectors
- Planes and lines in space
- Surfaces in space
- Parametric equations of space curves
- The Frenet trihedron
- Curvature and torsion of a space curve
- Tangent plane and normal line to a surface

Results of the first final exam.

Solutions to problems from the final exam.

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