Students can apply basic skills in the area of differential and integral calculus of single and multi-digit functions and implement their basic understanding of the role of linear algebra in mathematics and applications.

• Knowing and understanding the concept of the Riemann integral
• Understanding the most important methods of determining indefinite and definite integrals, also in higher dimensions
• Knowing the calculation and understanding the meaning of partial derivatives of multivariate real functions (k1,k2)
• Ability to solve systems of linear equations efficiently (k3)
• Understanding the concept of linear space and linear mappings (k2,k4)
• Understanding of the meaning of matrices and applying matrix methods to corresponding problems (k2,k3)
• Describing the effect of a linear map using eigenspaces and eigenvalues (k1,k2,k4)

• Riemann integral, substitution method, partial integration, improper integrals
• Fubini's theorem
• Functions of several real variables and their partial derivatives
• Determination of extreme values of multivariate real functions
• Gaussian elimination method for solving linear systems of equations
• R^n as a linear space, linear space in general
• Matrices for the representation of linear maps
• Linear maps between matrices as well as their products and inverses
• Eigenspace decomposition of linear maps