The students know basics of linear algebra, basics of the theory of ordinary differential equations (ODE) and systems of ODE and basics  of theory of functions of several variables and vector analysis.
They are able to solve systems of linear equations, to compute determinants, inverse matrices, eigenvalues and eigenvectors and to solve fitting problems using linear algebra.
They are able to solve linear ODE of 1st and 2nd order and apply them to electrical and mechanical engineering (RLC-circuit, harmonic oscillator, spring-mass-systems) and to calculate partial derivatives, directional derivatives, to find max , min and saddle points of functions, and to find the derivatives for scalar and vector fields.

Engineering mathematics 1

Linear algebra (matrices, systems of linear equations, rank, determinants, eigenvalue und eigenvectors, orthonormal matrices, least square methods, hermitic and unitary matrices).
ODE 1. and 2. order (linear, homogen und non-homogeneous), systems of linear ODE.
Basics of the theory of functions of several (real) variables and vector analysis
 - basics, partial derivative, total differential, tangent plane, directional derivative, extrema, applications
 - scalar-, vector fields, gradient, divergence, curl, del operator

Meyberg, K., Vachenauer, P., Höhere Mathematik 1 und 2, 5. Auflage, Springer, 1999
Papula, L., Mathematik für Ingenieure und Naturwissenschaftler, Band1 und 2, 9. Auflage, Vieweg, 2000

Integrated lessons (ILV), lessons, exercises, projects, use of CAS systems

Final and midterm exam