You know complex numbers and their arithmetic operations in their various representations and you are able to use them among other things for the description of alternating electrical currents.
You are familiar with geometric calculus. You are able to compute norm, inner products, orthogonal projection, and cross product of vectors and use vectors to describe geometric objects.
You are able to recognize systems of linear equations and use suitable methods to solve them. In addition, you can apply the linear least square method to overdetermined systems of linear equations.
You are familiar with the basic operations of matrix calculus. These include the calculation of matrix products, determinants, inverse matrices, etc
Real Numbers and Introduction to Complex Numbers
Number sets: real numbers and field axioms
Complex numbers and the complex plane
Calculus with complex numbers (summation and multiplication)
Polar form of complex numbers (polar coordinates, modulus and argument)
Geometric Calculus
Vectors in R^2 and R^3
Norm of a vector, inner product and angle between vectors
Orthogonal Projection
Parametric representations of lines and planes in R^3
Cross Product of vectors
Matrix Calculus
Matrizen, Matrixprodukt
Solution of systems of linear equations, Gauss elimination and row echelon form
LU decomposition
Linear least squares
Inverse Matrix
Determinant
Complex Numbers
Euler‘s formula and exponential form of complex numbers
Exponential and powers of complex numbers
Application of complex numbers to AC current.
Graphical representation of complex functions (Nyquist and Bode plots)
Lernbuch Lineare Algebra und Analytische Geometrie, Gerd Fischer, Florian Quiring, Springer Spektrum Verlag, 2. Auflage, http://dx.doi.org/10.1007/978-3-8348-2379-3
Lineare Algebra für Naturwissenschaftler und Ingenieure, Michael Ruhrländer, Pearson Studium ISBN 978-3-86894-271-2
Formeln, Tafeln, Begriffe (Mathematik, Physik, Chemie), Orell Füssli Verlag, ISBN 978-3-280-04059-1