Students are familiarised with vector spaces, linear mappings, eigenvalues and eigenvectors. They learn how to mathematically describe linear mappings on vector spaces, using vectors and matrices, and apply these concepts to Fourier analysis and to the solution of linear differential equations.
You are familiar with the abstract notion of a vector space and its subspaces. You can describe vectors as coordinate vectors with respect to some basis. In particular, you know the Fourier series as an application of this concept.
You are familiar with linear mappings between vector spaces and you are able to describe them with respect to arbitrary bases using matrices and vectors.
You can calculate eigenvalues and eigenvectors of linear mappings and examine matrices for their diagonalizability. You are able to apply the diagonalization of matrices as an important practical insight from linear algebra to technical contexts.
You are able to identify and to solve linear ordinary differential equations with constant coefficients.
Vector Spaces
Vector spaces and vector space axioms
Subspaces
Inner product, norm and orthonormal bases of vector spaces
Fourier Series
Linear Mappings
Examples of linear mappings (reflections, scalings, rotations and projections)
Fundamental spaces of a matrix (null space and column space)
Invertible linear mappings (isomorphisms)
Change of basis of a vector space
Eigenvalues and Eigenvectors
Calculation of eigenvalues and eigenvectors
Basis of eigenvectors and diagonalization of matrices
Applications of diagonalization (e.g. linear ordinary differential equations)
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, Tabellen, Begriffe (Mathematik, Physik, Chemie), Orell Füssli Verlag, ISBN 978-3-280-04029-4
Knowledge of mathematics of the „technische Berufsmaturität“
Knowledge of linear algebra 1 for ET/ST