Mathematics 3 - Linear algebra

Complex numbers and the complex exponential function. Second order linear differential equations. Systems of linear equations, Gauss-Jordan elimination, reduced echelon form, matrix algebra, determinants. Vector spaces, subspaces, linear dependence and independence. Inner products, orthogonality, orthogonal projections, Gram-Schmidt orthogonalization, and the method of least squares. Eigenvalues and eigenvectors, diagonalization, symmetric matrices and quadratic forms. First order systems of differential equations.

1. Knowledge. The student is able to recognize, understand and apply concepts and methods from linear algebra in Euclidean spaces and systems of differential equations.

2. Skills. The student is able to apply his or her knowledge of linear algebra and systems of differential equations to formulate and solve problems in mathematics and the natural sciences/technology, if necessary with the additional aid of mathematical software.

Lectures and compulsory exercises. Parts of this course can be taught in English.